Package list-dest: Theory of the list destructors
Information
| name | list-dest |
| version | 1.13 |
| description | Theory of the list destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| show | Data.Bool Data.List |
Files
- Package tarball list-dest-1.13.tgz
- Theory file list-dest.thy (included in the package tarball)
Defined Constants
- Data
- List
- case
- head
- null
- tail
- List
Theorems
⊦ ∀l. null l ⇔ l = []
⊦ ∀l. case [] (::) l = l
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. tail (h :: t) = t
⊦ ∀l. ¬(l = []) ⇒ head l :: tail l = l
⊦ (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
- List
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- F
- T
- List
- ::
- []
- Bool
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)
⊦ ∀t. (T ⇒ t ⇔ t) ∧ (t ⇒ T ⇔ T) ∧ (F ⇒ t ⇔ T) ∧ (t ⇒ t ⇔ T) ∧ (t ⇒ F ⇔ ¬t)