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Combinatory logic


 

:This article is about a topic in mathematical logic and theoretical computer science, and is not to be confused with combinatorial logic, a topic in electronics.

(C (B N (S I I)) Ω Z I)

◄ Combinatory logic: (C (C (B N (S I I)) Ω) I Z) (definition of Z)
Combinatory logic: (B N (S I I) Z Ω I) ►

~ Table of Content ~

►Introduction
►Combinatory logic in mathematics
►Combinatory logic in computing
►Summary of the lambda calculus
►Combinatory calculi
►:T] (by 5)
►(S λx.E1 λx.E2 a)
►((S λx.E1 λx.E2) a)
►...
►(S (K (S I)) T)
►(S (K (S I)) K) (by η-reduction)
►(K (S I) x (K x) y)
►(S I (K x) y)
►(I y (K x y))
►(y (K x y))
►(y x)
►T]
►T x)] (by rule 7)
►T
►(C I) (η-reduction)
►C*(traditional canonical notation : X* X I)
►I'(traditional canonical notation: X' C X)
►(I y x)
►(I (S I I) (I (S I I)))
►(S I I (I (S I I)))
►(S I I (S I I))
►(I Z (I Z))
►(Z (I Z))
►(Z Z)
►(C (C (B N (S I I)) Ω) I Z) (definition of Z)
►(C (B N (S I I)) Ω Z I)
►(B N (S I I) Z Ω I)
►(N (S I I Z) Ω I)
►(K Ω I) (definition of N)
►Ω
►(K I Ω I) (definition of N)
►(I I)

 

 

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