lambda-interpreter
Lambda calculus parser and interpreter with capture avoiding substitution. Evaluation by repeated beta-reduction of the leftmost, outermost redex with eta-conversion. Application is left associative and abstractions are right associative.
EBNF Grammar:
Term := Variable | "\" . Abstraction | "(" . Application . ")" | "(" . Term . ")"
Variable := < letters, numbers, symbols, etc. and can represent a constant, like "Y" >
Application := Term . " " . Term . {" " . Term}
Abstraction := Variable . "." . Term | Variable . " " . Abstraction
Syntax examples:
-
Y combinator:
(\f.((\x.(f (x x))) (\x.(f (x x))))) -
S combinator:
(\x y z.(x z (y z))) -
K combinator:
(\x y.x) -
I combinator:
(\x.x) -
if:
(\then else bool.(bool then else))
Examples:
- 2^10 with Church numerals
input: println(cnToInt(evalStr("(^ 10 2)")))
output: 1024
- SKK = I
input: println(evalStr("(S K K)"))
output: (\z.z)
- YK* = I
input: println(evalStr("(Y K*)"))
output: (\y.y)
- 4! with Church numerals
input: ((((\x.(\y.(y ((x x) y)))) (\x.(\y.(y ((x x) y))))) (\f.(\n.((((\n.((((\n.(\f.(\x.(((n (\g.(\h.(h (g f))))) (\u.x)) (\u.u))))) n) (\x.(\x.(\y.y)))) (\x.(\y.x)))) n) (\f.(\x.(f x)))) (((\m.(\n.((m ((\m.(\n.((m (\n.(\f.(\x.(f ((n f) x)))))) n))) n)) (\f.(\x.x))))) n) (f ((\n.(\f.(\x.(((n (\g.(\h.(h (g f))))) (\u.x)) (\u.u))))) n))))))) (\f.(\x.(f (f (f (f x)))))))
output: (\f.(\x.(f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f (f x))))))))))))))))))))))))))