elements.py

"""This is where the element functions are stored

(that is, functions directly corresponding to Vyxal elements). It's also where
the python equivalent of command is stored
"""

import collections
import itertools
import math
import random
import re
import string
import types
import urllib
from datetime import datetime
from typing import Callable, Union

import num2words
import sympy

from vyxal import dictionary
from vyxal.context import DEFAULT_CTX, Context
from vyxal.encoding import (
    base_27_alphabet,
    codepage_number_compress,
    codepage_string_compress,
)
from vyxal.helpers import *
from vyxal.LazyList import LazyList, lazylist

NUMBER_TYPE = "number"
SCALAR_TYPE = "scalar"

EPSILON = 1e-10


def process_element(
    expr: Union[str, Callable[..., Any]], arity: int
) -> tuple[str, int]:
    """Take a python expression and adds boilerplate for element functions to it

    expr can be a string, which will be added verbatim to the transpiled output,
    or a function, for which a function call will be generated.

    See documents/specs/Transpilation.md for information on what happens here.
    """
    if arity:
        arguments = ["third", "rhs", "lhs"][-arity:]
    else:
        arguments = ["_"]
    if isinstance(expr, types.FunctionType):
        pushed = f"{expr.__name__}({', '.join(arguments[::-1])}, ctx=ctx)"
    else:
        pushed = expr
    py_code = (
        f"{', '.join(arguments)} = pop(stack, {arity}, ctx); "
        f"stack.append({pushed})"
    )
    return py_code, arity


def absolute_difference(lhs, rhs, ctx):
    """Element ε
    (num, num) -> abs(a - b)
    (any, str) -> Transpose a (filling with b), join on newlines
    """
    ts = vy_type(lhs, rhs)
    if ts == (NUMBER_TYPE, NUMBER_TYPE):
        return abs(lhs - rhs)
    else:
        return vertical_join(lhs, rhs, ctx)


def add(lhs, rhs, ctx):
    """Element +
    (num, num) -> lhs + rhs
    (num, str) -> str(lhs) + rhs
    (str, num) -> lhs + str(rhs)
    (str, str) -> lhs + rhs
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs + rhs,
        (NUMBER_TYPE, str): lambda: str(lhs) + rhs,
        (str, NUMBER_TYPE): lambda: lhs + str(rhs),
        (str, str): lambda: lhs + rhs,
    }.get(ts, lambda: vectorise(add, lhs, rhs, ctx=ctx))()


def all_combos(lhs, ctx):
    """Element Þx
    (any) -> all combinations without replacement of lhs (all lengths)
    """
    all_without_replacement = map(
        lambda x: itertools.combinations(lhs, x), range(1, len(lhs) + 1)
    )

    @lazylist
    def gen():
        for combo in all_without_replacement:
            for item in combo:
                for x in itertools.permutations(item):
                    if all(isinstance(y, str) for y in x):
                        x = "".join(x)
                    yield vyxalify(x)

    return gen()


def all_combos_with_replacement(lhs, ctx):
    """Element Þ×
    (any) -> all combinations with replacement of lhs (all lengths)
    """
    all_with_replacement = map(
        lambda x: itertools.combinations_with_replacement(lhs, x),
        range(1, len(lhs) + 1),
    )

    @lazylist
    def gen():
        for combo in all_with_replacement:
            for x in combo:
                if all(isinstance(y, str) for y in x):
                    x = "".join(x)
                yield vyxalify(x)

    return gen()


def all_diagonals(lhs, ctx):
    """Element ÞD
    Diagonals of a matrix, starting with the main diagonal.
    """
    vector = [iterable(x, ctx=ctx) for x in lhs]
    all_diags = [[] for _ in range(len(vector) * 2 - 1)]
    start = 0
    print(vector)
    for row in vector:
        for i in range(len(vector)):
            all_diags[(start + i) % len(all_diags)].append(row[i])
        start -= 1
    return all_diags


def all_equal(lhs, ctx):
    """Element ≈
    (any) -> are all items in a the same?
    """
    lhs = iterable(lhs, ctx=ctx)
    if len(lhs) == 0:
        return 1
    else:
        first = lhs[0]
        for item in lhs[1:]:
            if not non_vectorising_equals(item, first, ctx):
                return 0
        return 1


def all_less_than_increasing(lhs, rhs, ctx):
    """Element Þ<
    (any, num): All values of a up to (not including) the first greater
                than or equal to b
    """
    lhs = iterable(lhs, ctx)

    @lazylist
    def gen():
        for elem in lhs:
            if elem < rhs:
                yield elem
            else:
                return

    return gen()


def all_partitions(lhs, ctx):
    """Element øṖ
    (any) -> all_partitions(a)
    """
    lhs = iterable(lhs, ctx=ctx)

    @lazylist
    def gen():
        shapes = integer_parts_or_join_spaces(len(lhs), ctx)
        yield from (wrap(lhs, shape, ctx) for shape in shapes)

    return gen()


def all_slices(lhs, rhs, ctx):
    """Element Þs
    (lst, int) -> Get all slices of a list, skipping a certain number of items
    """
    ts = vy_type(lhs, rhs)
    lhs, rhs = (rhs, lhs) if ts[1] != NUMBER_TYPE else (lhs, rhs)
    lhs = iterable(lhs, ctx=ctx)

    return LazyList(index(lhs, [start, None, rhs], ctx) for start in range(rhs))


def all_true(lhs, ctx):
    """Element A
    (lst) -> all of lhs is truthy?
    (str) -> is_vowel (vectorises over multichar strings)
    """
    if isinstance(lhs, str):
        if len(lhs) == 1:
            return int(lhs in "aeiouAEIOU")
        else:
            return [int(char in "aeiouAEIOU") for char in lhs]
    return int(all(iterable(lhs, ctx)))


def all_unique(lhs, ctx):
    """Element Þu
    (any) -> Are all elements of a unique?
    """
    return int(len(uniquify(lhs, ctx)) == len(iterable(lhs, ctx=ctx)))


def angle_bracketify(lhs, ctx):
    """Element øḂ
    (any) -> "<" + lhs + ">"
    (lst) -> vectorised
    """
    if vy_type(lhs, simple=True) is list:
        return vectorise(angle_bracketify, lhs)
    return "<" + str(lhs) + ">"


def anti_diagonal(lhs, ctx):
    """Element Þ\\
    (lst) -> Antidiagonal of matrix
    """
    lhs = [iterable(elem, ctx=ctx) for elem in iterable(lhs, ctx=ctx)]
    return [lhs[i][len(lhs) - i - 1] for i in range(len(lhs))]


def any_true(lhs, ctx):
    """Element a
    (lst) -> any of lhs is truthy?
    (str) -> is_capital_letter (vectorises over multichar strings)
    """
    if isinstance(lhs, str):
        if len(lhs) == 1:
            return int(91 >= ord(lhs) >= 65)
        else:
            return [int(91 >= ord(char) >= 65) for char in lhs]
    return int(any(iterable(lhs, ctx=ctx)))


def apply_at(lhs, rhs, other, ctx):
    """Element ¨M
    (lst, lst, fun) -> Map a function to elements of a list whose
                       indices are in another list
    """
    lhs = iterable(lhs, ctx=ctx)
    rhs = wrapify(rhs)
    for pos in rhs:
        lhs = assign_iterable(
            lhs, pos, safe_apply(other, index(lhs, pos, ctx), ctx=ctx), ctx
        )

    return lhs


def arccos(lhs, ctx):
    """Element ∆C
    (num) -> arccos(lhs)
    (str) -> arccos(expression)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.nsimplify(sympy.acos(lhs)),
        (str): lambda: str(sympy.nsimplify(sympy.acos(make_expression(lhs)))),
    }.get(ts, lambda: vectorise(arccos, lhs, ctx=ctx))()


def arcsin(lhs, ctx):
    """Element ∆S
    (num) -> arcsin(a)
    (str) -> arcsin(expression)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.nsimplify(sympy.asin(lhs)),
        (str): lambda: str(sympy.nsimplify(sympy.asin(make_expression(lhs)))),
    }.get(ts, lambda: vectorise(arcsin, lhs, ctx=ctx))()


def arctan(lhs, ctx):
    """Element ∆T
    (num) -> arctan(a)
    (str) -> arctan(expression)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.nsimplify(sympy.atan(lhs)),
        (str): lambda: str(sympy.nsimplify(sympy.atan(make_expression(lhs)))),
    }.get(ts, lambda: vectorise(arctan, lhs, ctx=ctx))()


def assign_iterable(lhs, rhs, other, ctx):
    """Element Ȧ
    (any, num, any) -> a but item b (0-indexed) is set to c
    """
    lhs = iterable(lhs, ctx=ctx)
    if type(rhs) is str:
        rhs = chr_ord(rhs, ctx)

    if vy_type(rhs, simple=True) is list:
        for item in rhs:
            lhs = assign_iterable(lhs, item, other, ctx)
        return lhs
    if type(lhs) is str:
        lhs = list(lhs)
        lhs[rhs] = other
        return vy_sum(lhs, ctx=ctx)
    else:
        lhs[rhs] = other
        return lhs


def base_255_string_compress(lhs, ctx):
    """Element øc
    (str) -> Compress a string of lowercase letters and spaces in base 255
    """
    return (
        "«"
        + to_base(
            from_base(lhs, base_27_alphabet, ctx),
            codepage_string_compress,
            ctx,
        )
        + "«"
    )


def base_255_number_compress(lhs, ctx):
    """Element øC
    (num) -> Compress a number in base 255
    """
    return "»" + to_base(lhs, codepage_number_compress, ctx) + "»"


def bitwise_and(lhs, rhs, ctx):
    """Element ⋏
    (num, num) -> a & b
    (num, str) -> b.center(a)
    (str, num) -> a.center(b)
    (str, str) -> a.center(len(b) - len(a))
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs & rhs,
        (NUMBER_TYPE, str): lambda: rhs.center(lhs),
        (str, NUMBER_TYPE): lambda: lhs.center(rhs),
        (str, str): lambda: lhs.center(abs(len(rhs) - len(lhs))),
    }.get(ts, lambda: vectorise(bitwise_and, lhs, rhs, ctx=ctx))()


def bitwise_or(lhs, rhs, ctx):
    """Element ⋎
    (num, num) -> a | b
    (num, str) -> b[:a]+b[a+1:]
    (str, num) -> a[:b]+a[b+1:]
    (str, str) -> merge_join(a,b)
    """
    ts = vy_type(lhs, rhs)
    if ts == (str, str):
        suffix_set = {lhs[-i:] for i in range(1, len(lhs) + 1)}
        prefix_set = {rhs[:i] for i in range(1, len(rhs) + 1)}
        common = suffix_set & prefix_set
        if len(common) == 0:
            return lhs + rhs
        common = sorted(common, key=lambda x: len(x))[-1]
        return lhs[: -len(common)] + common + rhs[len(common) :]
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs | rhs,
        (NUMBER_TYPE, str): lambda: rhs[:lhs] + rhs[lhs + 1 :],
        (str, NUMBER_TYPE): lambda: lhs[:rhs] + lhs[rhs + 1 :],
    }.get(ts, lambda: vectorise(bitwise_or, lhs, rhs, ctx=ctx))()


def bitwise_not(lhs, ctx):
    """Element ꜝ
    (num) -> ~a
    (str) -> any_upper(a)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: ~lhs,
        str: lambda: int(any(char.isupper() for char in lhs)),
    }.get(ts, lambda: vectorise(bitwise_not, lhs, ctx=ctx))()


def bitwise_xor(lhs, rhs, ctx):
    """Element ꘍
    (num, num) -> a ^ b
    (num, str) -> " " * a + b
    (str, num) -> a + " " * b
    (str, str) -> levenshtein_distance(a,b)
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs ^ rhs,
        (NUMBER_TYPE, str): lambda: " " * lhs + rhs,
        (str, NUMBER_TYPE): lambda: lhs + " " * rhs,
        (str, str): lambda: levenshtein_distance(lhs, rhs),
    }.get(ts, lambda: vectorise(bitwise_xor, lhs, rhs, ctx=ctx))()


def boolify(lhs, ctx):
    """Element ḃ
    (any) -> is truthy?
    """
    if vy_type(lhs, simple=True) is list:
        if ctx.truthy_lists:
            return any_true(lhs, ctx)
        else:
            return vectorise(boolify, lhs, ctx=ctx)
    else:
        return int(bool(lhs))


def bracketify(lhs, ctx):
    """Element øB
    (any) -> "[" + lhs + "]"
    (lst) -> vectorised
    """
    if vy_type(lhs, simple=True) is list:
        return vectorise(bracketify, lhs)
    return "[" + str(lhs) + "]"


def brackets_balanced(lhs, ctx):
    """Element øβ
    (str) -> is lhs balanced?
    """
    brackets = {"(": ")", "[": "]", "{": "}", "<": ">"}
    temp = []
    for char in lhs:
        if char in brackets:
            temp.append(brackets[char])
        elif char in brackets.values():
            if temp and temp[-1] != char:
                return 0
            elif not temp:
                return 0
            else:
                temp.pop()
    return int(len(temp) == 0)


def carmichael_function(lhs, ctx):
    """Element ∆¢
    (num) -> is lhs a Carmichael number?
    (str) -> local maxima
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.ntheory.reduced_totient(lhs),
        str: lambda: local_maxima(lhs),
    }.get(ts, lambda: vectorise(carmichael_function, lhs, ctx=ctx))()


def cartesian_over_list(lhs, ctx):
    """Element Þ*
    (lst) -> itertools.product(*lhs)
    """
    # todo maybe handle generators separately
    lhs = [iterable(elem, ctx=ctx) for elem in iterable(lhs, ctx=ctx)]
    return vyxalify(itertools.product(*lhs))


def cartesian_power(lhs, rhs, ctx):
    """Element ÞẊ
    (any, num) -> cartesian_power(a, b)
    (num, any) -> cartesian_power(b, a)
    """
    ts = vy_type(lhs, rhs)
    if NUMBER_TYPE not in ts:
        return rhs
    else:
        lhs, rhs = (lhs, rhs) if ts[-1] == NUMBER_TYPE else (rhs, lhs)
    return LazyList(
        "".join(x) if all(isinstance(y, str) for y in x) else x
        for x in itertools.product(iterable(lhs, ctx=ctx), repeat=int(rhs))
    )


def cartesian_product(lhs, rhs, ctx):
    """Element Ẋ
    (any, any) -> cartesian product of lhs and rhs
    (fun, any) -> Apply a to b until no change (fixpoint)
    (any, fun) -> Apply a to b until no change (fixpoint)
    """
    ts = vy_type(lhs, rhs)
    if types.FunctionType in ts:
        fn, arg = (lhs, rhs) if ts[0] == types.FunctionType else (rhs, lhs)
        prev = arg
        arg = safe_apply(fn, arg, ctx=ctx)
        while simplify(prev) != simplify(arg):
            prev = arg
            arg = safe_apply(fn, arg, ctx=ctx)
        return prev
    elif ts == (str, str):
        return [left + right for left in lhs for right in rhs]
    else:
        lhs = iterable(lhs, range, ctx=ctx)
        rhs = iterable(rhs, range, ctx=ctx)

        @lazylist
        def gen():
            if not (lhs and rhs):
                return

            diag_num = 0
            lhs_max = len(lhs) - 1 if isinstance(lhs, list) else None
            rhs_max = len(rhs) - 1 if isinstance(rhs, list) else None
            while True:
                lhs_start = max(0, diag_num - rhs_max) if rhs_max else 0
                lhs_end = min(diag_num, lhs_max) if lhs_max else diag_num
                # Whether at least 1 new pair was yielded
                touched = False
                for left in range(lhs_start, lhs_end + 1):
                    right = diag_num - left
                    if rhs_max and right > rhs_max:
                        continue
                    if not has_ind(rhs, right):
                        rhs_max = right
                        continue
                    if lhs_max and left > lhs_max:
                        break
                    if not has_ind(lhs, left):
                        lhs_max = left
                        break
                    touched = True
                    yield [lhs[left], rhs[right]]
                if not touched:
                    break
                diag_num += 1

        return gen()


def center(lhs, ctx):
    """Element øc
    (list) -> center align list by padding with spaces
    """
    focal = max(map(lambda x: len(iterable(x, ctx=ctx)), lhs))
    return [line.center(focal) for line in lhs]


def chr_ord(lhs, ctx):
    """Element C
    (num) -> chr(a)
    (str) -> ord(a)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: chr(int(lhs)),
        (str): lambda: list(map(ord, lhs)) if len(lhs) > 1 else ord(lhs),
    }.get(ts, lambda: vectorise(chr_ord, lhs, ctx=ctx))()


def combinations_with_replacement(lhs, rhs, ctx):
    """Element ↔
    (any, num) -> combinations of lhs of length rhs with replacement
    (any, non-num) -> remove elements in lhs that are not in rhs
    (fun, any) -> apply lhs on rhs until the result does not change. Collects intermediate values
    (any, fun) -> apply rhs on lhs until the result does not change. Collects intermediate values
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, ts[1]): lambda: vyxalify(
            itertools.product(iterable(rhs, ctx), repeat=lhs)
        ),
        (ts[0], NUMBER_TYPE): lambda: vyxalify(
            itertools.product(iterable(lhs, ctx), repeat=rhs)
        ),
        (types.FunctionType, ts[1]): lambda: fixed_point(lhs, rhs, ctx=ctx),
        (ts[0], types.FunctionType): lambda: fixed_point(rhs, lhs, ctx=ctx),
    }.get(ts, lambda: keep(lhs, rhs))()


def complement(lhs, ctx):
    """Element ⌐
    (num) -> 1 - a
    (str) -> a.split(",")
    """
    ts = vy_type(lhs)
    return {NUMBER_TYPE: lambda: 1 - lhs, str: lambda: lhs.split(",")}.get(
        ts, lambda: vectorise(complement, lhs, ctx=ctx)
    )()


def contains(lhs, rhs, ctx):
    """Element c
    (any, any) -> count of a in b
    """
    if list in vy_type(lhs, rhs, simple=True):
        lhs, rhs = (
            (rhs, lhs) if primitive_type(lhs) == SCALAR_TYPE else (lhs, rhs)
        )
        lhs = iterable(lhs, ctx=ctx)
        return int(rhs in lhs)
    return int(vy_str(rhs, ctx=ctx) in vy_str(lhs, ctx=ctx))


def coords_deepmap(lhs, rhs, ctx):
    """Element ÞZ
    (any, fun) -> For each value of a (all the way down) call b with the
                  coordinates of that value and put that at the
                  appropriate position in a.

    Or, as hyper said: for each value of a, call b with the coordinates
    of that value is just deepmap(b, multidimindex(a))

    https://chat.stackexchange.com/transcript/message/59662626#59662626
    """
    lhs, rhs = (lhs, rhs) if type(rhs) is types.FunctionType else (rhs, lhs)
    # arrange so that lhs is always the list and rhs is always the
    # function

    lhs = iterable(lhs, ctx=ctx)  # Make sure lhs is actually iterable

    def f(a, g, pos=()):
        return [
            f(b, g, (*pos, i))
            if isinstance(b, list)
            else safe_apply(g, [*pos, i], ctx=ctx)
            for i, b in enumerate(a)
        ]

    # the above curtosey of pxeger
    # https://chat.stackexchange.com/transcript/message/59662694#59662694
    # thank you very cool

    return f(lhs, rhs)


def copy_sign(lhs, rhs, ctx):
    """Element ∆±
    (num, num) -> math.copysign(a, b)
    """
    return multiply(
        vy_abs(lhs, ctx), (-1 if less_than(rhs, 0, ctx) else 1), ctx
    )


def cosine(lhs, ctx):
    """Element ∆c
    (num) -> cosine(a)
    (str) -> cosine(expression)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.nsimplify(sympy.cos(lhs)),
        str: lambda: str(sympy.nsimplify(sympy.cos(make_expression(lhs)))),
    }.get(ts, lambda: vectorise(cosine, lhs, ctx=ctx))()


def count_item(lhs, rhs, ctx):
    """Element O
    (any, any) -> returns the number of occurances of b in a
    """
    if (primitive_type(lhs), primitive_type(rhs)) == (SCALAR_TYPE, list):
        lhs, rhs = rhs, lhs
    if type(lhs) is str:
        rhs = str(rhs)
    return iterable(lhs, ctx=ctx).count(rhs)


def counts(lhs, ctx):
    """Element Ċ
    (any) -> Counts: [[x, a.count(x)] for x in a]"""
    temp = uniquify(lhs, ctx=ctx)
    return [[x, count_item(lhs, x, ctx)] for x in temp]


def cumulative_sum(lhs, ctx):
    """Element ¦
    (any) -> cumulative sum of a
    """
    return LazyList(scanl(add, iterable(lhs, ctx=ctx), ctx))


def cumul_sum_sans_last_prepend_zero(lhs, ctx):
    """Element ÞR
    Remove the last item of the cumulative sums of a list and prepend 0.
    """

    return prepend(scanl(add, iterable(lhs, ctx=ctx), ctx)[:-1], 0, ctx)


def curly_bracketify(lhs, ctx):
    """Element øḃ
    (any) -> "[" + lhs + "]"
    (lst) -> vectorised
    """
    if vy_type(lhs, simple=True) is list:
        return vectorise(curly_bracketify, lhs)
    return "{" + str(lhs) + "}"


def custom_pad_left(lhs, rhs, other, ctx):
    """Element ø↲
    (any, num, str) -> pad a on the left with c to length b
    (any, str, num) -> pad a on the left with b to length c
    (lst, any, any) -> vectorised
    """
    if isinstance(lhs, LazyList):
        return vectorise(custom_pad_left, lhs, rhs, other)
    if isinstance(rhs, int):
        return lhs.ljust(rhs, other)
    if isinstance(other, int):
        return lhs.ljust(other, rhs)


def custom_pad_right(lhs, rhs, other, ctx):
    """Element ø↳
    (any, num, str) -> pad a on the right with c to length b
    (any, str, num) -> pad a on the right with b to length c
    (lst, any, any) -> vectorised
    """
    if isinstance(lhs, LazyList):
        return vectorise(custom_pad_left, lhs, rhs, other)
    if isinstance(rhs, int):
        return lhs.rjust(rhs, other)
    if isinstance(other, int):
        return lhs.rjust(other, rhs)


def decrement(lhs, ctx):
    """Element ‹
    (num) -> a - 1
    (str) -> a + "-"
    """
    ts = vy_type(lhs)
    return {NUMBER_TYPE: lambda: lhs - 1, str: lambda: lhs + "-"}.get(
        ts, lambda: vectorise(decrement, lhs, ctx=ctx)
    )()


def deep_flatten(lhs, ctx):
    """Element f
    (any) -> flatten list completely
    """

    @lazylist
    def gen():
        for item in iterable(lhs, ctx=ctx):
            if type(item) in (LazyList, list):
                yield from deep_flatten(item, ctx)
            else:
                yield item

    return gen()


def deltas(lhs, ctx):
    """Element ¯
    (any) -> deltas of a
    """
    lhs = iterable(lhs, ctx=ctx)
    return LazyList(
        subtract(lhs[i + 1], lhs[i], ctx=ctx) for i in range(len(lhs) - 1)
    )


def diagonal(lhs, ctx):
    """Element Þ/
    (any) -> diagonal of a
    """
    lhs = [iterable(elem, ctx=ctx) for elem in iterable(lhs, ctx=ctx)]
    return [lhs[i][i] for i in range(len(lhs))]


def divide(lhs, rhs, ctx):
    """Element /
    (num, num) -> a / b
    (num, str) -> b split into a even length pieces, possibly with an extra part
    (str, num) -> a split into b even length pieces, possibly with an extra part
    (str, str) -> split a on b
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: 0
        if rhs == 0
        else vyxalify(sympy.nsimplify(lhs / rhs)),
        (NUMBER_TYPE, str): lambda: wrap(rhs, len(rhs) // lhs, ctx),
        (str, NUMBER_TYPE): lambda: wrap(lhs, len(lhs) // rhs, ctx),
        (str, str): lambda: lhs.split(rhs),
    }.get(ts, lambda: vectorise(divide, lhs, rhs, ctx=ctx))()


def divisors(lhs, ctx):
    """Element K
    (num) -> divisors(a) # Factors or divisors of a
    (str) -> all substrings of a that occur more than once
    (lst) -> prefixes(a) # Prefixes of a
    """
    ts = vy_type(lhs)
    if ts == NUMBER_TYPE:
        return sympy.divisors(lhs)
    elif ts == str:
        return uniquify(
            LazyList(
                filter(
                    lambda substr: lhs.count(substr) > 1,
                    substrings(lhs, ctx),
                )
            ),
            ctx,
        )

    @lazylist
    def gen():
        temp = []
        for item in iterable(lhs, ctx=ctx):
            temp += [deep_copy(item)]
            yield temp

    return gen()


def divisor_sum(lhs, ctx):
    """Element ∆K
    (num) -> sum of proper divisors of a
    (str) -> stationary points of a
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: vy_sum(divisors(lhs, ctx)[:-1], ctx),
        str: lambda: stationary_points(lhs),
    }.get(ts, lambda: vectorise(divisor_sum, lhs, ctx=ctx))()


def dot_product(lhs, rhs, ctx):
    """Element Þ•
    Return the dot product of lhs and rhs
    """
    return vy_sum(multiply(lhs, rhs, ctx), ctx)


def dyadic_maximum(lhs, rhs, ctx):
    """Element ∴
    (any, any) -> max(a, b)
    """
    return lhs if strict_greater_than(lhs, rhs, ctx) else rhs


def dyadic_minimum(lhs, rhs, ctx):
    """Element ∵
    (any, any) -> min(a, b)
    """
    return lhs if strict_less_than(lhs, rhs, ctx) else rhs


def e_digits(lhs, ctx):
    """Element ∆Ė
    (int) -> e_digits(a)
    (str) -> evaluate as sympy
    """
    if vy_type(lhs) == NUMBER_TYPE:
        estr = str(sympy.N(sympy.E, int(lhs) + 2))
        estr = estr[0] + estr[2:-1]
        return LazyList(map(int, estr))
    elif vy_type(lhs) is str:
        return sympy.nsimplify(lhs, rational=True)
    else:
        return vectorise(e_digits, lhs, ctx=ctx)


def element_wise_dyadic_maximum(lhs, rhs, ctx):
    """Element Þ∴
    (lst, lst) -> max(a, b)
    """
    lhs, rhs = iterable(lhs, ctx=ctx), iterable(rhs, ctx=ctx)
    return LazyList(
        dyadic_maximum(lhs[i], rhs[i], ctx) for i in range(len(lhs))
    )


def element_wise_dyadic_minimum(lhs, rhs, ctx):
    """Element Þ∵
    (lst, lst) -> min(a, b)
    """
    lhs, rhs = iterable(lhs, ctx=ctx), iterable(rhs, ctx=ctx)
    return LazyList(
        dyadic_minimum(lhs[i], rhs[i], ctx) for i in range(len(lhs))
    )


def equals(lhs, rhs, ctx):
    """Element =
    (num, num) -> lhs == rhs
    (num, str) -> str(lhs) == rhs
    (str, num) -> lhs == str(rhs)
    (str, str) -> lhs == rhs
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(
            bool(
                abs(simplify(lhs - rhs)) < EPSILON
                or abs(simplify(lhs - rhs)) < EPSILON * abs(lhs)
            )
        ),
        (NUMBER_TYPE, str): lambda: int(str(lhs) == rhs),
        (str, NUMBER_TYPE): lambda: int(lhs == str(rhs)),
        (str, str): lambda: int(lhs == rhs),
    }.get(ts, lambda: vectorise(equals, lhs, rhs, ctx=ctx))()


def euclidean_distance(lhs, rhs, ctx):
    """Element ∆d
    (num, num) -> distance between a and b
    """
    return square_root(
        vy_sum(exponent(subtract(lhs, rhs, ctx), 2, ctx), ctx), ctx
    )


def evenly_distribute(lhs, rhs, ctx):
    """Element Þ…
    (list, num) -> Evenly distribute a over all elements of b,
                   adding each part
    """
    lhs = iterable(lhs, ctx=ctx)
    if not lhs:
        return lhs

    each = rhs // len(lhs)
    extra = rhs - each * len(lhs)

    if isinstance(lhs, list):
        return [
            lhs[i] + each + 1 if i < extra else lhs[i] + each
            for i in range(len(lhs))
        ]

    @lazylist
    def gen():
        i = 0
        for elem in lhs:
            if i < extra:
                yield elem + each + 1
            else:
                yield elem + each
            i += 1

    return gen()


def exclusive_one_range(lhs, ctx):
    """Element ɽ
    (num) -> range(1, a)
    (str) -> a.lower()
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: LazyList(range(1, int(lhs))),
        str: lambda: lhs.lower(),
    }.get(ts, lambda: vectorise(exclusive_one_range, lhs, ctx=ctx))()


def exclusive_zero_range(lhs, ctx):
    """Element ʁ
    (num) -> range(0, a)
    (str) -> mirror(a)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: LazyList(range(0, int(lhs))),
        str: lambda: merge(lhs, reverse(lhs, ctx)[1:], ctx),
    }.get(ts, lambda: vectorise(exclusive_zero_range, lhs, ctx=ctx))()


def exp2_or_eval(lhs, ctx):
    """Element E
    (num) -> 2 ** a
    (str) -> eval(a)
    """
    ts = vy_type(lhs)

    return {
        NUMBER_TYPE: lambda: 2 ** lhs,
        str: lambda: vy_eval(lhs, ctx),
    }.get(ts, lambda: vectorise(exp2_or_eval, lhs, ctx=ctx))()


def expe(lhs, ctx):
    """Element ∆e
    (num) -> e ** a
    (str) -> simplify expression a
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.exp(lhs),
        str: lambda: str(sympy.simplify(make_expression(lhs))),
    }.get(ts, lambda: vectorise(expe, lhs, ctx=ctx))()


def expe_minus_1(lhs, ctx):
    """Element ∆E
    (num) -> (e ** a) - 1
    (str) -> expand expression a
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.exp(lhs) - 1,
        str: lambda: str(sympy.expand(make_expression(lhs))),
    }.get(ts, lambda: vectorise(expe_minus_1, lhs, ctx=ctx))()


def exponent(lhs, rhs, ctx):
    """Element e
    (num, num) -> a ** b (exponentiation)
    (num, str) -> append b[0] to b until b is length a (spaces if b is empty)
    (str, num) -> append a[0] to a until a is length b (spaces if a is empty)
    (str, str) -> regex.search(pattern=a, string=b).span() (Length of regex match)
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs ** rhs,
        (NUMBER_TYPE, str): lambda: rhs
        + ((rhs[0] or " ") * (int(lhs) - len(rhs))),
        (str, NUMBER_TYPE): lambda: lhs
        + ((lhs[0] or " ") * (int(rhs) - len(lhs))),
        (str, str): lambda: list(re.search(lhs, rhs).span()),
    }.get(ts, lambda: vectorise(exponent, lhs, rhs, ctx=ctx))()


def factorial(lhs, ctx):
    """Element ¡
    (num) -> factorial(a) (math.gamma(a + 1))
    (str) -> a.sentence_case()
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: vyxalify(sympy.factorial(abs(lhs))),
        # Because otherwise, it returns a very unhelpful factorial obj
        str: lambda: sentence_case(lhs),
    }.get(ts, lambda: vectorise(factorial, lhs, ctx=ctx))()


def factorials(_, ctx):
    """Element Þ!
    An infinite lazylist of factorials
    """

    def gen():
        i = 0
        while True:
            yield factorial(i, ctx)
            i += 1

    return LazyList(gen(), isinf=True)


def factorial_of_range(lhs, ctx):
    """Element øF
    (num, num) -> factorial of range
    (num, str) -> vectorised
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: math.factorial(lhs),
        str: lambda: vectorise(factorial_of_range, lhs, ctx=ctx),
    }.get(ts, lambda: vectorise(factorial_of_range, lhs, ctx=ctx))()


def fibonaacis(_, ctx):
    """Element ÞF
    An infinite lazylist of fibonaaci numbers
    """

    def gen():
        i = 0
        while True:
            yield sympy.fibonacci(i + 1)
            i += 1

    return LazyList(gen(), isinf=True)


def find(lhs, rhs, ctx):
    """Element ḟ
    (any, any) -> a.find(b)
    (any, fun) -> truthy indices of mapping b over a
    """
    ts = vy_type(lhs, rhs)
    if types.FunctionType not in ts:
        lhs, rhs = (
            (rhs, lhs)
            if primitive_type(rhs) != SCALAR_TYPE
            and primitive_type(lhs) == SCALAR_TYPE
            else (lhs, rhs)
        )
        pos = 0
        lhs = iterable(lhs, ctx=ctx)
        if vy_type(lhs) is LazyList and lhs.infinite:
            while strict_less_than(
                lhs[pos], rhs, ctx
            ) or not non_vectorising_equals(lhs[pos], rhs, ctx):
                if non_vectorising_equals(index(lhs, pos, ctx), rhs, ctx):
                    return pos
                pos += 1
            return -1
        while pos < len(lhs):
            if non_vectorising_equals(index(lhs, pos, ctx), rhs, ctx):
                return pos
            pos += 1
        return -1
    else:
        return {
            (ts[0], types.FunctionType): lambda: LazyList(
                (
                    i
                    for i in range(len(iterable(lhs, ctx=ctx)))
                    if safe_apply(rhs, iterable(lhs, ctx=ctx)[i], ctx=ctx)
                )
            ),
            (types.FunctionType, ts[1]): lambda: LazyList(
                (
                    i
                    for i in range(len(iterable(rhs, ctx=ctx)))
                    if safe_apply(lhs, iterable(rhs, ctx=ctx)[i], ctx=ctx)
                )
            ),
        }.get(ts)()


def first_integer(lhs, ctx):
    """Element ṅ
    (num) -> abs(a) <= 1
    (str) -> pad with 0s to nearest multiple of 8
    (lst) -> "".join(a)
    (fun) -> first integer x where a(x) is truthy
    """
    if isinstance(lhs, types.FunctionType):
        value = 1

        while not safe_apply(lhs, value, ctx=ctx):
            value += 1

        return value

    ts = vy_type(lhs, simple=True)
    return {
        (NUMBER_TYPE): lambda: int(bool(abs(lhs) <= 1)),
        (str): lambda: lhs.zfill(len(lhs) + (8 - len(lhs) % 8)),
        (list): lambda: join(lhs, "", ctx),
    }.get(ts, lambda: vectorise(first_integer, lhs, ctx=ctx))()


def flatten_by(lhs, rhs, ctx):
    """Element Þf
    (lst, num) -> Flatten a by depth b
    (any, lst) -> Flatten b by depth 1, push a as well
    """
    flat = []

    if rhs == 0:
        return lhs
    elif vy_type(lhs, simple=True) is list:
        for item in lhs:
            if vy_type(item, simple=True) is list:
                flat += flatten_by(item, int(rhs - 1), ctx)
            else:
                flat.append(item)
    else:
        flat.append(lhs)
    return flat


def flip_brackets_vertical_mirror(lhs, ctx):
    """Element øṀ
    (str) -> vertical_mirror(a, mapping = flip brackets and slashes)
    """
    result = lhs.split("\n")
    for i in range(len(result)):
        result[i] += invert_brackets(result[i])[::-1]
    return "\n".join(result)


def flip_brackets_vertical_palindromise(lhs, ctx):
    """Element øM
    (str) -> lhs vertically palindromised without duplicating the center, with brackets flipped.
    """
    result = lhs.split("\n")
    for i in range(len(result)):
        result[i] += invert_brackets(result[i][:-1][::-1])
    return "\n".join(result)


def foldl_columns(lhs, rhs, ctx):
    """Element ÞC
    (lst, fun) -> reduce the columns of a by function b
    """
    lhs, rhs = (lhs, rhs) if vy_type(lhs, simple=True) is list else (rhs, lhs)
    lhs = transpose(iterable(lhs, ctx=ctx), ctx=ctx)
    return [foldl(rhs, col, ctx=ctx) for col in lhs]


def foldl_rows(lhs, rhs, ctx):
    """Element ÞR
    (lst, fun) -> reduce the rows of a by function b
    """
    lhs, rhs = (lhs, rhs) if vy_type(lhs, simple=True) is list else (rhs, lhs)

    return [foldl(rhs, row, ctx=ctx) for row in iterable(lhs, ctx=ctx)]


def function_call(lhs, ctx):
    """Element †
    (fun) -> lhs()
    (num) -> count of prime factors
    (str) -> vyxal exec lhs
    (lst) -> vectorised not
    """
    # Modifies lhs, because lhs = stack
    top = pop(lhs, 1, ctx=ctx)
    ts = vy_type(top, simple=True)
    if isinstance(top, types.FunctionType):
        lhs += wrapify(top(lhs, top, ctx=ctx))
        return None
    return {
        NUMBER_TYPE: lambda: len(prime_factorisation(top, ctx)),
        str: lambda: exec(top) or [] if not ctx.online else [],
        list: lambda: vectorised_not(top, ctx=ctx),
    }.get(ts)()


def from_base(lhs, rhs, ctx):
    """Element β
    Convert lhs from base rhs to base 10
    """
    ts = vy_type(lhs, rhs)
    if ts == (str, str):
        return from_base_alphabet(lhs, rhs)
    elif ts[-1] == NUMBER_TYPE:
        lhs = [chr(x) if type(x) is str else x for x in iterable(lhs)]
        return from_base_digits(lhs, rhs)
    else:
        raise ValueError("from_base: invalid types")


def gen_from_fn(lhs, rhs, ctx):
    """Element Ḟ
    (num, num) -> sympy.N(a, b) (evaluate a to b decimal places)
    (num, str) -> every ath letter of b
    (str, num) -> every bth letter of a
    (str, str) -> replace spaces in a with b
    (lst, num) -> every bth item of a
    (fun, any) -> Generator from function a with initial vector b
    """
    ts = vy_type(lhs, rhs, simple=True)
    if types.FunctionType not in ts:
        return {
            (NUMBER_TYPE, NUMBER_TYPE): lambda: str(sympy.N(lhs, rhs)),
            (NUMBER_TYPE, str): lambda: rhs[::lhs],
            (str, NUMBER_TYPE): lambda: lhs[::rhs],
            (str, str): lambda: lhs.replace(" ", rhs),
            (list, NUMBER_TYPE): lambda: index(lhs, [None, None, rhs], ctx),
            (NUMBER_TYPE, list): lambda: index(rhs, [None, None, lhs], ctx),
        }.get(ts, lambda: vectorise(gen_from_fn, lhs, rhs, ctx=ctx))()

    lhs, rhs = (rhs, lhs) if ts[0] is types.FunctionType else (lhs, rhs)
    lhs = iterable(lhs, ctx=ctx)

    @lazylist
    def gen():
        yield from lhs

        made = lhs

        while True:
            next_item = safe_apply(rhs, *made, ctx=ctx)
            made.append(next_item)
            yield next_item

    return gen()


def general_quadratic_solver(lhs, rhs, ctx):
    """Element ∆Q
    (num, num) -> roots(a, b) # x^2 + ax + b = 0
    (num, str) -> evaluate single variable expression b with x=a
    (str, num) -> evaluate single variable expression a with x=b
    (str, str) -> solve a and b simulatenously
    """
    ts = vy_type(lhs, rhs)
    x, y = sympy.symbols("x y")
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: sympy.solve(
            sympy.Eq(x ** 2 + lhs * x + rhs, 0), x
        ),
        (NUMBER_TYPE, str): lambda: make_expression(rhs).subs(x, lhs),
        (str, NUMBER_TYPE): lambda: make_expression(lhs).subs(x, rhs),
        (str, str): lambda: dict_to_list(
            sympy.solve([make_equation(lhs), make_equation(rhs)], (x, y))
        ),
    }.get(ts, lambda: vectorise(general_quadratic_solver, lhs, rhs, ctx=ctx))()


def grade_up(lhs, ctx):
    """Element ⇧
    (lst) -> graded_up(a)
    (str) -> a.upper()
    (num) -> a + 2
    """
    ts = vy_type(lhs)
    return {(NUMBER_TYPE): lambda: lhs + 2, (str): lambda: lhs.upper()}.get(
        ts,
        lambda: LazyList(
            map(
                lambda x: x[0],
                sorted(enumerate(deep_copy(lhs)), key=lambda x: x[-1]),
            ),
        ),
    )()


def grade_down(lhs, ctx):
    """Element ⇩
    (lst) -> graded_down(a)
    (str) -> a.lower()
    (num) -> a - 2
    """
    ts = vy_type(lhs)
    return {(NUMBER_TYPE): lambda: lhs - 2, (str): lambda: lhs.lower()}.get(
        ts,
        lambda: LazyList(
            map(
                lambda x: x[0],
                sorted(
                    enumerate(deep_copy(lhs)), key=lambda x: x[-1], reverse=True
                ),
            ),
        ),
    )()


def greater_than(lhs, rhs, ctx):
    """Element <
    (num, num) -> a > b
    (num, str) -> str(a) > b
    (str, num) -> a > str(b)
    (str, str) -> a > b
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(bool(lhs > rhs)),
        (NUMBER_TYPE, str): lambda: int(str(lhs) > rhs),
        (str, NUMBER_TYPE): lambda: int(lhs > str(rhs)),
        (str, str): lambda: int(lhs > rhs),
    }.get(ts, lambda: vectorise(greater_than, lhs, rhs, ctx=ctx))()


def greater_than_or_equal(lhs, rhs, ctx):
    """Element ≥
    (num, num) -> a ≥ b
    (num, str) -> str(a) ≥ b
    (str, num) -> a ≥ str(b)
    (str, str) -> a ≥ b
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(bool(lhs >= rhs)),
        (NUMBER_TYPE, str): lambda: int(str(lhs) >= rhs),
        (str, NUMBER_TYPE): lambda: int(lhs >= str(rhs)),
        (str, str): lambda: int(lhs >= rhs),
    }.get(ts, lambda: vectorise(greater_than_or_equal, lhs, rhs, ctx=ctx))()


def group_consecutive(lhs, ctx):
    """Element Ġ
    (lst) -> Group consecutive identical items
    (str) -> Group consecutive identical characters
    (num) -> Group consecutive identical digits"""
    typ = vy_type(lhs)

    if typ == NUMBER_TYPE:
        lhs = digits(lhs)

    if len(lhs) < 1:
        return lhs

    def gen():
        prev = lhs[0]
        no_found = 1

        for item in lhs[1:]:
            if not non_vectorising_equals(prev, item, ctx):
                yield [prev] * no_found
                prev = item
                no_found = 1
            else:
                no_found += 1
        yield [prev] * no_found

    if typ is LazyList:
        return LazyList(gen())

    res = list(gen())

    return res


def group_on_words(lhs, ctx):
    """Element øW
    (str) -> Group lhs on sequences of letters
    """
    result, word = [], ""
    for char in lhs:
        if char in string.ascii_letters:
            word += char
        else:
            if word:
                result.append(word)
            word = ""
            result.append(char)
    if word:
        result.append(word)
    return result


def halve(lhs, ctx):
    """Element ½
    (num) -> lhs / 2
    (str) -> a split into two strings of equal lengths (as close as possible)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.Rational(lhs, 2),
        str: lambda: wrap(lhs, math.ceil(len(lhs) / 2), ctx=ctx),
    }.get(ts, lambda: vectorise(halve, lhs, ctx=ctx))()


def head(lhs, ctx):
    """Element h
    (any) -> a[0]
    """
    return next(
        iter(lhs) if type(lhs) is str else iter(iterable(lhs, ctx=ctx)),
        "" if type(lhs) is str else 0,
    )


def head_remove(lhs, ctx):
    """Element Ḣ
    (lst) -> a[1:] or [] if empty
    (str) -> a[1:] or '' if empty
    (num) -> Remove first digit or do nothing if <1"""
    if vy_type(lhs, simple=True) in (list, str):
        return lhs[1:] if lhs else lhs
    if lhs < 1:
        return lhs
    if isinstance(lhs, int):
        return int(str(lhs)[1:])
    assert isinstance(lhs, sympy.Rational)
    return sympy.Rational(str(float(lhs))[1:])


def inclusive_one_range(lhs, ctx):
    """Element ɾ
    (num) -> range(1, a + 1)
    (str) -> a.uppercase()
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: LazyList(range(1, int(lhs) + 1)),
        str: lambda: lhs.upper(),
    }.get(ts, lambda: vectorise(inclusive_one_range, lhs, ctx=ctx))()


def inclusive_zero_range(lhs, ctx):
    """Element ʀ
    (num) -> range(0, a + 1)
    (str) -> [char is alphabetical? for char in a]
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: LazyList(range(0, int(lhs) + 1)),
        str: lambda: scalarify(
            [int(char in string.ascii_letters) for char in lhs]
        ),
    }.get(ts, lambda: vectorise(inclusive_zero_range, lhs, ctx=ctx))()


def increment(lhs, ctx):
    """Element ›
    (num) -> lhs + 1
    (str) -> replace spaces with 0s
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: lhs + 1,
        str: lambda: lhs.replace(" ", "0"),
    }.get(ts, lambda: vectorise(increment, lhs, ctx=ctx))()


def index(lhs, rhs, ctx):
    """Element i
    (any, num) -> a[b] (Index)
    (str, str) -> enclose b in a # b[0:len(b)//2] + a + b[len(b)//2:]
    (any, [x]) -> a[:b] (0 to bth item of a)
    (any, [x,y]) -> a[x:y] (x to yth item of a)
    (any, [x,y,m]) -> a[x:y:m] (x to yth item of a, taking every mth)
    (num, any) -> b[a] (Index)
    """
    ts = vy_type(lhs, rhs)
    lhs = deep_copy(lhs)
    if ts == (str, str):
        # b[0:len(b)//2] + a + b[len(b)//2:]
        return lhs[: len(rhs) // 2] + rhs + lhs[len(rhs) // 2 :]

    elif ts == (LazyList, NUMBER_TYPE):
        return lhs[int(rhs)]

    elif ts[-1] == NUMBER_TYPE:
        if len(iterable(lhs)):
            return iterable(lhs, ctx=ctx)[int(rhs) % len(iterable(lhs, ctx))]
        else:
            return "" if ts[0] is str else 0

    elif ts[0] == NUMBER_TYPE:
        return index(rhs, lhs, ctx)

    elif ts[-1] == str:
        return vectorise(index, lhs, rhs, ctx=ctx)

    else:
        originally_string = False
        if isinstance(lhs, str):
            lhs = LazyList(list(lhs))
            originally_string = True
        temp = iterable(lhs, ctx=ctx)[
            slice(*[None if vy_type(v) != NUMBER_TYPE else int(v) for v in rhs])
        ]
        if originally_string:
            return "".join(temp)
        return temp


def index_indices_or_cycle(lhs, rhs, ctx):
    """Element İ
    (any, lst) -> [a[item] for item in b]
    (any, fun) -> apply b on a and collect unique values"""
    if types.FunctionType in [type(lhs), type(rhs)]:
        # swap lhs and rhs such that rhs contains the function
        lhs, rhs = (rhs, lhs) if type(lhs) is types.FunctionType else (lhs, rhs)
        prevs = []

        @lazylist
        def gen():
            curr = lhs
            while True:
                curr = deep_copy(safe_apply(rhs, curr, ctx=ctx))
                if curr in prevs:
                    yield from prevs
                    break

                prevs.append(curr)

        return gen()

    else:
        lhs = iterable(lhs)
        rhs = iterable(rhs)
        return vy_map(rhs, lambda item: lhs[item], ctx=ctx)


def infinite_cardinals(_, ctx=None):
    """Element Þc
    infinite sequence of cardinals
    """
    return LazyList(map(num2words.num2words, itertools.count(1)), isinf=True)


def infinite_ordinals(_, ctx=None):
    """Element Þo
    infinite list of place numbers starting at a - first, second,
    third, fourth, fifth, etc.

    This function returns an infinite generator that yields the word
    form of each ordinal number starting at first.
    """

    def gen():
        i = 1
        while True:
            yield num2words.num2words(i, to="ordinal")
            i += 1

    return LazyList(gen(), isinf=True)


def infinite_positives(_, ctx=None):
    """Element Þ∞
    An infinite list of positive numbers
    """

    @lazylist
    def gen():
        i = 1
        while True:
            yield i
            i += 1

    return gen()


def infinite_primes(_, ctx=None):
    """Element Þp
    An infinite list of primes
    """

    def gen():
        i = 1
        while True:
            i += 1
            if i == 2 or (i % 2 == 1 and is_prime(i, ctx)):
                yield i

    return LazyList(gen(), isinf=True)


def infinite_replace(lhs, rhs, other, ctx):
    """Element ¢
    (any, any, any) -> replace b in a with c until a doesn't change
    """
    orig_type = type(lhs)

    prev = deep_copy(lhs)
    while True:
        lhs = replace(lhs, rhs, other, ctx)
        if lhs == prev:
            break
        prev = deep_copy(lhs)

    if orig_type is int:
        try:
            return int(lhs)
        except ValueError:
            return lhs
    return lhs


def insert_or_map_nth(lhs, rhs, other, ctx):
    """Element Ṁ
    (any, num, any) -> a.insert(b, c) (Insert c at position b in a)
    (any, num, fun) -> c mapped over every bth item of a

    If `ind` is negative, the absolute value is used. If `ind` is greater than
    or equal to the LazyList's length, `other` is appended to the end.
    """
    lhs = iterable(lhs, ctx)
    assert vy_type(rhs) == NUMBER_TYPE

    if vy_type(other) != types.FunctionType:
        if vy_type(lhs) is str:
            return lhs[: int(rhs)] + str(other) + lhs[int(rhs) :]

        @lazylist
        def gen():
            i = 0
            for elem in lhs:
                if i == rhs:
                    yield other
                yield elem
                i += 1
            if i < rhs:
                yield other

        return gen()

    @lazylist
    def gen():
        i = 0
        for item in lhs:
            yield safe_apply(other, item, ctx=ctx) if i % rhs == 0 else item
            i += 1

    return gen()


def integer_divide(lhs, rhs, ctx):
    """Element ḭ
    (num, num) -> a // b (Floor division, floor(a / b))
    (str, num) -> (a divided into b pieces)[0]
    (num, str) -> (b divided into a pieces)[0]
    (any, fun) -> Right reduce a by b (foldr)
    (fun, any) -> Right reduce b by a (foldr)
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: 0 if rhs == 0 else lhs // rhs,
        (NUMBER_TYPE, str): lambda: divide(lhs, rhs, ctx=ctx)[0],
        (str, NUMBER_TYPE): lambda: divide(rhs, lhs, ctx=ctx)[0],
        (ts[0], types.FunctionType): lambda: foldl(
            rhs, reverse(iterable(lhs, ctx=ctx), ctx=ctx), ctx=ctx
        ),
        (types.FunctionType, ts[1]): lambda: foldl(
            lhs, reverse(iterable(rhs, ctx=ctx), ctx=ctx), ctx=ctx
        ),
    }.get(ts, lambda: vectorise(integer_divide, lhs, rhs, ctx=ctx))()


def integer_parts_or_join_spaces(lhs, ctx):
    """Element Ṅ
    (num) -> Integer partitions of a. [] if 0, all negative if n < 0
    (any) -> Join on spaces
    """
    if vy_type(lhs) == NUMBER_TYPE:
        if lhs == 0:
            return []
        sign = -1 if lhs < 0 else 1

        @lazylist
        def helper(n, minimum):
            for i in range(minimum, n // 2 + 1):
                for part in helper(n - i, i):
                    yield part + [i * sign]
            yield [n * sign]

        return helper(abs(lhs), 1)

    return join(lhs, " ", ctx)


def interleave(lhs, rhs, ctx):
    """Element Y
    (any, any) -> interleave a and b
    """
    # Essentially, Zf but whatever

    lhs = iterable(lhs, ctx=ctx)
    rhs = iterable(rhs, ctx=ctx)

    @lazylist
    def gen():
        lhs_iter = iter(lhs)
        rhs_iter = iter(rhs)
        while True:
            try:
                yield next(lhs_iter)
            except StopIteration:
                yield from rhs_iter
                break
            try:
                yield next(rhs_iter)
            except StopIteration:
                yield from lhs_iter
                break

    if type(lhs) is type(rhs) is str:
        return "".join(gen())
    else:
        return gen()


def into_two(lhs, ctx):
    """Element I
    (num) -> push a spaces
    (str) -> equivlaent to `qp`
    (lst) -> split a list into two halves
    """
    ts = vy_type(lhs, simple=True)
    return {
        NUMBER_TYPE: lambda: " " * int(lhs),
        str: lambda: quotify(lhs, ctx) + lhs,
        list: lambda: [
            index(lhs, [None, int(len(lhs) / 2) + len(lhs) % 2], ctx),
            index(lhs, [int(len(lhs) / 2) + len(lhs) % 2, None], ctx),
        ],
    }.get(ts)()


def is_divisible(lhs, rhs, ctx):
    """Element Ḋ
    (num, num) -> a % b == 0
    (num, str) -> a copies of b
    (str, num) -> b copies of a
    (str, str) -> b + " " + a ($ẋ)

    Beware, this function returns a singleton list for its first and
    fourth overloads and a list of copies of the top of the stack
    otherwise, not a single value!
    """
    ts = vy_type(lhs, rhs)

    def helper(lhs, rhs):
        ts = vy_type(lhs, rhs)
        return {
            (NUMBER_TYPE, NUMBER_TYPE): lambda: int(lhs % rhs == 0),
            (NUMBER_TYPE, str): lambda: [rhs] * lhs,
            (str, NUMBER_TYPE): lambda: [lhs] * rhs,
            (str, str): lambda: rhs + " " + lhs,
        }.get(ts, lambda: vectorise(helper, lhs, rhs, ctx=ctx))()

    return {
        (NUMBER_TYPE, str): lambda: [rhs] * lhs,
        (str, NUMBER_TYPE): lambda: [lhs] * rhs,
    }.get(ts, lambda: [helper(lhs, rhs)])()


def is_divisible_by_three(lhs, ctx):
    """Element ₃
    (num) -> a % 3 == 0
    (str) -> len(a) == 1
    """
    if vy_type(lhs) == NUMBER_TYPE:
        return int(lhs % 3 == 0)
    else:
        return int(len(lhs) == 1)


def is_divisible_by_five(lhs, ctx):
    """
    Element ₅
    (num) -> a % 5 == 0
    (str) -> a, len(a)
    """
    # wrap in list because you might need to return more than 1 item
    if vy_type(lhs) == NUMBER_TYPE:
        return [int(lhs % 5 == 0)]
    else:
        return [lhs, len(lhs)]


def is_even(lhs, ctx):
    """Element ₂
    (num) -> a % 2 == 0
    (str) -> len(a) % 2 == 0
    """
    if vy_type(lhs) == NUMBER_TYPE:
        return int(lhs % 2 == 0)
    else:
        return int(len(lhs) % 2 == 0)


def is_falsey(lhs, ctx):
    """Element ċ
    (any) -> a != 1
    """
    return vectorised_not(equals(lhs, 1, ctx=ctx), ctx=ctx)


def is_prime(lhs, ctx):
    """Element æ
    (num) -> is a prime?
    (str) -> case of a (1 if all letters in a are uppercase,
             0 if all letters in a are lowercase,
            -1 if mixed case)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: int(sympy.ntheory.isprime(lhs)),
        str: lambda: case_of(lhs),
    }.get(ts, vectorise(is_prime, lhs, ctx=ctx))()


def is_square(lhs, ctx):
    """Element ∆²
    (num) -> is square number?
    (str) -> square the expression
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: int(
            int(lhs) == lhs and sympy.ntheory.primetest.is_square(lhs)
        ),
        str: lambda: str(sympy.expand(make_expression(lhs + " ** 2"))),
    }.get(ts, vectorise(is_square, lhs, ctx=ctx))()


def join(lhs, rhs, ctx):
    """Element j
    (any, any) -> a.join(b)
    """
    return vy_str(rhs, ctx=ctx).join(
        map(lambda a: vy_str(a, ctx=ctx), iterable(lhs, ctx=ctx))
    )


def join_newlines(lhs, ctx):
    """Element ⁋
    (any) -> a.join("\n")
    """
    ret = []
    for n in iterable(lhs, ctx):
        if vy_type(n) in [list, LazyList]:
            ret.append(join(n, " ", ctx))
        else:
            ret.append(str(n))
    return "\n".join(ret)


def left_bit_shift(lhs, rhs, ctx):
    """Element ↲
    (num, num) -> a << b
    (num, str) -> a.ljust(b)
    (str, num) -> b.ljust(a)
    (str, str) -> a.ljust(len(b)-len(a))
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs << rhs,
        (NUMBER_TYPE, str): lambda: rhs.ljust(lhs),
        (str, NUMBER_TYPE): lambda: lhs.ljust(rhs),
        (str, str): lambda: lhs.ljust(len(rhs)),
    }.get(ts, lambda: vectorise(left_bit_shift, lhs, rhs, ctx=ctx))()


def length(lhs, ctx):
    """Element L
    (any) -> len(a)
    """
    return len(iterable(lhs, ctx=ctx))


def less_than(lhs, rhs, ctx):
    """Element <
    (num, num) -> a < b
    (num, str) -> str(a) < b
    (str, num) -> a < str(b)
    (str, str) -> a < b
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(bool(lhs < rhs)),
        (NUMBER_TYPE, str): lambda: int(str(lhs) < rhs),
        (str, NUMBER_TYPE): lambda: int(lhs < str(rhs)),
        (str, str): lambda: int(lhs < rhs),
    }.get(ts, lambda: vectorise(less_than, lhs, rhs, ctx=ctx))()


def less_than_or_equal(lhs, rhs, ctx):
    """Element ≤
    (num, num) -> a ≤ b
    (num, str) -> str(a) ≤ b
    (str, num) -> a ≤ str(b)
    (str, str) -> a ≤ b
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(bool(lhs <= rhs)),
        (NUMBER_TYPE, str): lambda: int(str(lhs) <= rhs),
        (str, NUMBER_TYPE): lambda: int(lhs <= str(rhs)),
        (str, str): lambda: int(lhs <= rhs),
    }.get(ts, lambda: vectorise(less_than_or_equal, lhs, rhs, ctx=ctx))()


def ljust(lhs, rhs, other, ctx):
    """Element ŀ
    (num, num, num) -> a <= c <= b
    (num, num, str) -> a by b grid of c
    (num, str, num) -> a by c grid of b
    (num, str, str) -> b.ljust(a,filler=c)
    (str, num, num) -> b by c grid of a
    (str, num, str) -> a.ljust(c,filler=b)
    (str, str, num) -> a.ljust(b,filler=c)
    (str, str, str) -> a.infinite_replace(b, c)
    (fun, fun, any) -> collect_until_false(predicate=a,
                       modifying_function=b, inital=c)
                       # Collect the results of apply a on c while b(c)
                       # is truthy
    """
    ts = vy_type(lhs, rhs, other)
    return {
        (NUMBER_TYPE, NUMBER_TYPE, NUMBER_TYPE): lambda: int(
            lhs <= other <= rhs
        ),
        (NUMBER_TYPE, NUMBER_TYPE, str): lambda: "\n".join([other * lhs] * rhs),
        (NUMBER_TYPE, str, NUMBER_TYPE): lambda: "\n".join([rhs * lhs] * other),
        (NUMBER_TYPE, str, str): lambda: vy_str(rhs, ctx=ctx).ljust(lhs, other),
        (str, NUMBER_TYPE, NUMBER_TYPE): lambda: "\n".join([lhs * other] * rhs),
        (str, NUMBER_TYPE, str): lambda: vy_str(lhs, ctx=ctx).ljust(rhs, other),
        (str, str, NUMBER_TYPE): lambda: vy_str(lhs, ctx=ctx).ljust(rhs, other),
        (str, str, str): lambda: infinite_replace(lhs, rhs, other, ctx),
        (
            types.FunctionType,
            types.FunctionType,
            ts[-1],
        ): lambda: collect_until_false(lhs, rhs, other, ctx),
        (
            ts[0],
            types.FunctionType,
            types.FunctionType,
        ): lambda: collect_until_false(rhs, other, lhs, ctx),
        (
            types.FunctionType,
            ts[1],
            types.FunctionType,
        ): lambda: collect_until_false(lhs, other, rhs, ctx),
    }.get(ts, lambda: vectorise(ljust, lhs, rhs, other, ctx=ctx))()


def log_10(lhs, ctx):
    """Element ∆τ
    (num) -> log10(a)
    (str) -> log10(a)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.log(lhs, 10),
        (str): lambda: str(sympy.log(make_expression(lhs), 10)),
    }.get(ts, lambda: vectorise(log_10, lhs, ctx=ctx))()


def log_2(lhs, ctx):
    """Element ∆l
    (num) -> log2(a)
    (str) -> log2(a)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.log(lhs, 2),
        (str): lambda: str(sympy.log(make_expression(lhs), 2)),
    }.get(ts, lambda: vectorise(log_2, lhs, ctx=ctx))()


def log_mold_multi(lhs, rhs, ctx):
    """Element •
    (num, num) -> log_lhs(rhs)
    (num, str) -> [char * lhs for char in rhs]
    (str, num) -> [char * rhs for char in lhs]
    (str, str) -> lhs.with_capitalisation_of(rhs)
    (lst, lst) -> lhs molded to the shape of rhs
    """
    ts = vy_type(lhs, rhs, simple=True)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: sympy.nsimplify(math.log(lhs, rhs)),
        (NUMBER_TYPE, str): lambda: "".join([char * lhs for char in rhs]),
        (str, NUMBER_TYPE): lambda: "".join([char * rhs for char in lhs]),
        (str, str): lambda: transfer_capitalisation(rhs, lhs),
        (list, list): lambda: mold(lhs, rhs),
    }.get(ts, lambda: vectorise(log_mold_multi, lhs, rhs, ctx=ctx))()


def lowest_common_multiple(lhs, rhs=None, ctx=None):
    """Element ∆Ŀ
    (num, num) -> lcm(a, b)
    """
    if rhs is None:
        return sympy.lcm(lhs)
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: sympy.nsimplify(
            sympy.lcm(lhs, rhs)
        ),
        (NUMBER_TYPE, str): lambda: -1,
        (str, NUMBER_TYPE): lambda: -1,
        (str, str): lambda: -1,
    }.get(ts, lambda: vectorise(lowest_common_multiple, lhs, rhs, ctx=ctx))()


def matrix_determinant(lhs, ctx):
    """Element ∆∆
    (mat) -> determinant(a)
    """
    lhs = pad_to_square(iterable(lhs, ctx=ctx))
    return sympy.det(sympy.Matrix(lhs))


def matrix_multiply(lhs, rhs, ctx):
    """Element ÞṀ
    (lst, lst) -> Matrix multiplication
    """
    rhs = transpose(rhs, ctx)

    return LazyList(
        [dot_product(row, column, ctx) for column in rhs] for row in lhs
    )


def max_by_function(lhs, rhs, ctx):
    """Element Þ↑
    (lst, fun) -> Maximum value of a by applying b to each element
    """
    lhs, rhs = (lhs, rhs) if isinstance(rhs, types.FunctionType) else (rhs, lhs)
    lhs = iterable(lhs, ctx=ctx)
    if len(lhs) == 0:
        return []
    elif len(lhs) == 1:
        return lhs[0]
    else:
        biggest, biggest_fn = lhs[0], safe_apply(rhs, lhs[0], ctx=ctx)
        for item in biggest[1:]:
            if safe_apply(rhs, item, ctx=ctx) > biggest_fn:
                biggest, biggest_fn = item, safe_apply(rhs, item, ctx=ctx)
        return biggest


def max_by_tail(lhs, ctx):
    """Element ↑
    (any) -> max(a, key=lambda x: x[-1])
    """
    lhs = iterable(lhs, ctx=ctx)
    if len(lhs) == 0:
        return []
    else:
        return max_by(lhs, key=tail, cmp=less_than, ctx=ctx)


def maximal_indices(lhs, ctx):
    """Element ÞM
    Return the indexes of maximal objects in lhs
    """

    @lazylist
    def gen():
        biggest = monadic_maximum(lhs, ctx=ctx)
        for i, item in enumerate(list(lhs)):
            if non_vectorising_equals(item, biggest, ctx=ctx):
                yield i

    return gen()


def mean(lhs, ctx):
    """Element ṁ
    (num) -> random.randint(0, a)
    (str) -> palindromise a
    (lst) -> arithmetic mean of a
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: random.randint(0, lhs),
        (str): lambda: palindromise(lhs, ctx),
    }.get(ts, lambda: divide(vy_sum(lhs, ctx), len(lhs), ctx))()


def median(lhs, ctx):
    """Element ∆ṁ
    Return the median of a list - the middle item(s)
    """
    lhs = iterable(vy_sort(lhs, ctx), ctx=ctx)
    if len(lhs) % 2 == 0:
        return [lhs[len(lhs) // 2 - 1], lhs[len(lhs) // 2]]
    return lhs[len(lhs) // 2]


def merge(lhs, rhs, ctx):
    """Element J
    (scl, scl) -> concatenate a and b
    (lst, scl) -> append b to a
    (scl, lst) -> prepend a to b
    (lst, lst) -> merged a and b
    """
    ts = vy_type(lhs, rhs, simple=True)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: vy_eval(
            str(lhs) + str(rhs), ctx=ctx
        ),
        (NUMBER_TYPE, str): lambda: add(lhs, rhs, ctx),
        (str, NUMBER_TYPE): lambda: add(lhs, rhs, ctx),
        (str, str): lambda: lhs + rhs,
        (list, ts[1]): lambda: concat(lhs, [rhs], ctx),
        (ts[0], list): lambda: concat([lhs], rhs, ctx),
        (list, list): lambda: concat(lhs, rhs, ctx),
    }.get(ts)()


def min_by_function(lhs, rhs, ctx):
    """Element Þ↓
    (lst, fun) -> Minimum value of a by applying b to each element
    """
    lhs, rhs = (lhs, rhs) if isinstance(rhs, types.FunctionType) else (rhs, lhs)
    lhs = iterable(lhs, ctx=ctx)
    if len(lhs) == 0:
        return []
    elif len(lhs) == 1:
        return lhs[0]
    else:
        smallest, smallest_fn = lhs[0], safe_apply(rhs, lhs[0], ctx=ctx)
        for item in smallest[1:]:
            if safe_apply(rhs, item, ctx=ctx) < smallest_fn:
                smallest, smallest_fn = item, safe_apply(rhs, item, ctx=ctx)
        return smallest


def min_by_tail(lhs, ctx):
    """Element ↓
    (any) -> min(a, key=lambda x: x[-1])
    """
    lhs = iterable(lhs, ctx=ctx)
    if len(lhs) == 0:
        return []
    else:
        return min_by(lhs, key=tail, cmp=less_than, ctx=ctx)


def mirror(lhs, ctx):
    """Element m
    (num) -> a + reversed(a) (as number)
    (str) -> a + reversed(a)
    (lst) -> Concatenate reversed(a) to a
    """
    if vy_type(lhs) in (NUMBER_TYPE, str):
        return add(lhs, reverse(lhs, ctx), ctx)
    else:
        return concat(lhs, reverse(lhs, ctx), ctx)


def mode(lhs, ctx):
    """Element ∆M
    Most common item in a list.
    Equivalent to Ċ↑h
    """
    item_counts = collections.Counter(iterable(lhs, ctx=ctx))
    return item_counts.most_common(1)[0][0]


def modulo(lhs, rhs, ctx):
    """Element %
    (num, num) -> a % b
    (num, str) -> (b split into a equal pieces)[-1]
    (str, num) -> (a split into b equal pieces)[-1]
    (str, str) -> a.format(b)
    """
    ts = vy_type(lhs, rhs, simple=True)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs % rhs,
        (NUMBER_TYPE, str): lambda: format_string(rhs, [lhs]),
        (str, NUMBER_TYPE): lambda: format_string(lhs, [rhs]),
        (str, str): lambda: format_string(lhs, [rhs]),
        (str, list): lambda: format_string(lhs, rhs),
    }.get(ts, lambda: vectorise(modulo, lhs, rhs, ctx=ctx))()


def modulo_3(lhs, ctx):
    """Element ǒ
    (num) -> a % 3
    (str) -> a split into chunks of size 2
    """
    return {
        (NUMBER_TYPE): lambda: lhs % 3,
        (str): lambda: [lhs[i : i + 2] for i in range(0, len(lhs), 2)],
    }.get(vy_type(lhs), lambda: vectorise(modulo_3, lhs, ctx=ctx))()


def mold_special(lhs, rhs, ctx):
    """Element Þṁ
    (lst, lst) -> mold, but don't reuse items"""
    lhs, rhs = iterable(lhs, ctx=ctx), iterable(rhs, ctx=ctx)
    return mold_without_repeat(lhs, rhs)


def monadic_maximum(lhs, ctx):
    """Element G
    (any) -> Maximal element of the input (deep flattens first)
    """
    lhs = deep_flatten(lhs, ctx)
    if len(lhs) == 0:
        return []
    else:
        return max_by(lhs, cmp=less_than, ctx=ctx)


def monadic_minimum(lhs, ctx):
    """Element g
    (any) -> Smallest item of a (deep flattens)
    """
    lhs = deep_flatten(lhs, ctx)
    if len(lhs) == 0:
        return []
    else:
        return min_by(lhs, cmp=less_than, ctx=ctx)


def multi_dimensional_search(lhs, rhs, ctx):
    """Element Þḟ
    (lst, any) -> Find the first occurrence of a in b and return as a
                  multidimensional index
    """
    lhs = iterable(lhs, ctx=ctx)
    indexes = enumerate_md(lhs)

    for ind in indexes:
        if non_vectorising_equals(
            multi_dimensional_index(lhs, ind, ctx), rhs, ctx
        ):
            return ind

    return []


def multi_dimensional_index(lhs, rhs, ctx):
    """Element Þi
    (lst, lst) -> a[b[0]][b[1]][b[2]]... Reduce by indexing with
                  a as initial value
    """
    for item in iterable(rhs, ctx=ctx):
        lhs = index(lhs, item, ctx)

    return lhs


def multiplicity(lhs, rhs, ctx):
    """Element Ǒ
    (num, num) -> number of times a divides b
    (str, str) -> Remove a from b until b does not change
    """
    ts = vy_type(lhs, rhs, simple=True)
    if ts == (NUMBER_TYPE, NUMBER_TYPE):
        times = 0
        while lhs % rhs == 0:
            lhs /= rhs
            times += 1
        return times
    elif ts == (str, str):
        return remove_until_no_change(lhs, rhs, ctx)
    else:
        return vectorise(multiplicity, lhs, rhs, ctx=ctx)


def multiply(lhs, rhs, ctx):
    """Element *
    (num, num) -> a * b
    (num, str) -> repeat b a times
    (str, num) -> repeat a b times
    (str, str) -> ring translate b according to a
    """
    ts = vy_type(lhs, rhs)

    if ts[0] is types.FunctionType:
        lhs.stored_arity = rhs
        return lhs

    elif ts[1] is types.FunctionType:
        rhs.stored_arity = lhs
        return rhs
    else:
        return {
            (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs * rhs,
            (NUMBER_TYPE, str): lambda: lhs * rhs,
            (str, NUMBER_TYPE): lambda: lhs * rhs,
            (str, str): lambda: ring_translate(lhs, rhs),
        }.get(ts, lambda: vectorise(multiply, lhs, rhs, ctx=ctx))()


def natural_log(lhs, ctx):
    """Element ∆L
    (num) -> ln(a)
    (str) -> inverse of expression a
    """
    x, y = sympy.symbols("x, y")
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.ln(lhs),
        (str): lambda: map(
            lambda ex: str(ex.subs(y, x)),
            wrapify(sympy.solve(y - make_expression(lhs), x)),
        ),
    }.get(ts, lambda: vectorise(natural_log, lhs, ctx=ctx))()


def n_choose_r(lhs, rhs, ctx):
    """Element ƈ
    (num, num) -> n choose r
    (num, str) -> [random.choice(b) for _ in range(a)]
    (str, num) -> [random.choice(a) for _ in range(b)]
    (str, str) -> does a have the same characters as b
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: sympy.binomial(lhs, rhs),
        (NUMBER_TYPE, str): lambda: [
            random.choice(rhs) for _ in range(abs(int(lhs)))
        ],
        (str, NUMBER_TYPE): lambda: [
            random.choice(lhs) for _ in range(abs(int(rhs)))
        ],
        (str, str): lambda: int(set(lhs) == set(rhs)),
    }.get(ts, lambda: vectorise(n_choose_r, lhs, rhs, ctx=ctx))()


def n_pick_r(lhs, rhs, ctx):
    """Element ∆ƈ
    (num, num) -> n_pick_r(a, b)
    (num, str) -> n_pick_r(a, len(b))
    (str, num) -> n_pick_r(len(a), b)
    (str, str) -> n_pick_r(len(a), len(b))
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: divide(
            factorial(lhs, ctx), factorial(lhs - rhs, ctx), ctx
        ),
        (NUMBER_TYPE, str): lambda: n_pick_r(lhs, len(rhs), ctx),
        (str, NUMBER_TYPE): lambda: n_pick_r(len(lhs), rhs, ctx),
        (str, str): lambda: n_pick_r(len(lhs), len(rhs), ctx),
    }.get(ts, lambda: vectorise(n_pick_r, lhs, rhs, ctx=ctx))()


def nearest_prime(lhs, ctx):
    """Element ∆p
    (num) -> nearest prime to a
    (str) -> python code from expression
    """
    ts = vy_type(lhs)
    if ts == NUMBER_TYPE:
        if lhs < 2:
            return 2
        elif is_prime(lhs, ctx):
            return lhs

    return {
        (NUMBER_TYPE): lambda: min(
            next_prime(lhs, ctx),
            prev_prime(lhs, ctx),
            key=lambda x: abs(x - lhs),
        ),
        (str): lambda: sympy.pycode(make_expression(lhs)),
    }.get(ts, lambda: vectorise(nearest_prime, lhs, ctx=ctx))()


def negate(lhs, ctx):
    """Element N
    (num) -> -a
    (str) -> swapcase of a
    """
    ts = vy_type(lhs)
    return {(NUMBER_TYPE): lambda: -lhs, (str): lambda: lhs.swapcase()}.get(
        ts, lambda: vectorise(negate, lhs, ctx=ctx)
    )()


def newline_split(lhs, ctx):
    """Element ↵
    (num) -> 10 ** a
    (str) -> a.split("\\n")
    """
    return {
        (NUMBER_TYPE): lambda: 10 ** lhs,
        (str): lambda: lhs.split("\n"),
    }.get(vy_type(lhs), lambda: vectorise(newline_split, lhs, ctx=ctx))()


def next_prime(lhs, ctx):
    """Element ∆Ṗ
    (num) -> next prime after a
    (str) -> discrimiant of a
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: sympy.nextprime(lhs),
        (str): lambda: sympy.discriminant(make_expression(lhs)),
    }.get(ts, lambda: vectorise(next_prime, lhs, ctx=ctx))()


def non_vectorising_equals(lhs, rhs, ctx):
    """Element ⁼
    (num, num) -> a == b
    (str, str) -> a == b
    (lst, lst) -> a == b
    """
    ts = vy_type(lhs, rhs, simple=True)
    return int(
        {
            (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs == rhs,
            (NUMBER_TYPE, str): lambda: str(lhs) == rhs,
            (str, NUMBER_TYPE): lambda: lhs == str(rhs),
            (str, str): lambda: lhs == rhs,
            (list, list): lambda: lhs == rhs,
        }.get(ts, lambda: 0)()
    )


def not_equals(lhs, rhs, ctx):
    """Element ≠
    (num, num) -> a != b
    (str, str) -> a != b
    (lst, lst) -> a != b
    """
    ts = vy_type(lhs, rhs, simple=True)
    return int(
        {
            (NUMBER_TYPE, str): lambda: str(lhs) != rhs,
            (str, NUMBER_TYPE): lambda: lhs != str(rhs),
        }.get(ts, lambda: lhs != rhs)()
    )


def nth_cardinal(lhs, ctx):
    """Element ∆ċ
    Given a number, return that number as a cardinal - minus one, zero,
    one, two, three etc
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: num2words.num2words(
            lhs, lang="en", to="cardinal"
        ),
        (str): lambda: lhs,
    }.get(ts, lambda: vectorise(nth_cardinal, lhs, ctx=ctx))()


def nth_e(lhs, ctx):
    """Element ∆ė
    (int) -> nth_e(a)
    (str) -> derivative of a
    """
    if type(lhs) is str:
        x = sympy.symbols("x")
        return str(sympy.diff(make_expression(lhs), x))
    elif vy_type(lhs) == NUMBER_TYPE:
        if lhs == 0:
            return 2
        elif lhs == 1:
            return 7
        else:
            return int(str(sympy.N(sympy.E, int(lhs) + 2))[lhs + 1])
    else:
        return vectorise(nth_e, lhs, ctx=ctx)


def nth_ordinal(lhs, ctx):
    """Element ∆o
    Nth item of Þo
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: num2words.num2words(
            lhs, lang="en", to="ordinal"
        ),
        (str): lambda: lhs,
    }.get(ts, lambda: vectorise(nth_ordinal, lhs, ctx=ctx))()


def nth_pi(lhs, ctx):
    """Element ∆i
    (int) -> nth_pi(a)
    (str) -> indefinte integral of a
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: pi_digits(int(lhs))[int(lhs)],
        (str): lambda: sympy.integrate(make_expression(lhs)),
    }.get(ts, lambda: vectorise(nth_pi, lhs, ctx=ctx))()


def one_slice(lhs, rhs, ctx):
    """Element Ż
    (any, num) -> a[1:b] (Slice from 1 until b)
    (num, any) -> b[1:a] (Slice from 1 until a)
    (str, str) -> re.match(pattern=a,string=b)
    """
    # no, not one_shot, one_slice.
    ts = vy_type(lhs, rhs)
    return {
        (ts[0], NUMBER_TYPE): lambda: index(
            iterable(lhs, ctx=ctx), [1, rhs], ctx
        ),
        (NUMBER_TYPE, ts[1]): lambda: index(
            iterable(rhs, ctx=ctx), [1, lhs], ctx
        ),
        (str, str): lambda: vyxalify(re.match(lhs, rhs).groups()),
    }.get(ts, lambda: vectorise(one_slice, lhs, rhs, ctx=ctx))()


def optimal_compress(lhs, ctx):
    """Element øD
    (str) -> return the most optimal dictionary compressed string
    """
    DP = [" " * (len(lhs) + 1)] * (len(lhs) + 1)
    DP[0] = ""
    for ind in range(1, len(lhs) + 1):
        for left in range(max(0, ind - dictionary.max_word_len), ind - 1):
            i = dictionary.word_index(lhs[left:ind])
            if i != -1:
                DP[ind] = min([DP[ind], DP[left] + i], key=len)
                break
        DP[ind] = min([DP[ind], DP[ind - 1] + lhs[ind - 1]], key=len)
    return "`" + DP[-1] + "`"


def orderless_range(lhs, rhs, ctx):
    """Element r
    (num, num) -> range(a,b) (Range form a to b)
    (num, str) -> append 0s to b to make it length a
    (str, num) -> preprend 0s to a to make it length b
    (any, fun) -> cumulative_reduce(a,function=b) (Prefixes of a reduced by b)
    (str, str) -> regex.has_match(pattern=a,string= b) ( Does b match a)
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: LazyList(
            range(int(lhs), int(rhs), (-1, 1)[int(bool(lhs < rhs))])
            # int(bool(...)) is needed because sympy decides to
            # return a special boolean class sometimes
        ),
        (NUMBER_TYPE, str): lambda: rhs + (" " * abs(len(rhs) - lhs))
        if len(rhs) < lhs
        else rhs,
        (str, NUMBER_TYPE): lambda: (" " * abs(len(lhs) - rhs)) + lhs
        if len(lhs) < rhs
        else lhs,
        (ts[0], types.FunctionType): lambda: scanl(
            multiply(rhs, 2, ctx), iterable(lhs, range, ctx=ctx), ctx=ctx
        ),
        (types.FunctionType, ts[1]): lambda: scanl(
            multiply(lhs, 2, ctx), iterable(rhs, range, ctx=ctx), ctx=ctx
        ),
        (str, str): lambda: int(re.compile(lhs).search(rhs)),
    }.get(ts, lambda: vectorise(orderless_range, lhs, rhs, ctx=ctx))()


def overlapping_groups(lhs, rhs, ctx):
    """Element l
    (any, num) -> Overlapping groups/windows of a of length b
    (any, any) -> length(a) == length(b)
    """
    if vy_type(rhs) != NUMBER_TYPE:
        return int(len(iterable(lhs, ctx=ctx)) == len(rhs))

    stringify = vy_type(lhs) is str

    @lazylist
    def gen():
        window = "" if stringify else []
        for item in iterable(lhs, ctx=ctx):
            if stringify:
                window += item
            else:
                window.append(item)
            if len(window) == rhs:
                yield window
                window = window[1:]

    return gen()


def palindromise(lhs, ctx):
    """Element ∞
    (num) -> equivalent to m
    (str) -> a + a[:-1:-1]
    (lst) -> a + a[:-1:-1]
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: mirror(lhs, ctx),
        str: lambda: lhs + lhs[:-1][::-1],
        list: lambda: lhs + lhs[:-1][::-1],
        LazyList: lambda: merge(
            deep_copy(lhs),
            reverse(index(deep_copy(lhs), [None, -1, None], ctx), ctx),
            ctx=ctx,
        ),
    }.get(ts)()


def parenthesise(lhs, ctx):
    """Element øb
    (any) -> "(" + lhs + ")"
    (lst) -> vectorised
    """
    if vy_type(lhs, simple=True) is list:
        return vectorise(parenthesise, lhs)
    return "(" + str(lhs) + ")"


def parity(lhs, ctx):
    """Element ∷
    (num) -> parity of a
    (str) -> parity of a
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: int(lhs % 2),
        (str): lambda: halve(lhs, ctx)[-1],
    }.get(ts, lambda: vectorise(parity, lhs, ctx=ctx))()


def parse_direction_arrow_to_integer(lhs, ctx):
    """Element ¨^
    (str) -> map characters in `>^<v` to integers
    """
    ts = vy_type(lhs)
    if ts is str and len(lhs) == 1:
        return {
            ">": 0,
            "^": 1,
            "<": 2,
            "v": 3,
        }.get(lhs, -1)
    else:
        return vectorise(parse_direction_arrow_to_integer, lhs, ctx=ctx)()


def parse_direction_arrow_to_vector(lhs, ctx):
    """Element ¨^
    (str) -> map characters in `>^<v` to direction vectors
    """
    ts = vy_type(lhs)
    if ts is str and len(lhs) == 1:
        return {
            ">": [+1, 0],
            "^": [0, +1],
            "<": [-1, 0],
            "v": [0, -1],
        }.get(lhs, [0, 0])
    else:
        return vectorise(parse_direction_arrow_to_vector, lhs, ctx=ctx)()


def permutations(lhs, ctx):
    """Element Ṗ
    (any) -> Permutations of a
    """
    lhs = iterable(lhs, ctx=ctx)
    return LazyList(
        map(
            lambda x: "".join(x) if all(isinstance(y, str) for y in x) else x,
            itertools.permutations(
                iterable(lhs, number_type=range, ctx=ctx), len(lhs)
            ),
        )
    )


def pluralise_count(lhs, rhs, ctx):
    """Element øP
    (str, num) -> count lhs lots of rhs
    (num, str) -> count rhs lots of lhs
    """
    if isinstance(lhs, int):
        return pluralise_count(rhs, lhs, ctx)
    return str(rhs) + " " + str(lhs) + "s" * (rhs != 1)


def polynomial_expr_from_coeffs(lhs, ctx):
    """Element ∆Ċ
    (num) -> symbolic math representation of polynomial of degree n
             where each coefficient is 1
    (str) -> a
    (lst) -> symbolic math representation of polynomial with coeffs in
             lhs
    """
    ts = vy_type(lhs)
    x = sympy.symbols("x")
    return {
        NUMBER_TYPE: lambda: str(sum(x ** arg for arg in range(0, lhs + 1))),
        str: lambda: lhs,
        list: lambda: str(
            sum(c * x ** i for i, c in enumerate(reverse(lhs, ctx)))
        ),
    }.get(ts, lambda: vectorise(polynomial_expr_from_coeffs, lhs, ctx=ctx))()


def polynomial_from_roots(lhs, ctx):
    """Element ∆ṙ
    (lst) -> Get the polynomial with coefficients from the roots of a polynomial
    """
    eqn = " * ".join(map(lambda x: "(x - " + str(x) + ")", lhs))
    x = sympy.symbols("x")
    return sympy.Poly(eqn, x).coeffs()


def polynomial_roots(lhs, ctx):
    """Element ∆P
    (lst) -> roots(a)
    """
    x = sympy.symbols("x")

    equation = make_expression(
        " + ".join(
            map(
                lambda power: "("
                + str(power[1])
                + ")x^("
                + str(power[0])
                + ")",
                enumerate(reverse(iterable(lhs, ctx=ctx), ctx=ctx)),
            )
        )
    )

    return vyxalify(sympy.solve(sympy.Eq(equation, 0), x))


def powerset(lhs, ctx):
    """Element ṗ
    (any) -> powerset of a
    """
    # TODO make this work with infinite Lazylists
    return LazyList(
        itertools.chain.from_iterable(
            itertools.combinations(iterable(lhs, ctx), r)
            for r in range(len(iterable(lhs, ctx)) + 1)
        )
    )


def prev_prime(lhs, ctx):
    """Element ∆ṗ
    (num) -> previous prime
    (str) -> factorise expression
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.prevprime(int(lhs)) if lhs >= 3 else 1,
        str: lambda: str(sympy.factor(make_expression(lhs))),
    }.get(ts, lambda: vectorise(prev_prime, lhs, ctx=ctx))()


def prime_factors(lhs, ctx):
    """Element ǐ
    (num) -> prime_factors(a) (with duplicates)
    (str) -> title_case(a)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: deep_flatten(
            [
                [key] * value
                for key, value in sympy.ntheory.factorint(int(lhs)).items()
            ],
            ctx=ctx,
        ),
        (str): lambda: lhs.title(),
    }.get(ts, lambda: vectorise(prime_factors, lhs, ctx=ctx))()


def prime_factorisation(lhs, ctx):
    """Element Ǐ
    (num) -> prime_factors(a) (no duplicates)
    (str) -> lhs + lhs[0]"""
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.ntheory.primefactors(int(lhs)),
        str: lambda: lhs + lhs[0],
    }.get(ts, lambda: vectorise(prime_factorisation, lhs, ctx=ctx))()


def prepend(lhs, rhs, ctx):
    """Element p
    (any, any) -> a.prepend(b) (Prepend b to a)
    """
    ts = vy_type(lhs, rhs)
    return {(ts[0], ts[1]): lambda: merge(rhs, lhs, ctx=ctx)}.get(
        ts, lambda: [rhs] + lhs
    )()


def product(lhs, ctx):
    """Element Π
    (lst) -> product(list)"""
    return vy_reduce(multiply, lhs, ctx=ctx)


def quadratic_solver(lhs, rhs, ctx):
    """Element ∆q
    (num, num) -> x such that ax^2 + bx = 0
    (num, str) -> evaluate single variable equation b with x=a
    (str, num) -> evaluate single variable equation a with x=b
    (str, str) -> solve equation a = b for x
    """
    ts = vy_type(lhs, rhs)
    x = sympy.symbols("x")
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: sympy.solve(
            sympy.Eq((lhs * x ** 2) + rhs * x, 0), x
        ),
        (NUMBER_TYPE, str): lambda: sympy.solve(
            sympy.Eq(make_expression(rhs), lhs), x
        ),
        (str, NUMBER_TYPE): lambda: sympy.solve(
            sympy.Eq(make_expression(lhs), rhs), x
        ),
        (str, str): lambda: sympy.solve(
            sympy.Eq(make_expression(lhs), make_expression(rhs)), x
        ),
    }.get(ts, lambda: vectorise(quadratic_solver, lhs, rhs, ctx=ctx))()


def quotify(lhs, ctx):
    """Element q
    (any) -> ` + a + ` (Quotify a)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: "`{}`".format(lhs),
        str: lambda: "`{}`".format(
            lhs.replace("\\", "\\\\").replace("`", "\\`")
        ),
        types.FunctionType: lambda: "`{}`".format(lhs.__name__),
    }.get(ts, lambda: quotify(vy_str(lhs, ctx=ctx), ctx))()


def rand_bits(lhs, ctx):
    """Element ÞB
    (int) -> rand_bits(a)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): [random.randint(0, 1) for i in range(lhs)],
        (str): lambda: [int(random.choice(bin(ord(c))[2:])) for c in lhs],
    }.get(ts, lambda: vectorise(rand_bits, lhs, ctx=ctx))()


def random_choice(lhs, ctx):
    """Element ℅
    (lst) -> random element of a
    (num) -> Random integer from 0 to a
    """
    return random.choice(iterable(lhs, range, ctx=ctx))


def remove_at_index(lhs, rhs, ctx):
    """Element ⟇
    (any, num) -> remove item b of a
    """

    lhs, rhs = (rhs, lhs) if vy_type(rhs) != NUMBER_TYPE else (lhs, rhs)
    lhs = iterable(lhs, ctx=ctx)

    return LazyList(item for i, item in enumerate(lhs) if i != rhs)


def regex_sub(lhs, rhs, other, ctx):
    """Element øṙ
    (str, str, str) -> Replace matches of a with c in b
    (any, any, fun) -> Apply c to matches of a in b
    """
    ts = (vy_type(lhs), vy_type(rhs), vy_type(other))

    if ts[-1] != types.FunctionType:
        return re.sub(
            vy_str(lhs, ctx=ctx), vy_str(other, ctx=ctx), vy_str(rhs, ctx=ctx)
        )
    else:
        parts = re.split("(" + lhs + ")", rhs)
        out = ""
        switch = 1
        for item in parts:

            if switch % 2:
                out += item
            else:
                out += safe_apply(other, item, ctx=ctx)
            switch += 1

        return out


def remove(lhs, rhs, ctx):
    """Element o
    (num, fun) -> first a positive integers where b is truthy
    (fun, num) -> first b positive integers where a is truthy
    (any, any) -> a.remove(b)
    """
    lhs = iterable(lhs)
    ts = vy_type(lhs)
    if set(vy_type(lhs, rhs)) == {types.FunctionType, NUMBER_TYPE}:
        lhs, rhs = (rhs, lhs) if ts is types.FunctionType else (lhs, rhs)

        @lazylist
        def gen():
            value = 1
            found = 0
            while found != rhs:
                if lhs(value):
                    yield value
                    found += 1
                value += 1

        return gen()
    if ts == str:
        return replace(lhs, rhs, "", ctx)
    elif ts == LazyList:
        return lhs.filter(lambda elem: elem != rhs)
    else:
        return [elem for elem in lhs if elem != rhs]


def remove_non_alphabets(lhs, ctx):
    """Element Ǎ
    (str) -> filter(isalpha, a)
    (num) -> 2 ** a
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: 2 ** lhs,
        str: lambda: "".join(filter(str.isalpha, lhs)),
    }.get(ts, lambda: vectorise(remove_non_alphabets, lhs, ctx=ctx))()


def remove_until_no_change(lhs, rhs, ctx):
    """Element øo
    (any, any) -> a.remove_until_no_change(b)
    """
    loop = True
    prev = deep_copy(lhs)

    while loop:
        if vy_type(rhs, simple=True) is list:
            for item in rhs:
                lhs = remove(lhs, item, ctx)
        else:
            lhs = remove(lhs, rhs, ctx=ctx)
        if non_vectorising_equals(lhs, prev, ctx):
            loop = False
        else:
            prev = deep_copy(lhs)

    return lhs


def repeat(lhs, rhs, ctx):
    """Element ẋ
    (str, num) -> a * b
    (num, str) -> b * a
    (any, num) -> Repeat a b times
    (str, str) -> a + " " + b
    (fun, any) -> repeat function a on b while the function results are not-unique
    (any, fun) -> repeat function b on a while the function results are not-unique
    """
    ts = vy_type(lhs, rhs)
    if types.FunctionType in ts:
        function, value = (
            (lhs, rhs) if ts[0] == types.FunctionType else (rhs, lhs)
        )

        @lazylist
        def gen():
            prev = value
            curr = value
            while True:
                curr = safe_apply(function, curr, ctx=ctx)
                if curr == prev:
                    break
                prev = curr
                yield curr

        return gen()
    elif ts == (str, NUMBER_TYPE):
        return lhs * int(abs(rhs))
    elif ts == (NUMBER_TYPE, str):
        return rhs * int(abs(lhs))
    elif ts == (str, str):
        return lhs + rhs
    elif ts[0] == NUMBER_TYPE:
        return LazyList(rhs for _ in range(int(abs(lhs))))
    elif ts[1] == NUMBER_TYPE:
        return LazyList(lhs for _ in range(int(abs(rhs))))
    else:
        return vectorise(repeat, lhs, rhs, ctx=ctx)


def replace(lhs, rhs, other, ctx):
    """Element V
    (any, any, any) -> a.replace(b, c)
    """
    if vy_type(lhs, simple=True) is not list:
        return str(lhs).replace(str(rhs), str(other))
    else:
        return [other if value == rhs else value for value in iterable(lhs)]


def replace_until_no_change(lhs, rhs, other, ctx):
    """Element øV
    (any,any,any) -> Replace rhs with other in lhs while lhs changes
    """
    prev = None
    while prev != lhs:
        prev = deep_copy(lhs)
        lhs = replace(lhs, rhs, other, ctx)
    return lhs


def request(lhs, ctx):
    """Element ¨U
    (str) -> Send a GET request to a URL if online"""
    x = urllib.request.urlopen(urlify(lhs)).read()
    try:
        return x.decode("utf-8")
    except UnicodeDecodeError:
        return x.decode("latin-1")


def reverse(lhs, ctx):
    """Element Ṙ
    (any) -> a reversed
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: reverse_number(lhs),
        str: lambda: lhs[::-1],
        list: lambda: lhs[::-1],
        LazyList: lambda: lhs.reversed(),
    }.get(ts)()


def right_bit_shift(lhs, rhs, ctx):
    """Element ↳
    (num, num) -> a << b
    (str, num) -> a.rjust(b, " ")
    (num, str) -> b.rjust(a, " ")
    (str, str) -> a.rjust(len(b)-len(a), " ")
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(lhs) >> int(rhs),
        (str, NUMBER_TYPE): lambda: lhs.rjust(int(rhs), " "),
        (NUMBER_TYPE, str): lambda: rhs.rjust(int(lhs), " "),
        (str, str): lambda: lhs.rjust(len(rhs), " "),
    }.get(ts, lambda: vectorise(right_bit_shift, lhs, rhs, ctx=ctx))()


def roman_numeral(lhs, ctx):
    """Element øṘ
    (num) -> roman numeral of a
    (str) -> a to decimal from roman numeral
    """
    ints = (1000, 900, 500, 400, 100, 90, 50, 40, 10, 9, 5, 4, 1)
    nums = (
        "M",
        "CM",
        "D",
        "CD",
        "C",
        "XC",
        "L",
        "XL",
        "X",
        "IX",
        "V",
        "IV",
        "I",
    )
    if vy_type(lhs) is NUMBER_TYPE:
        if not 0 < lhs < 4000:
            raise ValueError("Number must be between 1 and 3999")

        result = ""
        for i, n in enumerate(ints):
            count = int(lhs / n)
            result += nums[i] * count
            lhs -= n * count
        return result
    elif vy_type(lhs) is str:
        result = 0
        for i, n in enumerate(nums):
            while lhs.startswith(n):
                result += ints[i]
                lhs = lhs[len(n) :]
        return result
    elif vy_type(lhs) is list:
        return vectorise(roman_numeral, lhs, ctx=ctx)


def round_to(lhs, rhs, ctx):
    """Element ∆W
    (num, num) -> round(a, no_dec_places=b)
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: sympy.nsimplify(
            str(sympy.N(lhs, int(rhs) + 1)), rational=True
        ),
        (NUMBER_TYPE, str): lambda: -1,
        (str, NUMBER_TYPE): lambda: -1,
        (str, str): lambda: -1,
    }.get(ts, lambda: vectorise(round_to, lhs, rhs, ctx=ctx))()


# Written by copilot. Did NOT work.
def run_length_encoding(lhs, ctx):
    """Element øe
    (str) -> List of the form [[character, count], ...]
    """
    lhs = iterable(lhs, ctx=ctx)
    return LazyList(
        map(
            lambda elem: [elem[0], len(list(elem[1]))],
            itertools.groupby(lhs),
        )
    )


def run_length_decoding(lhs, ctx):
    """Element ød
    (lst) -> Run length decoding
    """
    temp = list(map(lambda elem: elem[0] * elem[1], lhs))
    if all(isinstance(x[0], str) for x in lhs):
        return "".join(temp)
    else:
        return LazyList(temp)


def sans_last_prepend_zero(lhs, ctx):
    """Element Þr
    Remove the last item of a list and prepend 0
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: tail_remove(lhs, ctx),  # prepending a 0 to
        # a number just makes it the same number
        str: lambda: "0" + lhs[:-1],  # leave as string
    }.get(ts, lambda: prepend(tail_remove(lhs, ctx), 0, ctx=ctx))()


def shuffle(lhs, ctx):
    """Element Þ℅
    (lst) -> Return a random permutation of a
    """
    temp = deep_copy(lhs)
    random.shuffle(temp)
    return temp


def sign_of(lhs, ctx):
    """
    (num) -> sign_of(a) (positive = 1, 0 = 0; negative = -1)
    (str) -> is a numeric
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.sign(lhs),
        str: lambda: int(lhs.isnumeric()),
    }.get(ts, lambda: vectorise(sign_of, lhs, ctx=ctx))()


def sine(lhs, ctx):
    """Element ∆s
    (num) -> sin(a)
    (str) -> sin(expression)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.nsimplify(sympy.sin(lhs)),
        str: lambda: str(sympy.nsimplify(sympy.sin(make_expression(lhs)))),
    }.get(ts, lambda: vectorise(sine, lhs, ctx=ctx))()


def slice_from(lhs, rhs, ctx):
    """Element ȯ
    (fun, num) -> First b integers for which a(x) is truthy
    (any, num) -> a[b:] (Slice from b to the end)
    (str, str) -> vertically merge a and b
    """
    ts = vy_type(lhs, rhs)
    if types.FunctionType in ts:
        function, count = (
            (lhs, rhs) if ts[0] is types.FunctionType else (rhs, lhs)
        )

        @lazylist
        def gen():
            found = 0
            item = 1
            while True:
                if found == count:
                    break
                res = safe_apply(function, item, ctx=ctx)
                if boolify(res, ctx=ctx):
                    found += 1
                    yield item
                item += 1

        return gen()

    else:
        return {
            (str, str): lambda: lhs + "\n" + rhs,
        }.get(ts, lambda: index(lhs, [rhs, None, None], ctx))()


def sort_by(lhs, rhs, ctx):
    """Element ṡ
    (any, fun) -> sorted(a, key=b) (Sort by b)
    (num, num) -> range(a, b + 1) (Inclusive range from a to b)
    (str, str) -> regex.split(pattern=b, string=a)
    """
    ts = vy_type(lhs, rhs)
    if types.FunctionType in ts:
        function, vector = (
            (lhs, rhs) if ts[0] is types.FunctionType else (rhs, lhs)
        )
        return sorted(
            iterable(vector, ctx=ctx),
            key=lambda x: safe_apply(function, x, ctx=ctx),
        )
    else:
        return {
            (NUMBER_TYPE, NUMBER_TYPE): lambda: range(lhs, rhs + 1)
            if lhs <= rhs
            else range(lhs, rhs - 1, -1),
            (str, str): lambda: re.split(rhs, lhs),
        }.get(ts, lambda: vectorise(sort_by, lhs, rhs, ctx=ctx))()


def split_on(lhs, rhs, ctx):
    """
    Element €
    (num, num) -> str(lhs).split(rhs)
    (num, str) -> str(lhs).split(rhs)
    (str, num) -> lhs.split(str(rhs))
    (str, str) -> lhs.split(rhs)

    """
    if [primitive_type(lhs), primitive_type(rhs)] == [SCALAR_TYPE, SCALAR_TYPE]:
        return str(lhs).split(str(rhs))

    else:
        ret, temp = [], []
        for item in iterable(lhs, ctx=ctx):
            if item == rhs:
                ret.append(temp[::])
                temp = []
            else:
                temp.append(item)
        if temp:
            ret.append(temp)
        return ret


def split_keep(lhs, rhs, ctx):
    """Element Ẇ
    (any, any) -> a.split_and_keep_delimiter(b) (Split and keep the delimiter)
    """
    if isinstance(lhs, str):
        return re.split(f"({re.escape(vy_str(rhs, ctx=ctx))})", lhs)
    else:
        lhs = iterable(lhs, ctx)

        def gen():
            temp = []
            for item in lhs:
                if item == rhs:
                    yield temp[::]
                    temp = [item]
                else:
                    temp.append(item)
            if temp:
                yield temp

        return LazyList(gen())


def square(lhs, ctx):
    """Element ²
    (num) -> a ** 2 (Squared)
    (str) -> a formatted as a square
    """

    def grid_helper(string):
        temp = string
        while not is_square(len(temp), ctx):
            temp += " "
        return wrap(temp, int(square_root(len(temp), ctx)), ctx)

    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: exponent(lhs, 2, ctx),
        str: lambda: grid_helper(lhs),
    }.get(ts, lambda: vectorise(square, lhs, ctx=ctx))()


def square_root(lhs, ctx):
    """Element √
    (num) -> sqrt(a)
    (str) -> every second character of a
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.sqrt(lhs),
        str: lambda: "".join(lhs[::2]),
    }.get(ts, lambda: vectorise(square_root, lhs, ctx=ctx))()


def strict_greater_than(lhs, rhs, ctx):
    """Element ¨>
    Non-vectorising greater than
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(bool(lhs > rhs)),
        (NUMBER_TYPE, str): lambda: int(str(lhs) > rhs),
        (str, NUMBER_TYPE): lambda: int(lhs > str(rhs)),
        (str, str): lambda: int(lhs > rhs),
    }.get(
        ts,
        lambda: int(
            bool(list(iterable(lhs, ctx=ctx)) > list(iterable(rhs, ctx=ctx)))
        ),
    )()


def strict_less_than(lhs, rhs, ctx):
    """Element ¨>
    Non-vectorising less than
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: int(bool(lhs < rhs)),
        (NUMBER_TYPE, str): lambda: int(str(lhs) < rhs),
        (str, NUMBER_TYPE): lambda: int(lhs < str(rhs)),
        (str, str): lambda: int(lhs < rhs),
    }.get(
        ts,
        lambda: int(
            bool(list(iterable(lhs, ctx=ctx)) < list(iterable(rhs, ctx=ctx)))
        ),
    )()


def strip(lhs, rhs, ctx):
    """Element P
    (any, any) -> a.strip(b)
    """

    def list_helper(left, right):
        """This doesn't make sense anywhere but here"""
        if vy_type(left) is LazyList:
            left = left.listify()
        if vy_type(right) is LazyList:
            right = right.listify()
        if len(left) == 0:
            return []  # how you gonna strip from nothing

        # Strip from the right side first
        # check to make sure there's stuff to strip

        if len(left) < len(right):
            # left is smaller than right
            # e.g. [1, 2, 3].strip([2, 3, 4, 5, 6])
            if left in (right[: len(left)], right[: len(left) : -1]):
                return []

        if left[-len(right) :] == right[::-1]:
            del left[-len(right) :]

        if left[: len(right)] == right:
            del left[: len(right)]

        return left

    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: vy_eval(
            vy_str(lhs, ctx=ctx).strip(vy_str(rhs, ctx=ctx)),
            ctx,
        ),
        (NUMBER_TYPE, str): lambda: vy_eval(
            vy_str(lhs, ctx=ctx).strip(rhs), ctx
        ),
        (str, NUMBER_TYPE): lambda: lhs.strip(str(rhs)),
        (str, str): lambda: lhs.strip(rhs),
    }.get(ts, lambda: list_helper(lhs, rhs))()


def starts_with(lhs, rhs, ctx):
    """Element øp
    (str, str) -> True if a starts with b
    """
    return int(lhs.startswith(rhs))


def sublists(lhs, ctx):
    """Element ÞS
    Sublists of a list.
    """

    @lazylist
    def gen():
        length = len(lhs)
        for size in range(1, length + 1):
            for sub in range((length - size) + 1):
                yield index(lhs, [sub, sub + size], ctx)

    return gen()


def substrings(lhs, ctx):
    """Element ǎ
    (num) -> ath prime
    (str) -> all substrings of a
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.ntheory.prime(int(lhs) + 1),
        str: lambda: LazyList(
            (
                lhs[i:j]
                for i in range(len(lhs) + 1)
                for j in range(1, len(lhs) + 1)
                if i < j
            )
        ),
    }.get(ts, lambda: vectorise(substrings, lhs, ctx=ctx))()


def subtract(lhs, rhs, ctx):
    """Element -
    (num, num) -> lhs - rhs
    (num, str) -> ("-" * lhs) + rhs
    (str, num) -> lhs + ("-" * rhs)
    (str, str) -> lhs.replace(rhs, "")
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: lhs - rhs,
        (NUMBER_TYPE, str): lambda: ("-" * lhs) + rhs,
        (str, NUMBER_TYPE): lambda: lhs + ("-" * rhs),
        (str, str): lambda: lhs.replace(rhs, ""),
    }.get(ts, lambda: vectorise(subtract, lhs, rhs, ctx=ctx))()


def symmetric_difference(lhs, rhs, ctx):
    """Element ⊍
    (any, any) -> set(a) ^ set(b)
    """
    lhs = uniquify(iterable(lhs, ctx=ctx), ctx)
    rhs = uniquify(iterable(rhs, ctx=ctx), ctx)

    @lazylist
    def gen():
        for item in lhs:
            if item not in rhs:
                yield item
        for item in rhs:
            if item not in lhs:
                yield item

    return gen()


def tail(lhs, ctx):
    """Element t
    (any) -> a[-1]
    """
    return (
        iterable(lhs, ctx)[-1]
        if len(iterable(lhs, ctx))
        else ""
        if type(lhs) is str
        else 0
    )


def tail_remove(lhs, ctx):
    """Element Ṫ
    (any) -> a[:-1] (All but the last item)
    """
    temp = index(iterable(lhs, ctx=ctx), [0, -1], ctx=ctx)
    if is_sympy(lhs) and all(isinstance(x, int) for x in temp):
        return int("".join(str(x) for x in temp or "0"))
    else:
        return temp


def tangent(lhs, ctx):
    """Element ∆t
    (num) -> tan(a)
    (str) -> tan(expression)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.nsimplify(sympy.tan(lhs)),
        str: lambda: str(sympy.nsimplify(sympy.tan(make_expression(lhs)))),
    }.get(ts, lambda: vectorise(tangent, lhs, ctx=ctx))()


def to_base(lhs, rhs, ctx):
    """Element τ
    Convert lhs from base 10 to base rhs
    """
    if vy_type(lhs) is not NUMBER_TYPE:
        raise ValueError("to_base only works on numbers")

    if vy_type(rhs) == NUMBER_TYPE:
        rhs = list(range(0, int(rhs)))
    else:
        rhs = iterable(rhs, ctx=ctx)
    if len(rhs) == 1:
        maximal_exponent = lhs
    else:
        maximal_exponent = int(log_mold_multi(lhs, len(rhs), ctx))

    res = []
    for i in range(maximal_exponent, -1, -1):
        digit, remaining = divmod(lhs, len(rhs) ** i)
        res.append(index(rhs, digit, ctx))
        lhs = remaining

    if all(isinstance(x, str) for x in res) and all(len(x) == 1 for x in res):
        return "".join(res)
    return res


def to_degrees(lhs, ctx):
    """Element ∆D
    (num) -> a * (180 / pi)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: lhs * (180 / sympy.pi),
        str: lambda: sympy.N(lhs) * (180 / sympy.pi),
    }.get(ts, lambda: vectorise(to_degrees, lhs, ctx=ctx))()


def to_radians(lhs, ctx):
    """Element ∆R
    (num) -> a * (pi / 180)
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: lhs * (sympy.pi / 180),
        str: lambda: sympy.N(lhs) * (sympy.pi / 180),
    }.get(ts, lambda: vectorise(to_radians, lhs, ctx=ctx))()


def totient(lhs, ctx):
    """Element ∆ṫ
    (num) -> Euler's totient function
    (str) -> local minima of a function
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: sympy.totient(lhs),
        str: lambda: local_minima(lhs),
    }.get(ts, lambda: vectorise(totient, lhs, ctx=ctx))()


def transliterate(lhs, rhs, other, ctx):
    """Element Ŀ
    (any, any, any) -> transliterate lhs according to the
                       mapping rhs->other
    """
    ts = (vy_type(lhs), vy_type(rhs), vy_type(other))
    if types.FunctionType in ts:
        if ts.count(types.FunctionType) < 2:
            raise TypeError(
                "Repeat while false requires two or three functions"
            )
        # Swap the arguments so that the scalar is always in other if
        # there's a scalar else leave as is

        functions = list(
            filter(lambda x: isinstance(x, types.FunctionType), ts)
        )
        scalars = list(
            filter(lambda x: not isinstance(x, types.FunctionType), ts)
        )

        function, predicate, scalar = functions + scalars

        result = collect_until_false(predicate, function, scalar)
        return safe_apply(function, result[-1], ctx=ctx)

    mapping = dict(vy_zip(iterable(rhs, ctx), iterable(other, ctx), ctx=ctx))

    ret = []

    for item in lhs:
        for x in mapping:
            if non_vectorising_equals(item, x, ctx):
                ret.append(mapping[x])
                break
        else:
            ret.append(item)

    if (
        type(lhs) is str
        and all(isinstance(x, str) for x in ret)
        and all(len(x) == 1 for x in ret)
    ):
        return "".join(ret)
    else:
        return ret


def truthy_indices(lhs, ctx):
    """Element T
    (any) -> indices of truthy elements
    (num) -> lhs * 3
    """
    if vy_type(lhs) in (types.FunctionType, NUMBER_TYPE):
        return multiply(lhs, 3, ctx)

    lhs = iterable(lhs, ctx=ctx)

    @lazylist
    def helper():
        for i, _ in enumerate(lhs):
            if lhs[i]:
                yield i

    return helper()


def uninterleave(lhs, ctx):
    """- element: "y"
    name: Uninterleave
    description: Push every other item of a, and the rest.
    arity: 1
    overloads:
      any: a[::2], a[1::2] (Every second item, the rest)
    vectorise: false
    tests:
      - '["abcde"] : "bd"'
      - "[[1,2,3,4]] : [2,4]"
    """
    lhs = iterable(lhs, ctx=ctx)
    return [
        index(deep_copy(lhs), [None, None, 2], ctx),
        index(lhs, [1, None, 2], ctx),
    ]


def union(lhs, rhs, ctx):
    """Element ∪
    (any, any) -> union of lhs and rhs
    """

    @lazylist
    def gen():
        seen = []
        for item in iterable(lhs, ctx=ctx):
            if item not in seen:
                yield item
                seen.append(item)
        for item in iterable(rhs, ctx=ctx):
            if item not in seen:
                yield item
                seen.append(item)

    return gen()


def uniquify(lhs, ctx):
    """Element U
    (any) -> only unique items of a
    """
    if type(lhs) is str:
        seen = ""
        for item in lhs:
            if item not in seen:
                seen += item
        return seen

    @lazylist
    def f():
        seen = []
        t = iterable(lhs, ctx=ctx)
        for item in t:
            if item not in seen:
                yield item
                seen.append(item)

    return f()


def uniquify_mask(lhs, ctx):
    """Element ÞU
    (any) -> A list of booleans describing which elements of a will
             remain after uniquifying.
    """
    lhs = iterable(lhs, ctx=ctx)
    # TODO (user/cgccuser): Reduce code duplication here?
    if isinstance(lhs, list):
        seen = set()
        mask = []
        for elem in lhs:
            if elem not in seen:
                mask.append(1)
                seen.add(elem)
            else:
                mask.append(0)
        return mask

    @lazylist
    def gen():
        seen = set()
        for elem in lhs:
            if elem not in seen:
                seen.add(elem)
                yield 1
            else:
                yield 0

    return gen()


def untruth(lhs, ctx):
    """Element Þǔ
    (any) -> [int(x in a) for x in range(max(a))]
    """
    lhs = iterable(lhs, ctx=ctx)
    return [int(x in lhs) for x in range(monadic_maximum(lhs, ctx) + 1)]


def unwrap(lhs, ctx):
    """Element Þẇ
    (lst) -> Take a and push a[0]+a[-1] and a[1:-1]
    """
    lhs = iterable(lhs, ctx=ctx)

    if vy_type(lhs) is str:
        return (lhs[0] + lhs[-1], lhs[1:-1])
    else:
        rest = head_remove(tail_remove(lhs, ctx), ctx)
        return ([lhs[0], lhs[-1]], rest)


def vectorise(function, lhs, rhs=None, other=None, explicit=False, ctx=None):
    """
    Maps a function over arguments
    Probably cursed but whatever.
    The explicit argument is mainly for stopping element-wise
    vectorisation happening.
    """
    if other is not None:
        # That is, three argument vectorisation
        # That is:

        ts = primitive_type(lhs), primitive_type(rhs), primitive_type(other)

        simple = {
            (SCALAR_TYPE, SCALAR_TYPE, SCALAR_TYPE): lambda: safe_apply(
                function, lhs, rhs, other, ctx=ctx
            ),
            (SCALAR_TYPE, SCALAR_TYPE, list): lambda: (
                safe_apply(function, lhs, rhs, x, ctx=ctx) for x in other
            ),
            (SCALAR_TYPE, list, SCALAR_TYPE): lambda: (
                safe_apply(function, lhs, x, other, ctx=ctx) for x in rhs
            ),
            (SCALAR_TYPE, list, list): lambda: (
                safe_apply(function, lhs, x, y, ctx=ctx)
                for x, y in vy_zip(rhs, other, ctx=ctx)
            ),
            (list, SCALAR_TYPE, SCALAR_TYPE): lambda: (
                safe_apply(function, x, rhs, other, ctx=ctx) for x in lhs
            ),
            (list, SCALAR_TYPE, list): lambda: (
                safe_apply(function, x, rhs, y, ctx=ctx)
                for x, y in vy_zip(lhs, other, ctx=ctx)
            ),
            (list, list, SCALAR_TYPE): lambda: (
                safe_apply(function, x, y, other, ctx=ctx)
                for x, y in vy_zip(lhs, rhs, ctx=ctx)
            ),
            (list, list, list): lambda: (
                safe_apply(function, x, y, z, ctx=ctx)
                for x, y in vy_zip(lhs, rhs, ctx=ctx)
                for z in other
            ),
        }

        if explicit:
            return LazyList(
                (
                    safe_apply(function, x, rhs, other, ctx=ctx)
                    for x in iterable(lhs, ctx=ctx)
                )
            )
        else:
            return LazyList(simple.get(ts)())
    elif rhs is not None:
        # That is, two argument vectorisation
        ts = primitive_type(lhs), primitive_type(rhs)
        simple = {
            (SCALAR_TYPE, SCALAR_TYPE): lambda: safe_apply(
                function, lhs, rhs, ctx=ctx
            ),
            (SCALAR_TYPE, list): lambda: (
                safe_apply(function, lhs, x, ctx=ctx) for x in rhs
            ),
            (list, SCALAR_TYPE): lambda: (
                safe_apply(function, x, rhs, ctx=ctx) for x in lhs
            ),
            (list, list): lambda: (
                safe_apply(function, x, y, ctx=ctx)
                for x, y in vy_zip(lhs, rhs, ctx=ctx)
            ),
        }

        explicit_dict = {
            (SCALAR_TYPE, SCALAR_TYPE): lambda: (
                safe_apply(function, x, rhs, ctx=ctx) for x in iterable(lhs)
            ),
            (SCALAR_TYPE, list): lambda: (
                safe_apply(function, lhs, x, ctx=ctx) for x in rhs
            ),
            (list, SCALAR_TYPE): lambda: (
                safe_apply(function, x, rhs, ctx=ctx) for x in lhs
            ),
            (list, list): lambda: (
                safe_apply(function, x, rhs, ctx=ctx) for x in lhs
            ),
        }

        if explicit:
            return LazyList(explicit_dict.get(ts)())
        else:
            return LazyList(simple.get(ts)())
    else:
        # That is, single argument vectorisation
        if explicit:
            lhs = iterable(lhs, range, ctx=ctx)
        else:
            lhs = iterable(lhs, ctx=ctx)

        return LazyList((safe_apply(function, x, ctx=ctx) for x in lhs))


def vectorised_not(lhs, ctx):
    """List overload for element †"""
    return {NUMBER_TYPE: lambda: int(not lhs), str: lambda: int(not lhs)}.get(
        vy_type(lhs), lambda: vectorise(vectorised_not, lhs, ctx=ctx)
    )()


def vectorised_sum(lhs, ctx):
    """Element Ṡ
    (any) -> the equivalent of v∑
    """
    return LazyList(
        vy_sum(iterable(x, ctx=ctx), ctx) for x in iterable(lhs, ctx=ctx)
    )


def vertical_join(lhs, rhs=" ", ctx=None):
    """Element §
    any: Transpose a (filling with b), join on newlines
    """
    # Make every list in lhs the same length, padding left with b
    lhs, rhs = iterable(lhs, ctx=ctx), iterable(rhs, ctx=ctx)
    max_length = max(len(x) for x in lhs)
    temp = [
        [rhs] * (len(x) < max_length and max_length - len(x)) + x
        if vy_type(x, simple=True) is list
        else rhs * (len(x) < max_length and max_length - len(x)) + x
        for x in lhs
    ]
    temp = [join(x, "", ctx) for x in transpose(temp, rhs, ctx=ctx)]
    return join(temp, "\n", ctx)


def vertical_mirror(lhs, rhs=None, ctx=None):
    """Element øṁ and øṀ"""
    if type(lhs) is str:
        if rhs:
            temp = [
                s + transliterate(rhs[0], rhs[1], s[::-1], ctx)
                for s in lhs.split("\n")
            ]
            return "\n".join(temp)
        else:
            return "\n".join([mirror(s, ctx) for s in lhs.split("\n")])
    elif vy_type(lhs) == NUMBER_TYPE:
        return mirror(lhs, ctx=ctx)
    else:
        return vectorise(vertical_mirror, lhs, rhs, ctx=ctx)


def vy_abs(lhs, ctx):
    """Elements ȧ
    (num) -> abs(a)
    (str) -> remove whitespace from a
    """
    return {
        NUMBER_TYPE: lambda: abs(lhs),
        str: lambda: "".join(lhs.split()),
    }.get(vy_type(lhs), lambda: vectorise(vy_abs, lhs, ctx=ctx))()


def vy_bin(lhs, ctx):
    """Element b
    (num) -> list of binary digits
    (str) -> binary of each codepoint
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: [int(x) for x in bin(int(lhs))[2:]],
        (str): lambda: vectorise(
            vy_bin, wrapify(chr_ord(lhs, ctx=ctx), None, ctx), ctx=ctx
        ),
    }.get(ts, lambda: vectorise(vy_bin, lhs, ctx=ctx))()


def vy_ceil(lhs, ctx):
    """Element ⌈
    (num) -> ceil(a)
    (str) -> a.split(' ') # split a on spaces
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: math.ceil(lhs),
        (str): lambda: lhs.split(" "),
    }.get(ts, lambda: vectorise(vy_ceil, lhs, ctx=ctx))()


def vy_divmod(lhs, rhs, ctx):
    """Element ḋ
    (num, num) -> [lhs // rhs, lhs % rhs]
    (iterable, num) -> combinations of a with length b
    (str, str) ->  overwrite the start of a with b
    """
    ts = vy_type(lhs, rhs, simple=True)

    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: [lhs // rhs, lhs % rhs],
        (NUMBER_TYPE, str): lambda: vyxalify(
            map(vy_sum, itertools.combinations(rhs, lhs))
        ),
        (str, NUMBER_TYPE): lambda: vyxalify(
            map(vy_sum, itertools.combinations(lhs, rhs))
        ),
        (str, str): lambda: rhs + lhs[len(rhs) :],
        (list, NUMBER_TYPE): lambda: vyxalify(itertools.combinations(lhs, rhs)),
        (NUMBER_TYPE, list): lambda: vyxalify(itertools.combinations(rhs, lhs)),
    }.get(ts, lambda: vectorise(vy_divmod, lhs, rhs, ctx=ctx))()


def vy_enumerate(lhs, ctx):
    """Element ė
    (any) -> Zip with a range of the same length
    """
    return LazyList(enumerate(iterable(lhs, ctx=ctx)))


def vy_exec(lhs, ctx):
    """Element Ė
    (str) -> vy_exec(a)
    (num) -> 1 / a

    Beware, this doesn't return a single value, it returns a list!
    If lhs is a str, it executes it and returns an empty list.
    Otherwise, it wraps the result in a singleton list.
    """
    if vy_type(lhs) is str:
        import vyxal.transpile

        stack = ctx.stacks[-1]
        exec(vyxal.transpile.transpile(lhs))
        return []

    def helper(lhs):
        if vy_type(lhs) == NUMBER_TYPE:
            return divide(1, lhs, ctx)
        else:
            return vectorise(helper, lhs, ctx=ctx)

    return [helper(lhs)]


def vy_filter(lhs: Any, rhs: Any, ctx):
    """Element F
    (any, fun) -> Keep elements in a that b is true for
    (any, any) -> Remove elements of a that are in b
    """
    ts = vy_type(lhs, rhs)
    if ts[0] == types.FunctionType:
        return LazyList(
            filter(
                lambda x: safe_apply(lhs, x, ctx=ctx),
                iterable(rhs, range, ctx=ctx),
            )
        )
    elif ts[1] == types.FunctionType:
        return LazyList(
            filter(
                lambda x: safe_apply(rhs, x, ctx=ctx),
                iterable(lhs, range, ctx=ctx),
            )
        )
    elif ts == (str, str):
        return "".join(elem for elem in lhs if elem not in rhs)
    return LazyList([elem for elem in lhs if elem not in rhs])


def vy_floor(lhs, ctx):
    """Element ⌊
    (num) -> floor(a)
    (str) -> integer part of a
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: math.floor(lhs),
        (str): lambda: int(
            "".join([char for char in lhs if char in "0123456789"] or "0")
        ),
    }.get(ts, lambda: vectorise(vy_floor, lhs, ctx=ctx))()


def vy_gcd(lhs, rhs=None, ctx=None):

    ts = vy_type(lhs, rhs)

    if rhs is None:
        return math.gcd(*iterable(lhs, ctx=ctx))
    return {
        (NUMBER_TYPE, NUMBER_TYPE): lambda: math.gcd(lhs, rhs),
        (NUMBER_TYPE, str): lambda: vy_gcd(
            lhs, wrapify(chr_ord(rhs, ctx), None, ctx), ctx=ctx
        ),
        (str, str): lambda: max(
            set(suffixes(lhs, ctx)) & set(suffixes(rhs, ctx)), key=len
        ),
    }.get(ts, lambda: vectorise(vy_gcd, lhs, rhs, ctx=ctx))()


def vy_hex(lhs, ctx):
    """Element H
    (num) -> hex(a)
    (str) -> int(a, 16)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: hex(lhs)[2:],
        (str): lambda: int(lhs, 16),
    }.get(ts, lambda: vectorise(vy_hex, lhs, ctx=ctx))()


def vy_int(item: Any, base: int = 10, ctx: Context = DEFAULT_CTX):
    """Converts the item to the given base. Lists are treated as if
    each item was a digit.

    Used for multiple elements, and has to be here because it uses
    functions defined only here."""
    t_item = type(item)
    if t_item not in [str, float, int, complex]:
        ret = 0
        for element in item:
            ret = multiply(ret, base, ctx)
            ret = add(ret, element, ctx)
        return ret
    elif t_item is str:
        try:
            return int(item, base)
        except ValueError:
            return 0
    elif t_item is complex:
        return item.real
    elif t_item is float:
        return int(item)
    elif t_item:
        return vy_int(iterable(item, ctx=ctx), base)


def vy_map(lhs, rhs, ctx):
    """Element M
    (any, fun) -> apply function b to each element of a
    (any, any) -> a paired with each item of b
    """
    ts = vy_type(lhs, rhs)
    if types.FunctionType not in ts:
        return LazyList([[lhs, x] for x in iterable(rhs, range, ctx=ctx)])

    function, itr = (rhs, lhs) if ts[-1] is types.FunctionType else (lhs, rhs)
    itr = iterable(itr, range, ctx=ctx)

    @lazylist
    def gen():
        for element in itr:
            yield safe_apply(function, element, ctx=ctx)

    return gen()


def vy_sort(lhs, ctx):
    """
    (any) -> sorted(a)
    """
    # This one deviates from the usual type dictionary, because lambas
    # just don't cut it.
    if isinstance(lhs, int):
        if lhs >= 0:
            return int("".join(sorted(str(lhs))))
        else:
            return int("".join(sorted(str(-lhs)))) * -1
    if vy_type(lhs) == NUMBER_TYPE:
        sign = 1 if lhs >= 0 else -1
        number = str(sympy.N(abs(lhs), 15))
        parts = ["".join(sorted(x.strip("0"))) for x in number.split(".")]
        return sympy.nsimplify(".".join(parts), rational=True) * sign

    elif isinstance(lhs, str):
        return "".join(sorted(lhs))
    else:
        return LazyList(sorted(lhs))


def vy_str(lhs, ctx=None):
    """Element S
    (any) -> str(s)
    """
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: str(sympy.nsimplify(lhs, rational=True))
        if ctx is not None and not ctx.print_decimals
        else str(eval(sympy.pycode(sympy.nsimplify(lhs)))),
        (str): lambda: lhs,  # wow so complex and hard to understand /s
        (types.FunctionType): lambda: vy_str(
            safe_apply(lhs, *ctx.stacks[-1], ctx=ctx), ctx
        ),
    }.get(
        ts,
        lambda: ("⟨ " if ctx.vyxal_lists else "[")
        + (" | " if ctx.vyxal_lists else ", ").join(
            map(
                lambda x: vy_repr(x, ctx),
                list(lhs) or [],
            )
        )
        + (" ⟩" if ctx.vyxal_lists else "]"),
    )()


def vy_sum(lhs, ctx=None):
    """Element ∑
    (any) -> reduce a by addition
    """
    return foldl(add, iterable(lhs, ctx=ctx), ctx=ctx)


def vy_print(lhs, end="\n", ctx=None):
    """Element ,
    (any) -> send to stdout
    """
    ctx.printed = True
    ts = vy_type(lhs)

    if ts is LazyList:
        lhs.output(end, ctx)
    elif ts is list:
        vy_print(vy_str(lhs, ctx=ctx), end, ctx)
    elif ts is types.FunctionType:
        res = lhs(ctx.stacks[-1], lhs, ctx=ctx)[
            -1
        ]  # lgtm[py/call-to-non-callable]
        vy_print(res, ctx=ctx)
    else:
        if is_sympy(lhs):
            if ctx.print_decimals:
                lhs = eval(sympy.pycode(sympy.nsimplify(lhs)))
            else:
                lhs = sympy.nsimplify(sympy.N(lhs, 50), rational=True)
        if ctx.online:
            ctx.online_output[1] += vy_str(lhs, ctx=ctx) + end
        else:
            print(lhs, end=end)


def vy_reduce(lhs, rhs, ctx):
    """Element R
    (any, fun) -> Reduce a by function b
    (fun, any) -> Reduce b by function a
    """
    ts = vy_type(lhs, rhs)
    return {
        (ts[0], types.FunctionType): lambda: foldl(
            rhs, iterable(lhs, ctx=ctx), ctx=ctx
        ),
        (types.FunctionType, ts[1]): lambda: foldl(
            lhs, iterable(rhs, ctx=ctx), ctx=ctx
        ),
    }.get(ts)()


def vy_repr(lhs, ctx):
    ts = vy_type(lhs)
    return {
        (NUMBER_TYPE): lambda: vy_str(lhs, ctx),
        (str): lambda: "`" + lhs.replace("`", "\\`") + "`",
        (types.FunctionType): lambda: vy_repr(
            safe_apply(lhs, *ctx.stacks[-1], ctx=ctx), ctx
        )
        # actually make the repr kinda make sense
    }.get(
        ts,
        lambda: ("⟨ " if ctx.vyxal_lists else "[")
        + (" | " if ctx.vyxal_lists else ", ").join(
            map(
                lambda x: vy_repr(x, ctx),
                list(lhs) or [],
            )
        )
        + (" ⟩" if ctx.vyxal_lists else "]"),
    )()


def vy_round(lhs, ctx):
    """Element ṙ
    (num) -> round(a)
    (str) -> quad palindromize with overlap
    (lst) -> vectorised
    """
    ts = vy_type(lhs)
    return {
        NUMBER_TYPE: lambda: round(lhs),
        str: lambda: vertical_mirror(lhs, ctx=ctx)
        + "\n"
        + vertical_mirror(lhs, ctx=ctx)[::-1],
    }.get(ts, vectorise(vy_round, lhs, ctx=ctx))()


def vy_type(item, rhs=None, other=None, simple=False):
    """
    Get the Vyxal-friendly type(s) of 1-3 values.
    If only `item` is given, returns the Vyxal type of `item`.
    If both`item` and `rhs` or all three (`item`, `rhs`, and `other`)
    are given, then it returns a tuple containing their types.

    Returns `list` for lists
    Returns `str` for strings
    Returns `NUMBER_TYPE` if a value is int, complex, float, or sympy
    Returns `LazyList` for `LazyList`s if `simple` is `False`
      (the default) but `list` if `simple` is `True`
    """
    if other is not None:
        return (
            vy_type(item, simple=simple),
            vy_type(rhs, simple=simple),
            vy_type(other, simple=simple),
        )
    elif rhs is not None:
        return (vy_type(item, simple=simple), vy_type(rhs, simple=simple))
    elif (x := type(item)) in (int, complex, float) or is_sympy(item):
        assert x is not float
        return NUMBER_TYPE
    elif simple and isinstance(item, LazyList):
        return list
    else:
        return x


def vy_zip(lhs, rhs, ctx):
    """Element Z
    (any, any) -> zip(a, b)
    (any, fun) -> zip(a,map(b,a)) (Zipmap, map and zip)
    """
    if isinstance(lhs, types.FunctionType):
        return vy_zip(
            rhs,
            LazyList(map(lambda x: safe_apply(lhs, x, ctx=ctx), rhs)),
            ctx=ctx,
        )
    elif isinstance(rhs, types.FunctionType):
        return vy_zip(
            lhs,
            LazyList(map(lambda x: safe_apply(rhs, x, ctx=ctx), lhs)),
            ctx=ctx,
        )
    else:

        @lazylist
        def f():
            left = iter(iterable(lhs))
            right = iter(iterable(rhs))
            while True:
                exhausted = 0
                try:
                    left_item = next(left)
                except StopIteration:
                    left_item = 0
                    exhausted += 1

                try:
                    right_item = next(right)
                except StopIteration:
                    right_item = 0
                    exhausted += 1
                if exhausted == 2:
                    break
                else:
                    yield [left_item, right_item]

        return f()


def wrap(lhs, rhs, ctx):
    """Element ẇ
    (any, num) -> a wrapped in chunks of length b
    (any, fun) -> Apply b to every second item of a
    (fun, any) -> Apply a to every second item of b
    (str, str) -> split a on first occurance of b
    """
    # Because textwrap.wrap doesn't consistently play nice with spaces
    ts = vy_type(lhs, rhs)
    if types.FunctionType in ts:
        function, vector = (
            (lhs, rhs) if ts[0] is types.FunctionType else (rhs, lhs)
        )
        return LazyList(
            safe_apply(function, vector[i], ctx=ctx) if i % 2 else vector[i]
            for i in range(len(vector))
        )

    else:
        if ts == (str, str):
            return list(lhs.partition(rhs)[::2])

        else:
            vector, chunk_size = (
                (iterable(lhs, ctx=ctx), rhs)
                if ts[1] == NUMBER_TYPE or all(isinstance(x, int) for x in rhs)
                else (iterable(rhs, ctx=ctx), lhs)
            )
            if vy_type(rhs, simple=True) is list:

                @LazyList
                def gen():
                    slice_start = 0
                    for pos in rhs:
                        yield index(
                            iterable(lhs, ctx=ctx),
                            [slice_start, slice_start + pos],
                            ctx,
                        )
                        slice_start += pos

                return gen()

            ret, temp = [], []

            for item in vector:
                temp.append(item)
                if len(temp) == chunk_size:
                    if all(type(x) is str for x in temp):
                        ret.append("".join(temp))
                    else:
                        ret.append(temp[::])
                    temp = []

            if len(temp) < chunk_size and temp:
                if all(type(x) is str for x in temp):
                    ret.append("".join(temp))
                else:
                    ret.append(temp[::])
            return ret


def zero_matrix(lhs, ctx):
    """Element Þm
    Return a matrix with dimensions each item of a, where the first is the
    innermost and the last is the outermost
    """
    mat = []
    temp = 0
    for ind in iterable(lhs, ctx=ctx):
        mat = []
        for _ in range(ind):
            mat.append(temp)
        temp = deep_copy(mat)

    return mat


def zero_slice(lhs, rhs, ctx):
    """Element Ẏ
    (any, num) -> a[0:b]
    (num, any) -> b[0:a]
    (str, str) -> regex.findall(pattern=a,string=b) (Find all matches for a regex)
    """
    ts = vy_type(lhs, rhs)
    return {
        (ts[0], NUMBER_TYPE): lambda: index(
            iterable(lhs, ctx=ctx), [0, rhs], ctx=ctx
        ),
        (NUMBER_TYPE, ts[1]): lambda: index(
            iterable(rhs, ctx=ctx), [0, lhs], ctx=ctx
        ),
        (str, str): lambda: re.findall(lhs, rhs),
    }.get(ts, lambda: vectorise(zero_slice, lhs, rhs, ctx=ctx))()


def zfiller(lhs, rhs, ctx):
    """Element ∆Z
    zfill to rhs
    """
    ts = vy_type(lhs, rhs)
    return {
        (NUMBER_TYPE, str): lambda: rhs.zfill(lhs),
        (str, NUMBER_TYPE): lambda: lhs.zfill(rhs),
        (NUMBER_TYPE, list): lambda: [0 for i in range(max(0, lhs - len(rhs)))]
        + rhs,
        (list, NUMBER_TYPE): lambda: [0 for i in range(max(0, rhs - len(lhs)))]
        + lhs,
        (str, str): lambda: lhs.zfill(len(rhs)),
    }.get(ts, lambda: vectorise(zfiller, lhs, rhs, ctx=ctx))()


elements: dict[str, tuple[str, int]] = {
    "¬": process_element("sympy.nsimplify(int(not lhs))", 1),
    "∧": process_element("lhs and rhs", 2),
    "⟑": process_element("rhs and lhs", 2),
    "∨": process_element("lhs or rhs", 2),
    "⟇": process_element(remove_at_index, 2),
    "÷": (
        "lhs = pop(stack, 1, ctx); stack += iterable(lhs, ctx=ctx)",
        1,
    ),
    "×": process_element("'*'", 0),
    "•": process_element(log_mold_multi, 2),
    "†": (
        "top = function_call(stack, ctx)\n"
        + "if top is not None: stack.append(top)",
        1,
    ),
    "€": process_element(split_on, 2),
    "½": process_element(halve, 1),
    "↔": process_element(combinations_with_replacement, 2),
    "¢": process_element(infinite_replace, 3),
    "⌐": process_element(complement, 1),
    "æ": process_element(is_prime, 1),
    "ʀ": process_element(inclusive_zero_range, 1),
    "ʁ": process_element(exclusive_zero_range, 1),
    "ɾ": process_element(inclusive_one_range, 1),
    "ɽ": process_element(exclusive_one_range, 1),
    "ƈ": process_element(n_choose_r, 2),
    "∞": process_element(palindromise, 1),
    "!": process_element("len(stack)", 0),
    '"': process_element("[lhs, rhs]", 2),
    "$": (
        "rhs, lhs = pop(stack, 2, ctx); stack.append(rhs); "
        "stack.append(lhs)",
        2,
    ),
    "%": process_element(modulo, 2),
    "*": process_element(multiply, 2),
    "+": process_element(add, 2),
    ",": ("top = pop(stack, 1, ctx); vy_print(top, ctx=ctx)", 1),
    "-": process_element(subtract, 2),
    "/": process_element(divide, 2),
    ":": (
        "top = pop(stack, 1, ctx); stack.append(deep_copy(top)); "
        "stack.append(top)",
        1,
    ),
    "<": process_element(less_than, 2),
    "=": process_element(equals, 2),
    ">": process_element(greater_than, 2),
    "?": (
        "ctx.use_top_input = True; lhs = get_input(ctx); "
        "ctx.use_top_input = False; stack.append(lhs)",
        0,
    ),
    "A": process_element(all_true, 1),
    "B": process_element("vy_int(lhs, 2)", 1),
    "C": process_element(chr_ord, 1),
    "D": (
        "top = pop(stack, 1, ctx); stack.append(top);"
        "stack.append(deep_copy(top)); stack.append(deep_copy(top));",
        1,
    ),
    "E": process_element(exp2_or_eval, 1),
    "F": process_element(vy_filter, 2),
    "G": process_element(monadic_maximum, 1),
    "H": process_element(vy_hex, 1),
    "I": process_element(into_two, 1),
    "J": process_element(merge, 2),
    "K": process_element(divisors, 1),
    "L": process_element(length, 1),
    "M": process_element(vy_map, 2),
    "N": process_element(negate, 1),
    "O": process_element(count_item, 2),
    "P": process_element(strip, 2),
    "Q": process_element("exit()", 0),
    "R": (
        "if len(stack) > 1 and types.FunctionType "
        "in vy_type(stack[-1], stack[-2]):\n"
        "    rhs, lhs = pop(stack, 2, ctx);"
        "    stack.append(vy_reduce(lhs, rhs, ctx))\n"
        "else:\n"
        "    stack.append(vectorise(reverse, pop(stack, 1, ctx), ctx=ctx))",
        2,
    ),
    "S": process_element(vy_str, 1),
    "T": process_element(truthy_indices, 1),
    "U": process_element(uniquify, 1),
    "V": process_element(replace, 3),
    "W": (
        "temp = list(deep_copy(stack))\n"
        "pop(stack, len(stack), ctx)\n"
        "stack.append(temp); print(stack)",
        0,
    ),
    # X doesn't need to be implemented here, because it's already a structure
    "Y": process_element(interleave, 2),
    "Z": process_element(vy_zip, 2),
    "^": ("stack += wrapify(stack, len(stack), ctx)", 0),
    "_": ("pop(stack, 1, ctx)", 1),
    "a": process_element(any_true, 1),
    "b": process_element(vy_bin, 1),
    "c": process_element(contains, 2),
    "d": process_element("multiply(lhs, 2, ctx)", 1),
    "e": process_element(exponent, 2),
    "f": process_element(deep_flatten, 1),
    "g": process_element(monadic_minimum, 1),
    "h": process_element(head, 1),
    "i": process_element(index, 2),
    "j": process_element(join, 2),
    "l": process_element(overlapping_groups, 2),
    "m": process_element(mirror, 1),
    "n": process_element("ctx.context_values[-1]", 0),
    "o": process_element(remove, 2),
    "p": process_element(prepend, 2),
    "q": process_element(quotify, 1),
    "r": process_element(orderless_range, 2),
    "s": process_element(vy_sort, 1),
    "t": process_element(tail, 1),
    "u": process_element("-1", 0),
    "w": process_element("[lhs]", 1),
    "x": process_element("", 2),
    "y": ("stack += uninterleave(pop(stack, 1, ctx), ctx)", 1),
    "z": process_element("vy_zip(lhs, deep_copy(lhs), ctx)", 1),
    "↑": process_element(max_by_tail, 1),
    "↓": process_element(min_by_tail, 1),
    "∴": process_element(dyadic_maximum, 2),
    "∵": process_element(dyadic_minimum, 2),
    "∷": process_element(parity, 1),
    "¤": process_element("''", 0),
    "ð": process_element("' '", 0),
    "β": process_element(from_base, 2),
    "τ": process_element(to_base, 2),
    "›": process_element(increment, 1),
    "‹": process_element(decrement, 1),
    "ȧ": process_element(vy_abs, 1),
    "ḃ": process_element(boolify, 1),
    "ċ": process_element(is_falsey, 1),
    "ḋ": process_element(vy_divmod, 2),
    "ė": process_element(vy_enumerate, 1),
    "ḟ": process_element(find, 2),
    "ġ": (
        "top = pop(stack, 1, ctx)\n"
        "if vy_type(top, simple=True) is list:\n"
        "    stack.append(vy_gcd(top, ctx=ctx))\n"
        "else:\n"
        "    stack.append(vy_gcd(pop(stack, 1, ctx), top, ctx))\n",
        2,
    ),
    "ḣ": (
        "top = iterable(pop(stack, 1, ctx), ctx=ctx);"
        " stack.append(head(top, ctx));"
        " stack.append(top[1:])",
        1,
    ),
    "ḭ": process_element(integer_divide, 2),
    "ŀ": process_element(ljust, 3),
    "ṁ": process_element(mean, 1),
    "ṅ": process_element(first_integer, 1),
    "ȯ": process_element(slice_from, 2),
    "ṗ": process_element(powerset, 1),
    "ṙ": process_element(vy_round, 1),
    "ṡ": process_element(sort_by, 2),
    "ṫ": (
        "top = iterable(pop(stack, 1, ctx), ctx=ctx);"
        " stack.append(index(top, [None, -1], ctx));"
        " stack.append(tail(top, ctx))",
        1,
    ),
    "ẇ": process_element(wrap, 2),
    "ẋ": process_element(repeat, 2),
    "ẏ": process_element("LazyList(range(0, len(iterable(lhs, ctx))))", 1),
    "ż": process_element("LazyList(range(1, len(iterable(lhs, ctx)) + 1))", 1),
    "√": process_element(square_root, 1),
    "₀": process_element("10", 0),
    "₁": process_element("100", 0),
    "₂": process_element(is_even, 1),
    "₃": process_element(is_divisible_by_three, 1),
    "₄": process_element("26", 0),
    "₅": (
        "top = pop(stack, 1, ctx); stack += is_divisible_by_five(top, ctx)",
        1,
    ),
    "₆": process_element("64", 0),
    "₇": process_element("128", 0),
    "₈": process_element("256", 0),
    "¶": process_element("'\\n'", 0),
    "⁋": process_element(join_newlines, 1),
    "§": process_element(vertical_join, 1),
    "ε": process_element(absolute_difference, 2),
    "¡": process_element(factorial, 1),
    "∑": process_element(vy_sum, 1),
    "¦": process_element(cumulative_sum, 1),
    "≈": process_element(all_equal, 1),
    "Ȧ": process_element(assign_iterable, 3),
    "Ḃ": (
        "top = pop(stack, 1, ctx); stack.append(deep_copy(top)); "
        "stack.append(reverse(top, ctx))",
        1,
    ),
    "Ċ": process_element(counts, 1),
    "Ḋ": (
        "rhs, lhs = pop(stack, 2, ctx); stack += is_divisible(lhs, rhs, ctx)",
        2,
    ),
    "Ė": (
        "stack += vy_exec(pop(stack, 1, ctx), ctx)",
        1,
    ),
    "Ḟ": process_element(gen_from_fn, 2),
    "Ġ": process_element(group_consecutive, 1),
    "Ḣ": process_element(head_remove, 1),
    "İ": process_element(index_indices_or_cycle, 2),
    "Ŀ": process_element(transliterate, 3),
    "Ṁ": process_element(insert_or_map_nth, 3),
    "Ṅ": process_element(integer_parts_or_join_spaces, 1),
    "Ȯ": (
        "if len(stack) > 1: stack.append(index(stack, -2, ctx))\n"
        "else: stack.append(get_input(ctx))",
        0,
    ),
    "Ṗ": process_element(permutations, 1),
    "Ṙ": process_element(reverse, 1),
    "Ṡ": process_element(vectorised_sum, 1),
    "Ṫ": process_element(tail_remove, 1),
    "Ẇ": process_element(split_keep, 2),
    "Ẋ": process_element(cartesian_product, 2),
    "Ẏ": process_element(zero_slice, 2),
    "Ż": process_element(one_slice, 2),
    "⁰": process_element("ctx.inputs[0][0][-1]", 0),
    "¹": process_element("ctx.inputs[0][0][-2]", 0),
    "²": process_element(square, 1),
    "∇": (
        "third, second, first = pop(stack, 3, ctx); "
        "stack.append(third); stack.append(first); "
        "stack.append(second)",
        3,
    ),
    "⌈": process_element(vy_ceil, 1),
    "⌊": process_element(vy_floor, 1),
    "¯": process_element(deltas, 1),
    "±": process_element(sign_of, 1),
    "₴": ("top = pop(stack, 1, ctx); vy_print(top, end='', ctx=ctx)", 1),
    "…": (
        "top = pop(stack, 1, ctx); "
        "vy_print(top, end='\\n', ctx=ctx); stack.append(top)",
        1,
    ),
    "□": (
        "if ctx.inputs[0]: stack.append(ctx.inputs[0][0])\n"
        "else:\n"
        "    input_list, temp = [], input()\n"
        "    while temp:\n"
        "        input_list.append(vy_eval(temp))\n"
        "        temp = input()",
        0,
    ),
    "↳": process_element(right_bit_shift, 2),
    "↲": process_element(left_bit_shift, 2),
    "⋏": process_element(bitwise_and, 2),
    "⋎": process_element(bitwise_or, 2),
    "꘍": process_element(bitwise_xor, 2),
    "ꜝ": process_element(bitwise_not, 1),
    "℅": process_element(random_choice, 1),
    "≤": process_element(less_than_or_equal, 2),
    "≥": process_element(greater_than_or_equal, 2),
    "≠": process_element(not_equals, 2),
    "⁼": process_element(non_vectorising_equals, 2),
    "∪": process_element(union, 2),
    "∩": process_element(transpose, 1),
    "⊍": process_element(symmetric_difference, 2),
    "£": ("ctx.register = pop(stack, 1, ctx)", 1),
    "¥": process_element("ctx.register", 0),
    "⇧": process_element(grade_up, 1),
    "⇩": process_element(grade_down, 1),
    "Ǎ": process_element(remove_non_alphabets, 1),
    "ǎ": process_element(substrings, 1),
    "Ǐ": process_element(prime_factorisation, 1),
    "ǐ": process_element(prime_factors, 1),
    "Ǒ": process_element(multiplicity, 2),
    "ǒ": process_element(modulo_3, 1),
    "Ǔ": (
        "rhs = pop(stack, 1, ctx)\n"
        + "if vy_type(rhs) == NUMBER_TYPE: \n"
        + "    lhs = pop(stack, 1, ctx)\n"
        + "    stack.append(merge(index(lhs, [rhs, None, None], ctx), "
        + "index(lhs, [None, rhs, None], ctx), ctx))\n"
        + "else:\n"
        + "    stack.append(merge(index(rhs, [1, None, None], ctx), "
        + "index(rhs, 0, ctx), ctx))\n",
        2,
    ),
    "ǔ": (
        "rhs = pop(stack, 1, ctx)\n"
        + "if vy_type(rhs) == NUMBER_TYPE: \n"
        + "    lhs = pop(stack, 1, ctx)\n"
        + "    stack.append(merge(index(lhs, [-rhs, None, None], ctx), "
        + "index(lhs, [None, -rhs, None], ctx), ctx))\n"
        + "else:\n"
        + "    stack.append(merge(index(rhs, -1, ctx), "
        + "index(rhs, [None, -1, None], ctx), ctx))\n",
        2,
    ),
    "↵": process_element(newline_split, 1),
    "¼": process_element("ctx.global_array.pop()", 0),
    "⅛": ("lhs = pop(stack,1,ctx); ctx.global_array.append(lhs)", 1),
    "¾": process_element("list(deep_copy(ctx.global_array))", 0),
    "Π": process_element(product, 1),
    "„": (
        "temp = wrapify(stack, len(stack), ctx)[::-1]; "
        "stack += temp[1:] + [temp[0]]",
        0,
    ),
    "‟": (
        "temp = wrapify(stack, len(stack), ctx)[::-1]; "
        "stack += [temp[-1]] + temp[:-1]",
        0,
    ),
    "∆²": process_element(is_square, 1),
    "∆c": process_element(cosine, 1),
    "∆C": process_element(arccos, 1),
    "∆s": process_element(sine, 1),
    "∆S": process_element(arcsin, 1),
    "∆t": process_element(tangent, 1),
    "∆T": process_element(arctan, 1),
    "∆q": process_element(quadratic_solver, 2),
    "∆Q": process_element(general_quadratic_solver, 2),
    "∆P": process_element(polynomial_roots, 1),
    "∆ƈ": process_element(n_pick_r, 2),
    "∆i": process_element(nth_pi, 1),
    "∆ė": process_element(nth_e, 1),
    "∆I": process_element("pi_digits(lhs)", 1),
    "∆Ė": process_element(e_digits, 1),
    "∆f": process_element("sympy.fibonacci(lhs + 1)", 1),
    "∆±": process_element(copy_sign, 2),
    "∆K": process_element(divisor_sum, 1),
    "∆e": process_element(expe, 1),
    "∆E": process_element(expe_minus_1, 1),
    "∆L": process_element(natural_log, 1),
    "∆l": process_element(log_2, 1),
    "∆τ": process_element(log_10, 1),
    "∆d": process_element(euclidean_distance, 2),
    "∆D": process_element(to_degrees, 1),
    "∆R": process_element(to_radians, 1),
    "∆Ṗ": process_element(next_prime, 1),
    "∆ṗ": process_element(prev_prime, 1),
    "∆p": process_element(nearest_prime, 1),
    "∆ṙ": process_element(polynomial_from_roots, 1),
    "∆W": process_element(round_to, 2),
    "∆Ŀ": (
        "top = pop(stack, 1, ctx)\n"
        "if vy_type(top, simple=True) is list:\n"
        "    stack.append(lowest_common_multiple(top, ctx=ctx))\n"
        "else:\n"
        "    stack.append(lowest_common_multiple(pop(stack, 1, ctx), top, ctx))\n",
        2,
    ),
    "∆Z": process_element(zfiller, 2),
    "∆ċ": process_element(nth_cardinal, 1),
    "∆o": process_element(nth_ordinal, 1),
    "∆M": process_element(mode, 1),
    "∆ṁ": process_element(median, 1),
    "∆ṫ": process_element(totient, 1),
    "∆Ċ": process_element(polynomial_expr_from_coeffs, 1),
    "∆¢": process_element(carmichael_function, 1),
    "øḂ": process_element(angle_bracketify, 1),
    "øḃ": process_element(curly_bracketify, 1),
    "øb": process_element(parenthesise, 1),
    "øB": process_element(bracketify, 1),
    "øβ": process_element(brackets_balanced, 1),
    "øc": process_element(base_255_string_compress, 1),
    "øC": process_element(base_255_number_compress, 1),
    "øĊ": process_element(center, 1),
    "ød": process_element(run_length_decoding, 1),
    "øD": process_element(optimal_compress, 1),
    "øḋ": process_element("str(eval(sympy.pycode(lhs)))", 1),
    "øe": process_element(run_length_encoding, 1),
    "ø↲": process_element(custom_pad_left, 3),
    "ø↳": process_element(custom_pad_right, 3),
    "øM": process_element(flip_brackets_vertical_palindromise, 1),
    "øṁ": process_element(vertical_mirror, 1),
    "øṀ": process_element(flip_brackets_vertical_mirror, 1),
    "øW": process_element(group_on_words, 1),
    "øP": process_element(pluralise_count, 2),
    "øp": process_element(starts_with, 2),
    "øṖ": process_element(all_partitions, 1),
    "øo": process_element(remove_until_no_change, 2),
    "øV": process_element(replace_until_no_change, 3),
    "øF": process_element(factorial_of_range, 1),
    "øṙ": process_element(regex_sub, 3),
    "øṘ": process_element(roman_numeral, 1),
    "Þ*": process_element(cartesian_over_list, 1),
    "Þo": process_element(infinite_ordinals, 0),
    "Þc": process_element(infinite_cardinals, 0),
    "Þp": process_element(infinite_primes, 0),
    "Þx": process_element(all_combos, 1),
    "Þ×": process_element(all_combos_with_replacement, 1),
    "Þu": process_element(all_unique, 1),
    "ÞẊ": process_element(cartesian_power, 2),
    "ÞB": process_element(rand_bits, 1),
    "ÞU": process_element(uniquify_mask, 1),
    "Þf": (
        "rhs = pop(stack, 1, ctx)\n"
        "if vy_type(rhs) != NUMBER_TYPE:\n"
        "    stack.append(flatten_by(rhs, 1, ctx))\n"
        "else:\n"
        "    stack.append(flatten_by(pop(stack, 1, ctx), rhs, ctx))\n",
        2,
    ),
    "Þǔ": process_element(untruth, 1),
    "Þi": process_element(multi_dimensional_index, 2),
    "Þḟ": process_element(multi_dimensional_search, 2),
    "Þm": process_element(zero_matrix, 1),
    "Þ…": process_element(evenly_distribute, 2),
    "Þ<": process_element(all_less_than_increasing, 2),
    "ÞD": process_element(all_diagonals, 1),
    "ÞS": process_element(sublists, 1),
    "ÞṪ": process_element(transpose, 2),
    "ÞṀ": process_element(matrix_multiply, 2),
    "Þ•": process_element(dot_product, 2),
    "ÞḊ": process_element(matrix_determinant, 1),
    "Þ\\": process_element(anti_diagonal, 1),
    "Þ/": process_element(diagonal, 1),
    "Þ↓": process_element(min_by_function, 2),
    "Þ↑": process_element(max_by_function, 2),
    "ÞZ": process_element(coords_deepmap, 2),
    "ÞF": process_element(fibonaacis, 0),
    "Þ!": process_element(factorials, 0),
    "Þ℅": process_element(shuffle, 1),
    "ÞC": process_element(foldl_columns, 2),
    "ÞR": process_element(foldl_rows, 2),
    "Þṁ": process_element(mold_special, 2),
    "ÞM": process_element(maximal_indices, 1),
    "Þ∞": process_element(infinite_positives, 0),
    "Þ∴": process_element(element_wise_dyadic_maximum, 2),
    "Þ∵": process_element(element_wise_dyadic_minimum, 2),
    "Þs": process_element(all_slices, 2),
    "Þ¾": ("ctx.global_array = []", 0),
    "Þr": process_element(sans_last_prepend_zero, 1),
    "ÞR": process_element(cumul_sum_sans_last_prepend_zero, 1),
    "Þẇ": (
        "res = unwrap(pop(stack, 1, ctx), ctx); "
        "stack.append(res[0]); stack.append(res[1])",
        1,
    ),
    "¨□": process_element(parse_direction_arrow_to_integer, 1),
    "¨^": process_element(parse_direction_arrow_to_vector, 1),
    "¨,": ("top = pop(stack, 1, ctx); vy_print(top, end=' ', ctx=ctx)", 1),
    "¨…": (
        "top = pop(stack, 1, ctx); vy_print(top, end=' ', ctx); "
        "stack.append(top)",
        1,
    ),
    "¨M": process_element(apply_at, 3),
    "¨U": ("if ctx.online: stack.append(request(pop(stack, 1, ctx), ctx))", 1),
    "¨>": process_element(strict_greater_than, 2),
    "¨<": process_element(strict_less_than, 2),
    "¨ẇ": ("stack.append(wrapify(stack, pop(stack, 1, ctx), ctx)[::-1])", 1),
    "kA": process_element('"ABCDEFGHIJKLMNOPQRSTUVWXYZ"', 0),
    "ke": process_element("sympy.E", 0),
    "kf": process_element('"Fizz"', 0),
    "kb": process_element('"Buzz"', 0),
    "kF": process_element('"FizzBuzz"', 0),
    "kH": process_element('"Hello, World!"', 0),
    "kh": process_element('"Hello World"', 0),
    "k1": process_element("1000", 0),
    "k2": process_element("10000", 0),
    "k3": process_element("100000", 0),
    "k4": process_element("1000000", 0),
    "ka": process_element('"abcdefghijklmnopqrstuvwxyz"', 0),
    "kL": process_element(
        '"abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"', 0
    ),
    "kd": process_element('"0123456789"', 0),
    "k6": process_element('"0123456789abcdef"', 0),
    "k^": process_element('"0123456789ABCDEF"', 0),
    "ko": process_element('"01234567"', 0),
    "kp": process_element("string.punctuation", 0),
    "kP": process_element(
        '"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ'
        '!\\"#$%&\\\'()*+,-./:;<=>?@[\\\\]^_`{|}~"',
        0,
    ),
    "kw": process_element('" \\t\\n\\r\\u000b\\u000c"', 0),
    "kr": process_element(
        '"0123456789abcdefghijklmnopqrstuvwxyzABCDEFGHIJKLMNOPQRSTUVWXYZ"', 0
    ),
    "kB": process_element(
        '"ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz"', 0
    ),
    "kZ": process_element('"ZYXWVUTSRQPONMLKJIHGFEDCBA"', 0),
    "kz": process_element(' "zyxwvutsrqponmlkjihgfedcba"', 0),
    "kl": process_element(
        '"ZYXWVUTSRQPONMLKJIHGFEDCBAzyxwvutsrqponmlkjihgfedcba"', 0
    ),
    "ki": process_element("sympy.pi", 0),
    "kn": process_element("math.nan", 0),
    "kg": process_element("sympy.nsimplify('1/2 + sqrt(5)/2')", 0),
    "kD": process_element('datetime.now().strftime("%Y-%m-%d")', 0),
    "kN": process_element(
        'LazyList(eval(datetime.now().strftime("[%H,%M,%S]")))', 0
    ),
    "kḋ": process_element('datetime.now().strftime("%d/%m/%Y")', 0),
    "kḊ": process_element('datetime.now().strftime("%m/%d/%Y")', 0),
    "kð": process_element(
        'LazyList(eval(datetime.now().strftime("[%d,%m,%Y]")))', 0
    ),
    "kβ": process_element('"{}[]<>()"', 0),
    "kḂ": process_element('"()[]{}"', 0),
    "kḃ": process_element("'([{'", 0),
    "kß": process_element('"()[]"', 0),
    "k≤": process_element('"([{<"', 0),
    "k≥": process_element('")]}"', 0),
    "kΠ": process_element('")]}>"', 0),
    "kv": process_element('"aeiou"', 0),
    "kV": process_element('"AEIOU"', 0),
    "k∨": process_element('"aeiouAEIOU"', 0),
    "k⟇": process_element("vyxal.encoding.codepage", 0),
    "k½": process_element("LazyList([1,2])", 0),
    "kḭ": process_element("2 ** 32", 0),
    "k₁": process_element("LazyList([1, 1])", 0),
    "k+": process_element("LazyList([1, -1])", 0),
    "k-": process_element("LazyList([-1, 1])", 0),
    "k≈": process_element("LazyList([0, 1])", 0),
    "k/": process_element('"/\\\\"', 0),
    "kR": process_element("360", 0),
    "kW": process_element('"https://"', 0),
    "k℅": process_element('"http://"', 0),
    "k↳": process_element('"https://www."', 0),
    "k²": process_element('"http://www."', 0),
    "k¶": process_element("512", 0),
    "k⁋": process_element("1024", 0),
    "k¦": process_element("2048", 0),
    "kṄ": process_element("4096", 0),
    "kṅ": process_element("8192", 0),
    "k¡": process_element("2 ** 14", 0),
    "kε": process_element("2 ** 15", 0),
    "k₴": process_element("2 ** 16", 0),
    "k×": process_element("2 ** 31", 0),
    "k⁰": process_element('"bcdfghjklmnpqrstvwxyz"', 0),
    "k¹": process_element('"bcdfghjklmnpqrstvwxz"', 0),
    "kT": process_element('"[]<>-+.,"', 0),
    "kṗ": process_element('LazyList(["()","[]","{}","<>"])', 0),
    "kṖ": process_element('"([{<>}])"', 0),
    "kS": process_element('"ඞ"', 0),
    "k₂": process_element("2 ** 20", 0),
    "k₃": process_element("2 ** 30", 0),
    "k∪": process_element('"aeiouy"', 0),
    "k⊍": process_element('"AEIOUY"', 0),
    "k∩": process_element('"aeiouyAEIOUY"', 0),
    "k□": process_element("[[0,1],[1,0],[0,-1],[-1,0]]", 0),
    "kṘ": process_element('"IVXLCDM"', 0),
}
modifiers: dict[str, str] = {
    "&": (
        "stack.append(ctx.register)\n"
        "ctx.register = safe_apply(function_A, "
        "pop(stack, function_A.arity, ctx), ctx=ctx)\n"
    ),
    "v": (
        "arguments = wrapify(stack, function_A.arity, ctx=ctx)\n"
        "stack.append"
        "(vectorise(function_A, *(arguments[::-1]), explicit=True, ctx=ctx))"
        "\n"
    ),
    "~": (
        "ctx.retain_popped = True\n"
        "arguments = wrapify(stack, function_A.arity, ctx=ctx)\n"
        "ctx.retain_popped = False\n"
        "stack.append(safe_apply(function_A, *(arguments[::-1]), ctx=ctx))\n"
    ),
    "₌": (
        "stack_copy = list(deep_copy(stack))\n"
        "arguments_A = wrapify(stack_copy, function_A.arity, ctx=ctx)\n"
        "arguments_B = wrapify(stack, function_B.arity, ctx=ctx)\n"
        "stack.append(safe_apply(function_A, *(arguments_A[::-1]), ctx=ctx))\n"
        "stack.append(safe_apply(function_B, *(arguments_B[::-1]), ctx=ctx))\n"
    ),
    "₍": (
        "stack_copy = list(deep_copy(stack))\n"
        "arguments_A = wrapify(stack_copy, function_A.arity, ctx=ctx)\n"
        "arguments_B = wrapify(stack, function_B.arity, ctx=ctx)\n"
        "res_A = safe_apply(function_A, *(arguments_A[::-1]), ctx=ctx)\n"
        "res_B = safe_apply(function_B, *(arguments_B[::-1]), ctx=ctx)\n"
        "stack.append([res_A, res_B])\n"
    ),
    "ƒ": (
        "function_A.stored_arity = 2\n"
        "stack.append(vy_reduce(function_A, pop(stack, 1, ctx), ctx))"
    ),
    "ɖ": (
        "function_A.stored_arity = 2\n"
        "stack.append(scanl(function_A, pop(stack, 1, ctx), ctx))"
    ),
    "ß": (
        "if boolify(pop(stack, 1, ctx), ctx):\n"
        "    stack.append(function_A)\n"
        "    function_call(stack, ctx)"
    ),
}