Package option-dest: Theory of the option destructors
Information
| name | option-dest |
| version | 1.15 |
| description | Theory of the option destructors |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| show | Data.Bool Data.Option |
Files
- Package tarball option-dest-1.15.tgz
- Theory file option-dest.thy (included in the package tarball)
Defined Constants
- Data
- Option
- case
- isNone
- isSome
- Option
Theorems
⊦ ∀x. case none some x = x
⊦ (isNone none ⇔ T) ∧ ∀a. isNone (some a) ⇔ F
⊦ (isSome none ⇔ F) ∧ ∀a. isSome (some a) ⇔ T
⊦ (∀b f. case b f none = b) ∧ ∀b f a. case b f (some a) = f a
Input Type Operators
- →
- bool
- Data
- Option
- option
- Option
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- F
- T
- Option
- none
- some
- Bool
Assumptions
⊦ T
⊦ (∃) = λP. P ((select) P)
⊦ (∀) = λp. p = λx. T
⊦ ∀x. x = x ⇔ T
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀x. x = none ∨ ∃a. x = some a
⊦ (∧) = λp q. (λf. f p q) = λf. f T T
⊦ (∃) = λP. ∀q. (∀x. P x ⇒ q) ⇒ q
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀NONE' SOME'. ∃fn. fn none = NONE' ∧ ∀a. fn (some a) = SOME' a