Combinatoly logic

Combinatoly logic

次の二つのλ計算から全ての計算が作られる

(以下鳥名はTo Mock a Mockingbirdより)

S = λx.λy.λz(x z (y z))

K = λx.λy(x) = Const

Identity Bird

I = SKK = λx(x) = id

Bluebird(ルリツグミ)

B = S(KS)K = λx.λy.λz(x (y z)) = (.)

Cardinal(ショウジョウコウカンチョウ(猩々紅冠鳥))

C = S(BBS)(KK)= λx.λy.λz(xzy) = flip

Mockingbird(マネシツグミ)

M = SII = λx(xx)

Lark(ヒバリ)

L = CBM = λx.λy(x(yy))

Why Bird

Y = SLL = λx(x(λx))