Functions

Functions operate on data, which can either be an argument or the result of another function.

Single Byte Nilads

Character	Function
®	Retrieve the value from the register
³	First input (third command line argument) or 100
⁴	Second input (fourth command line argument) or 16
⁵	Third input (fifth command line argument) or 10
⁶	Fourth input (sixth command line argument) or " "
⁷	Fifth input (seventh command line argument) or "\n"
⁸	Sixth input (eighth command line argument) or []
⁹	Seventh input (ninth command line argument) or 256
⍺	Left Argument or 0.1
⍵	Right Argument or 1 (TODO)
π	Pi

Single Byte Monads

Character	Function
~	Bitwise NOT
√	Square Root
‘	Decrement
’	Increment
¹	Identity
²	Square
!	Factorial(z) if z is a nonnegative integer, -Factorial(abs(z)) if z is a negative integer, Gamma(z + 1) otherwise
A	Absolute Value
B	Convert integer to binary
Ḅ	Convert binary to integer
D	Convert integer to decimal
Ḋ	List Partitions
Ḍ	Convert decimal to integer
E	1 if all elements are equal, otherwise 0
Ė	Enumerate; returns [[1, z[1]], [2, z[2]], ...]
F	Flatten list completely
G	Format as a grid
H	Convert integer to hexadecimal
Ḣ	Pop and return the first value of a list
Ḥ	Convert hexadecimal to integer
İ	Inverse; 1 / z for integers and upside-down (wherever applicable) for characters
J	Range of length (range(len(z)))
L	Length
Ḷ	Lowered Range; 0 .. z - 1
Ṇ	Logical NOT; does not vectorize
P	Product
Ṗ	Permutations
R	Range; 1 .. z
S	Sum
Ṣ	Sort a list
Ṡ	Sign of a real number or conjugate of a complex number
T	Indices of truthy elements
Ṫ	Pop and return the last value of a list
Ṭ	Return an array of 1 and 0 with 1 at the indices of z
U	Return the unique elements of z in order by their first occurrence
W	Wrap; return [z]
Ẇ	Sublists; return all contiguous subslices of z
X	Random element of a list, random integer in the range 1 .. z if z is an integer, random float from 0 to z if z is a float
Ẏ	Tighten; flatten by 1 level
Z	Integer Partitions; all lists of positive integers that sum to z
∆	Deltas; return differences of consecutive pairs
↔	Reverse each sublist to the last level
↕	Reverse a list; does not vectorize
¬	Logical NOT; vectorizes
↙	Transpose a matrix
↘	Anti-transpose a matrix
↶	Rotate a matrix by 90 degrees
↷	Rotate a matrix by -90 degrees
↻	Rotate a matrix by 180 degrees
⁽	Prefixes
⁾	Suffixes

Single Byte Dyads

Character	Function
_	Subtraction
+	Addition
±	[x + y, x - y]
*	Exponentiation
×	Multiplication
÷	Floating-Point Division
:	Integer Division
%	Modulus
&	Bitwise AND
|	Bitwise OR
^	Bitwise XOR
<	Less-than
≤	Less-than or equal
=	Equals; does not vectorize
e	Equals; vectorizes
≈	Similar; same length if lists, within 1 of each other if numbers
n	Not Equals; vectorizes
≠	Not Equals; does not vectorize
≥	Greater-than or equal
>	Greater-than
»	Maximum
«	Minimum
,	Pair; return [x, y]
;	Concatenate/Append
·	Dot Product
←	Rotate rows left
→	Rotate rows right
↑	Rotate left; does not vectorize
↓	Rotate right; does not vectorize
b	Convert x to base y
ḃ	Convert x to bijective base y
ċ	Combinations of x with y elements
ė	1 if x is an element of y, otherwise 0
ẹ	0 if x is an element of y, otherwise 1
g	GCD
ḣ	Head; get first y elements of x
ḥ	Head; get all but last y elements of x
j	Join x with separator y
l	LCM
m	Modular; get every yth element of x. Append to its reverse if y is 0
ṁ	Mold; shape the contents of x like y. Repeats elements of x if necessary
r	Range [x, y]
ṙ	Range (x, y)
ṛ	Range [x, y)
s	Slice x into lists of length y
ṡ	Return overlapping slices of length y of x
ŝ	Slice x into y lists of similar length
ṣ	Split x at occurrences of y
ṫ	Tail; get all but first y elements of x
ṭ	Tail; get last y elements of x
ẏ	Flatten x by y layers
z	Zip x with filler y
ż	Zip; Interleave x with y
ẓ	Zip x with y

Assorted Nilads (Ø)

Character	Function
ØX	Random float in the range [0, 1)

Assorted Monads (Æ)

Character	Function
ÆC	Count primes up to (including) z
ÆĊ	Count composites up to (including) z
ÆR	Inclusive Prime Range
ÆS	Sine
ÆṢ	Arcsine
ÆT	Tangent
ÆṬ	Arctangent
ÆA	Cosine
ÆẠ	Arccosine
Æs	Sinh
Æṣ	Arcsinh
Æa	Cosh
Æạ	Arccosh
Æt	Tanh
Æṭ	Arctanh
ÆṪ	Totient
ÆU	Remove adjacent equal elements
ÆI	1 if z is an integer else 0
Æṁ	Median
Æṃ	Mode
Æm	Arithmetic Mean
Æ∆	zth triangular number
Æσ	Standard Deviation
Æ√	Integer Square Root

Assorted Monads (Œ)

Character	Function
ŒB	Bounce; yield z[:-1] + z[::-1]. Vectorizes to layer 1
ŒḄ	Bounce; yield z[:-1] + z[::-1]. Does not vectorize
ŒD	Matrix Diagonals. Starts from the small diagonal in the bottom left corner
ŒḊ	Matrix Antidiagonals. Starts from the small diagonal in the bottom right corner
ŒḌ	Reconstruct a matrix from its diagonals; diagonals can be in any rotation but must be in the right order
ŒM	Matrix Diagonals. Starts with the main diagonal
ŒṀ	Matrix Antidiagonals. Starts with the main antidiagonal
Œ_	Yield [] given an argument. Suppresses output
ŒT	Count the number of truthy elements
ŒṖ	Powerset
Œg	Group equal elements
Œr	Run-Length Encode
Œṙ	Run-Length Decode
Œ√	1 if z is a perfect square else 0

Assorted Dyads (æ)

Character	Function
æ←	Cyclic Predecessor of element x in y
æ→	Cyclic Successor of element x in y
æ«	Left Bit-Shift; x * 2 ^ y
æ»	Right Bit-Shift; x * 2 ^ -y; returns an integer
æ√	General Root; x ^ (1 / y)
æx	Random integer in the range [x, y]

Assorted Dyads (œ)

Character	Function
œc	Choose; nCr
œp	Pick; nPr
œ←	Cyclic Predecessor of sublist x in y
œ→	Cyclic Successor of sublist x in y
œx	Random float in the range [x, y)
œḷ	Left Argument; x
œṛ	Right Argument; y