Henlang

Name

The name has many meanings. First of all, henlang is short for incomprehensible language. Next, hen stands for japanese 変 which means strange. Finally, hen is an animal also known as chicken, and Chicken Scheme is my favorite Scheme implementation.

Syntax and features

Comments

From % till end of line.

% henlang does not see this line
1+(2)

Operators

Henlang treats several special characters as operators. Unlike functions, they have higher precedence.

• a←b assigns value of b to a. a is unevaled.
• 'a does not eval a. Just like in Scheme.
• a:b returns a cons pair of a and b. Just like (cons a b) in Scheme.
• &f escapes function f so it does not get evaluated. Thus, it can be passed as a capital argument.
• ¤ name [var:val ...] { scope } is just like let in Scheme. The name is optional; if name is passed, it can be used for recursion. If var is a list, return value of val is destructured: ¤ [[a, b]:[1, 2]] {} binds 1 to a and 2 to b. Last expression in scope is returned. If there are no expressions in scope, void is returned.
• λ arg1, arg2... { body } is lambda. There can be no arguments or an empty body.

Functions

Reference

Special values

Expr	Meaning
⊤	True
⊥	False
∅	Empty list

Arithmetics

Expr	Meaning
a+	a as a number.
a-	a negated.
a+(n...)	Sum of a and ns.
a-(n...)	Difference of a and ns.
a/(n...)	a divided by ns.
a*(n...)	a multiplied by ns.
a^(n...)	a to power of ns.
a√	Square root of a.
a√(n)	n root of a.

Comparison

Expr	Meaning
a=(b...)	⊤ if a is equal to b..., ⊥ otherwise.
a<(b...)	⊤ if a is lower than b..., ⊥ otherwise.
a>(b...)	⊤ if a is greater than b..., ⊥ otherwise.
a≤(b...)	⊤ if a is lower than or equal to b..., ⊥ otherwise.
a≥(b...)	⊤ if a is greater than or equal to b..., ⊥ otherwise.

If you suffix any of the functions above with !, they will return ⊥ or the matching arguments instead.

% =! is kinda useless, but there may be some applications for it.
2=(3,1+(1)) % ⊤
2=!(3,1+(1)) % 2
2=(3) % ⊥
2=!(3) % ⊥

% Others are useful for sure.
3>(2,1) % ⊤
3>!(2,1) % 3
1>(2) % ⊥
1>!(2) % ⊥

Also, there are shortcuts for >(0) and <(0):

Expr|Meaning a+?|a>(0) a-?|a<(0)

Set operations

Expr	Meaning
b_	Length of b.
e∈(b) b∋(e)	⊤ if e is in list b.
e∉(b) b∌(e)	⊤ if e is not in list b.
a∧(b)	⊤ if a and b.
a∨(b)	⊤ if a or b.
a∩(b)	Intersection of a and b.
a∪(b)	Union of a and b.
a∖(b)	Difference of a and b.
b∀(p)	⊤ if all elements of b satisfy predicate p.
b∃(p)	⊤ if at least one element of b satisfies p.
bE!(p)	Find all elements of b that satisfy p and return them.

Examples

Find all positive numbers in a list

list←[3-,2-,1-,0,1,2,3]
list∃!(+?)$
% [1,2,3]

Fibonacci

Fibonacci←λn{
  1ι∋n⇒nι;
  n-(1)Fibonacci+(n-(2)Fibonacci)
}

Factorial

Factorial←λn{
  n=(0)⇒1;
  n-(1)Factorial(n)
}