Package pair: Product types

Information

namepair
version1.28
descriptionProduct types
authorJoe Leslie-Hurd <joe@gilith.com>
licenseMIT
checksumf93d9d061f37e7bab379271c2736cf41cd584720
requiresbool
showData.Bool
Data.Pair

Files

Defined Type Operator

Defined Constants

Theorems

x. (fst x, snd x) = x

a b. fst (a, b) = a

a b. snd (a, b) = b

x. a b. x = (a, b)

p. (x. p x) a b. p (a, b)

p. (x. p x) a b. p (a, b)

p. (a b. p (a, b)) x. p x

p. (f. p f) f. p (λa b. f (a, b))

p. (f. p f) f. p (λa b. f (a, b))

f. fn. a b. fn (a, b) = f a b

p. (x y. p x y) z. p (fst z) (snd z)

p. (x y. p x y) z. p (fst z) (snd z)

f. (λx. f x) = λ(a, b). f (a, b)

f. (λ(x, y). f x y) = λp. f (fst p) (snd p)

a b a' b'. (a, b) = (a', b') a = a' b = b'

p. (f. p f) f. p (λ(a, b). f a b)

p. (f. p f) f. p (λ(a, b). f a b)

p. ((a, b). p a b) a b. p a b

p. ((a, b). p a b) a b. p a b

p. (select (a, b). p a b) = select x. p (fst x) (snd x)

p. ((a, b, c). p a b c) a b c. p a b c

p. ((a, b, c). p a b c) a b c. p a b c

p q. (a b. p a b) (a b. p a b q (a, b)) q (select (a, b). p a b)

(f. (λ(a, b). f (a, b)) = f) (f. (λ(a, b, c). f (a, b, c)) = f)
  f. (λ(a, b, c, d). f (a, b, c, d)) = f

External Type Operators

External Constants

Assumptions

¬

¬

t. t t

p. p

t. t ¬t

(¬) = λp. p

() = λp. p ((select) p)

t. (x. t) t

t. (λx. t x) = 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 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 )

p x. p x p ((select) p)

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

x y. x = y y = x

t1 t2. t1 t2 t2 t1

() = 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

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

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

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

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

t1 t2 t3. (t1 t2) t3 t1 t2 t3

p x. (y. p y y = x) (select) p = x

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

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

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

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