Package list-dest: List type destructors
Information
| name | list-dest |
| version | 1.43 |
| description | List type destructors |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool list-def list-thm |
| show | Data.Bool Data.List |
Files
- Package tarball list-dest-1.43.tgz
- Theory source file list-dest.thy (included in the package tarball)
Defined Constants
- Data
- List
- case
- head
- null
- tail
- List
Theorems
⊦ null []
⊦ ∀l. null l ⇔ l = []
⊦ ∀l. case [] (::) l = l
⊦ ∀h t. ¬null (h :: t)
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. tail (h :: t) = t
⊦ ∀b f. case b f [] = b
⊦ ∀l. ¬null l ⇒ head l :: tail l = l
⊦ ∀b f h t. case b f (h :: t) = f h t
External Type Operators
- →
- bool
- Data
- List
- list
- List
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ¬
- ⊥
- ⊤
- List
- ::
- []
- Bool
Assumptions
⊦ ⊤
⊦ ¬⊥ ⇔ ⊤
⊦ ¬⊤ ⇔ ⊥
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. (⊤ ⇔ t) ⇔ t
⊦ ∀t. (t ⇔ ⊤) ⇔ t
⊦ ∀t. ⊥ ⇒ t ⇔ ⊤
⊦ ∀t. ⊤ ⇒ t ⇔ t
⊦ ∀t. (⊥ ⇔ t) ⇔ ¬t
⊦ ∀t. (t ⇔ ⊥) ⇔ ¬t
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. ¬(h :: t = [])
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀p. (∀x. ∃y. p x y) ⇔ ∃y. ∀x. p x (y x)
⊦ ∀p. p [] ∧ (∀h t. p t ⇒ p (h :: t)) ⇒ ∀l. p l
⊦ ∀b f. ∃fn. fn [] = b ∧ ∀h t. fn (h :: t) = f h t (fn t)