Package option-map-def: Definition of the option map function
Information
| name | option-map-def |
| version | 1.12 |
| description | Definition of the option map function |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-01-13 |
| requires | bool option-def |
| show | Data.Bool Data.Option |
Files
- Package tarball option-map-def-1.12.tgz
- Theory source file option-map-def.thy (included in the package tarball)
Defined Constant
- Data
- Option
- map
- Option
Theorems
⊦ ∀f. map f none = none
⊦ ∀f a. map f (some a) = some (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. ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀r. (∀x. ∃y. r x y) ⇔ ∃f. ∀x. r x (f x)
⊦ ∀b f. ∃fn. fn none = b ∧ ∀a. fn (some a) = f a