Theory "combin"

Parents     bool

Signature

Constant Type
C :('a -> 'b -> 'c) -> 'b -> 'a -> 'c
I :'a -> 'a
K :'a -> 'b -> 'a
S :('a -> 'b -> 'c) -> ('a -> 'b) -> 'a -> 'c
W :('a -> 'a -> 'b) -> 'a -> 'b
o :('c -> 'b) -> ('a -> 'c) -> 'a -> 'b

Definitions

K_DEF
|- K = (\x y. x)
S_DEF
|- S = (\f g x. f x (g x))
I_DEF
|- I = S K K
C_DEF
|- combin$C = (\f x y. f y x)
W_DEF
|- W = (\f x. f x x)
o_DEF
|- !f g. f o g = (\x. f (g x))


Theorems

o_THM
|- !f g x. (f o g) x = f (g x)
o_ASSOC
|- !f g h. f o g o h = (f o g) o h
K_THM
|- !x y. K x y = x
S_THM
|- !f g x. S f g x = f x (g x)
C_THM
|- !f x y. combin$C f x y = f y x
W_THM
|- !f x. W f x = f x x
I_THM
|- !x. I x = x
I_o_ID
|- !f. (I o f = f) /\ (f o I = f)