発見者 一点基底 S K 他
  \x.xSK X(X(X(XX))) X(X(XX)) I = XX, iotaで使われている
John Barkley Rosser \x.xKSK X(XX) XXX  
Corrado Bohm \x.x(fS(KI))K X(XX) XX  
Henk Barendregt \x.x(fS(KK))K X(XXX) XXX  
Jeroen Fokker \f.fS(\xyz.x) X(XX) XX  
Carew Meredith \abcd.cd(a(Kd)) V(XXX(XX)(XXXX(XXXX(VV))(K(XXXX)))) XXXX(XXXX(XXX(XX))(XX))(XX) V = XXXX(K(XXXX))とする

let’s 簡約

iotaのものを簡約する

# XX = I
XX a
    = (\x.xSK) (\y.ySK) a
    = ((\y.ySK) SK) a
    = ((S SK) K) a
    = ((SK) (KK)) a
    = SK (KK) a
    = (Ka) (KKa)
    = a
    = I a

# X(X(XX)) = K
X(X(XX))
    = X(XI)
    = (\x.xSK) ((\y.ySK) I)
    = (\x.xSK) (I SK)
    = (\x.xSK) (SK)
    = (SK SK)
    = ((KK) (SK))
    = K

# X(X(X(XX))) = S
X(X(X(XX)))
    = XK
    = (\x.xSK) K
    = KSK
    = S

参考