lambda-calculus-with-js/idea0.txt

Using JS' anonymous functions to perform lambda calculus

2λa 0 b 0
3(a 0 b) 0
1a 1b 1c 1d

lambda = sign | func | call
sign = (1x)+ 0
func = 2 sign lambda
call = 3 lambda lambda

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(λa.a b)
3	2	100	100	110
130	120	1110100	1110100	1111100
2 130	2 120	2 a	2 a	2 b
c f a a b

c	λz.λw.(P (z w)) = λz.λw.(z w)
f	λx.(P λa.x) = λx.(λz.λw.(z w) λa.x) = λx.λw.(λa.x w)
a	(P a) = (λx.λw.(λa.x w) a) = λw.(λa.a w)
a	(P a) = (λw.(λa.a w) a) = λa.a
b	(P b) = (λa.a b)

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λa.λb.(a b)
f 1 f 2 c 1 2

f a	λx.(P λa.x) = λx.(λn.n λa.x) = λx.λa.x
f	λy.(P λi.y) = λx.λa.x
f b	λy.(P λb.y) = λy.(λx.λa.x λb.y) = λy.λa.λb.y
c	λz.λw.(P (z w)) = λz.λw.(λy.λa.λb.y (z w)) = λz.λw.λa.λb.(z w)
a	(P a) = (λz.λw.λa.λb.(z w) a) = λw.λa.λb.(a w)
b	(P b) = (λw.λa.λb.(a w) b) = λa.λb.(a b)

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f = λP.λx.(P λa.x)
c = λP.λz.λw.(P (z w))
* = λP.(P *)

a = λs.λr.λn.(s (n r))

Y = λp.(λf.λa.(p (f f)) λf.λa.(p (f f)))

λ .
( )
a

3 0