Package probability-thm: Properties of probability
Information
| name | probability-thm |
| version | 1.8 |
| description | Properties of probability |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-11-10 |
| requires | bool list natural pair probability-def |
| show | Data.Bool Data.List Data.Pair Number.Natural Probability.Random |
Files
- Package tarball probability-thm-1.8.tgz
- Theory file probability-thm.thy (included in the package tarball)
Theorems
⊦ ∀n r. length (fst (bits n r)) = n
⊦ ∀d n r. length (fst (fromRandom d n r)) = n
Input Type Operators
- →
- bool
- Data
- List
- list
- Pair
- ×
- List
- Number
- Natural
- natural
- Natural
- Probability
- Random
- random
- Random
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ⊤
- List
- ::
- []
- fromRandom
- length
- Pair
- ,
- fst
- Bool
- Number
- Natural
- suc
- zero
- Natural
- Probability
- Random
- bit
- bits
- Random
Assumptions
⊦ ⊤
⊦ bits = fromRandom bit
⊦ length [] = 0
⊦ ∀t. t ⇒ t
⊦ ∀t. (∀x. t) ⇔ t
⊦ ∀t. (λx. t x) = t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. t ⇒ ⊤ ⇔ ⊤
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀x y. fst (x, y) = x
⊦ ∀p x. p x ⇒ p ((select) p)
⊦ ∀xy. ∃x y. xy = (x, y)
⊦ ∀h t. length (h :: t) = suc (length t)
⊦ ∀d r. fromRandom d 0 r = ([], r)
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀m n. suc m = suc n ⇔ m = n
⊦ ∀f. ∃fn. ∀x y. fn (x, y) = f x y
⊦ ∀p. p 0 ∧ (∀n. p n ⇒ p (suc n)) ⇒ ∀n. p n
⊦ ∀d r n.
fromRandom d (suc n) r =
let (h, r') ← d r in let (t, r'') ← fromRandom d n r' in (h :: t, r'')