Package list-length: The list length function

Information

namelist-length
version1.28
descriptionThe list length function
authorJoe Hurd <joe@gilith.com>
licenseMIT
requiresbool
natural
list-def
list-thm
list-dest
showData.Bool
Data.List
Number.Natural

Files

Defined Constant

Theorems

length [] = 0

l. length l = 0 l = []

h t. length (h :: t) = suc (length t)

l. ¬(l = []) length (tail l) = length l - 1

l n. length l = suc n h t. l = h :: t length t = n

Input Type Operators

Input Constants

Assumptions

T

¬F T

¬T F

F p. p

(¬) = λp. p F

() = λp. p ((select) p)

t. (x. t) t

t. (x. t) t

t. (λx. t x) = t

() = λp. p = λx. T

t. ¬¬t t

t. (T t) t

t. F t F

t. T t t

t. F t T

t. t T T

t. F t t

t. T t T

t. t F t

n. ¬(suc n = 0)

t. (F t) ¬t

t. t F ¬t

() = λp q. p q p

t. (t T) (t F)

n. suc n - 1 = n

h t. ¬(h :: t = [])

h t. tail (h :: t) = t

() = λp q. (λf. f p q) = λf. f T T

p. ¬(x. p x) x. ¬p x

() = λp. q. (x. p x q) q

m n. suc m = suc n m = n

() = 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

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

p. (x. y. p x y) y. x. p x (y x)

P. P [] (a0 a1. P a1 P (a0 :: a1)) x. P x

h1 h2 t1 t2. h1 :: t1 = h2 :: t2 h1 = h2 t1 = t2

NIL' CONS'.
    fn. fn [] = NIL' a0 a1. fn (a0 :: a1) = CONS' a0 a1 (fn a1)