Package option-dest: Theory of the option destructors

Information

Files

• Package tarball option-dest-1.14.tgz
• Theory file option-dest.thy (included in the package tarball)

Defined Constants

• Data
  • Option
    • isNone
    • isSome
    • case.none.some

Theorems

⊦ ∀x. case.none.some none some x = x

⊦ (isNone none ⇔ T) ∧ ∀a. isNone (some a) ⇔ F

⊦ (isSome none ⇔ F) ∧ ∀a. isSome (some a) ⇔ T

⊦ (∀b f. case.none.some b f none = b) ∧
  ∀b f a. case.none.some b f (some a) = f a

Input Type Operators

• →
• bool
• Data
  • Option
    • option

Input Constants

• =
• select
• Data
  • Bool
    • ∀
    • ∧
    • ⇒
    • ∃
    • ∨
    • F
    • T
  • Option
    • none
    • some

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