Package option-dest: Option type destructors
Information
| name | option-dest |
| version | 1.50 |
| description | Option type destructors |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| requires | bool option-def option-thm |
| show | Data.Bool Data.Option |
Files
- Package tarball option-dest-1.50.tgz
- Theory source file option-dest.thy (included in the package tarball)
Defined Constants
- Data
- Option
- case
- isNone
- isSome
- Option
Theorems
⊦ isNone none
⊦ ¬isSome none
⊦ ∀a. isSome (some a)
⊦ ∀a. ¬isNone (some a)
⊦ ∀x. case none some x = x
⊦ ∀b f. case b f none = b
⊦ ∀b f a. case b f (some a) = f a
External Type Operators
- →
- bool
- Data
- Option
- option
- Option
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- ⊥
- ⊤
- Option
- none
- some
- Bool
Assumptions
⊦ ⊤
⊦ (∃) = λp. p ((select) p)
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. (t ⇔ ⊤) ⇔ t
⊦ ∀t. (t ⇔ ⊥) ⇔ ¬t
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀x. x = none ∨ ∃a. x = some a
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀r. (∀x. ∃y. r x y) ⇔ ∃f. ∀x. r x (f x)
⊦ ∀b f. ∃fn. fn none = b ∧ ∀a. fn (some a) = f a