Package list-dest: Theory of the list destructors

Information

Files

• Package tarball list-dest-1.1.tgz
• Theory file list-dest.thy (included in the package tarball)

Defined Constants

• Data
  • List
    • case
    • head
    • null
    • tail

Theorems

⊦ ∀l. null l ⇔ l = []

⊦ ∀l. case [] (::) l = l

⊦ ∀h t. tail (h :: t) = t

⊦ ∀t h. head (h :: t) = h

⊦ (null [] ⇔ T) ∧ ∀h t. null (h :: t) ⇔ F

⊦ (∀b f. case b f [] = b) ∧ ∀b f h t. case b f (h :: t) = f h t

Input Type Operators

• →
• bool
• Data
  • List
    • list

Input Constants

• =
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∨
    • ¬
    • select
    • F
    • T
  • List
    • ::
    • []

Assumptions

⊦ T

⊦ F ⇔ ∀p. p

⊦ (¬) = λp. p ⇒ F

⊦ (∃) = λP. P ((select) P)

⊦ (∀) = λP. P = λx. T

⊦ ∀x. x = x ⇔ T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ ∀h t. ¬(h :: t = [])

⊦ (¬T ⇔ F) ∧ (¬F ⇔ T)

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀x. x = [] ∨ ∃a0 a1. x = a0 :: a1

⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r

⊦ ∀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)

⊦ ∀t. ((T ⇔ t) ⇔ t) ∧ ((t ⇔ T) ⇔ t) ∧ ((F ⇔ t) ⇔ ¬t) ∧ ((t ⇔ F) ⇔ ¬t)