Package list-nub: The list nub function

Information

namelist-nub
version1.28
descriptionThe list nub function
authorJoe Hurd <joe@gilith.com>
licenseMIT
requiresbool
natural
set
list-def
list-length
list-reverse
list-member
showData.Bool
Data.List
Number.Natural
Set

Files

Defined Constants

Theorems

nubReverse [] = []

l. nub (nub l) = nub l

l. nubReverse (nubReverse l) = nubReverse l

l. toSet (nub l) = toSet l

l. toSet (nubReverse l) = toSet l

l. length (nub l) length l

l. length (nubReverse l) length l

l. nub l = reverse (nubReverse (reverse l))

l x. member x (nub l) member x l

l x. member x (nubReverse l) member x l

h t.
    nubReverse (h :: t) =
    if member h t then nubReverse t else h :: nubReverse t

Input Type Operators

Input Constants

Assumptions

T

¬F T

length [] = 0

n. n n

F p. p

x. ¬member x []

t. t ¬t

(¬) = λp. p F

() = λP. P ((select) P)

t. (x. t) t

() = λp. p = λx. T

t. (t T) t

t. F t t

t. T t T

t. t T T

l. reverse (reverse l) = l

t. (F t) ¬t

l. length (reverse l) = length l

() = λp q. p q p

t. (t T) (t F)

t1 t2. (if F then t1 else t2) = t2

t1 t2. (if T then t1 else t2) = t1

x y. x = y y = x

x l. member x l x toSet l

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

l x. member x (reverse l) member x l

() = λp q. (λf. f p q) = λf. f T T

m n. suc m suc n m n

() = λp q. r. (p r) (q r) r

s t. (x. x s x t) s = t

m n. m suc n m = suc n m n

x h t. member x (h :: t) x = h member x t

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

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