Combinator calculus


THEOREM   

Let \(Ix = x\), \(Kxy = x\) and \(Sxyz = xz(yz)\). Then \(I = SKK\).

Proof available

THEOREM   

Let \(Kxy = x\), \(Sxyz = xz(yz)\), and \(Bxyz = x(yz)\). Then \(B = S(KS)K\).

Proof available

THEOREM   

Let \(Kxy = x\), \(Sxyz = xz(yz)\), and \(Cxyz = xzy\). Then \(C = S(S(K(S(KS)K))S)(KK)\).

Proof available

THEOREM   

Let \(Kxy = x\), \(Sxyz = xz(yz)\), and \(Wxy = xyy\). Then \(W = SS(SK)\).

Proof available

THEOREM   

Let \(Kxy = x\), \(Wxy = xyy\), and \(Ix = x\). Then \(I = WK\).

Proof available

THEOREM   

Let \(Bxyz = x(yz)\), \(Cxyz = xzy\), and \(Wxy = xyy\). Then \(S = B(B(BW)C)(BB)\).

Proof available

Parent topics