Theory "operator"

Parents     bool

Signature

Constant Type
LEFT_ID :('a -> 'b -> 'b) -> 'a -> bool
ASSOC :('a -> 'a -> 'a) -> bool
MONOID :('a -> 'a -> 'a) -> 'a -> bool
RIGHT_ID :('a -> 'b -> 'a) -> 'b -> bool
FCOMM :('a -> 'b -> 'a) -> ('c -> 'a -> 'a) -> bool
COMM :('a -> 'a -> 'b) -> bool

Definitions

ASSOC_DEF
|- !f. ASSOC f = !x y z. f x (f y z) = f (f x y) z
COMM_DEF
|- !f. COMM f = !x y. f x y = f y x
FCOMM_DEF
|- !f g. FCOMM f g = !x y z. g x (f y z) = f (g x y) z
RIGHT_ID_DEF
|- !f e. RIGHT_ID f e = !x. f x e = x
LEFT_ID_DEF
|- !f e. LEFT_ID f e = !x. f e x = x
MONOID_DEF
|- !f e. MONOID f e = ASSOC f /\ RIGHT_ID f e /\ LEFT_ID f e


Theorems

ASSOC_CONJ
|- ASSOC $/\
ASSOC_DISJ
|- ASSOC $\/
FCOMM_ASSOC
|- !f. FCOMM f f = ASSOC f
MONOID_CONJ_T
|- MONOID $/\ T
MONOID_DISJ_F
|- MONOID $\/ F