Package list-dest-def: Definition of the list destructors

Information

Files

• Package tarball list-dest-def-1.14.tgz
• Theory file list-dest-def.thy (included in the package tarball)

Defined Constants

• Data
  • List
    • Data.List.head
    • Data.List.null
    • Data.List.tail
    • Data.List.case.[].::

Theorems

⊦ ∀h t. Data.List.head (Data.List.:: h t) = h

⊦ ∀h t. Data.List.tail (Data.List.:: h t) = t

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

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

Input Type Operators

• →
• bool
• Data
  • List
    • Data.List.list

Input Constants

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

Assumptions

⊦ T

⊦ (∃) = λP. P ((select) P)

⊦ (∀) = λp. p = λx. T

⊦ (⇒) = λp q. p ∧ q ⇔ p

⊦ (∧) = λp q. (λf. f p q) = λf. f T T

⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q

⊦ ∀NIL' CONS'.
    ∃fn.
      fn Data.List.[] = NIL' ∧
      ∀a0 a1. fn (Data.List.:: a0 a1) = CONS' a0 a1 (fn a1)