Dadidadida: λ - Negation

Wednesday, September 21, 2005

λ - Negation

Given:

T ≡ λxy.x
F ≡ λxy.y
~ ≡ λx.x(λuv.v)(λab.a)

What is ~T ?

~T = (λx.x(λuv.v)(λab.a))(λcd.c)
(λcd.c)(λuv.v)(λab.a) = TFT
λuv.v = F

Hence ~T = F

Conversely, what is ~F ?

~F = (λx.x(λuv.v)(λab.a))(λcd.d)
(λcd.d)(λuv.v)(λab.a) = FFT
λab.a = T

Hence ~F = T

# posted by rot13(Unafba Pune) @ 12:26 AM

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