a very shitty lambda calculus.

• literally just untyped lambda calculus.
• no named parameters, only de bruijn indices written as multiple dots.
• you can write ints but they're just syntax sugar for church numerals.
• the evaluator is really bad right now and will die on anything recursive. (to be fixed later.)
• basic subtraction can take, like, between seconds and minutes to run.

• lambda: \
• access closest variable: ., second closest: ..
• numerals: 0, 1, 2, ...
• call a with b as an argument: a b
• left associative: a b c is (a b) c
• create a global variable: name: value

so, the identity function $\lambda x. x$ is \..

the church encoding of the number two — $\lambda f. \lambda x. f (f x)$ — is written as \\.. (.. .).

i've implemented a couple of basic definitions:

true: \\..
false: \\.

pair: \\\. ... ..
first: \. true
second: \. false

ident: \.
if: ident

pred: \\\... (\\. (.. ....)) (\..) (\.)
succ: (+ 1)
+: \\\\.... .. (... .. .)
*: \\\\.... (... ..) .
-: \\(. pred) ..
/: \\\\ ((.... \\. ..) \..) ((.... \((.... \\. ..) \(.... (. ..))) \.) .)
exp: \\. ..

&&: \\.. . ..
||: \\.. .. .

is_0: \. (\false) true
<=: \\is_0 (- .. .)
==: \\&& (<= .. .) (<= . ..)

opam switch create .
dune exec lamb