Package function: Function operators and combinators

Information

namefunction
version1.55
descriptionFunction operators and combinators
authorJoe Leslie-Hurd <joe@gilith.com>
licenseMIT
checksum35d4e6c28baaee5cee8c39751d651af7d7cfe5dc
requiresbool
showData.Bool
Function

Files

Defined Constants

Theorems

id = λx. x

const = λx y. x

x. id x = x

Combinator.w = λf x. f x x

x. Combinator.s const x = id

f. f id = f

f. id f = f

f. flip (flip f) = f

() = λf g x. f (g x)

flip = λf x y. f y x

Combinator.s = λf g x. f x (g x)

x y. const x y = x

f x. Combinator.w f x = f x x

f. surjective f y. x. y = f x

f g x. (f g) x = f (g x)

f x y. flip f x y = f y x

f g x. Combinator.s f g x = f x (g x)

f g h. f (g h) = f g h

f g h. f g h = f (g h)

f. injective f x1 x2. f x1 = f x2 x1 = x2

f g. (x. y. g y = f x) h. f = g h

f. (y. x. f x = y) p. (x. p (f x)) y. p y

f. (y. x. f x = y) p. (x. p (f x)) y. p y

f g. (x y. g x = g y f x = f y) h. f = h g

p f g. (x. p x y. g y = f x) h. x. p x f x = g (h x)

p f g.
    (x y. p x p y g x = g y f x = f y) h. x. p x f x = h (g x)

External Type Operators

External Constants

Assumptions

¬

¬

t. t t

() = λp. p ((select) p)

t. (x. t) t

() = λp. p = λx.

t. ¬¬t t

t. ( t) t

t. (t ) t

t. t t

t. t t

t. ( t) ¬t

t. (t ) ¬t

() = λp q. p q p

t. (t ) (t )

f y. (let x y in f x) = f y

x y. x = y y = x

x y. x = y y = x

() = λp q. (λf. f p q) = λf. f

p. ¬(x. p x) x. ¬p x

p. ¬(x. p x) x. ¬p x

() = λp. q. (x. p x q) q

f g. (x. f x = g x) f = g

() = λp q. r. (p r) (q r) r

p q. p (x. q x) x. p q x

r. (x. y. r x y) f. x. r x (f x)