B,C,K,W system

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The B, C, K, W system is a variant of combinatory logic that was used by Haskell Curry in his doctoral thesis Grundlagen der kombinatorischen Logik. It uses the combinators B, C, K, and W, whereas the later and more widely known presentations of combinatory logic are based on S and K. The combinators are defined as follows:

• B x y z = x (y z)

• C x y z = x z y

• K x y = x

• W x y = x y y

Intuitively,

• B x y is the function composition x o y
• C x y z swaps the arguments y and z
• K x y ignores the second argument y
• W x y copies the argument y.

[edit] References

• Curry, Haskell B.; Grundlagen der kombinatorischen Logik; Amer. J. Math.; 52:509-536;789-834 (1930)