Package parser-stream-def: Definition of parse streams
Information
| name | parser-stream-def |
| version | 1.95 |
| description | Definition of parse streams |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-11-04 |
| checksum | 60c72d68bc25cf3a3a9eb8516d6bf56a6dc892cf |
| requires | bool list natural option probability |
| show | Data.Bool Data.List Data.Option Data.Pair Number.Natural Parser.Stream Probability.Random |
Files
- Package tarball parser-stream-def-1.95.tgz
- Theory source file parser-stream-def.thy (included in the package tarball)
Defined Type Operator
- Parser
- Stream
- stream
- Stream
Defined Constants
- Parser
- Stream
- append
- case
- cons
- eof
- error
- fromList
- fromRandom
- isProperSuffix
- isSuffix
- length
- map
- toList
- Stream
Theorems
⊦ length eof = 0
⊦ length error = 0
⊦ toList error = none
⊦ toList eof = some []
⊦ ∀s. ¬isProperSuffix s eof
⊦ ∀s. ¬isProperSuffix s error
⊦ ∀s. append [] s = s
⊦ ∀f. map f eof = eof
⊦ ∀f. map f error = error
⊦ ∀l. fromList l = append l eof
⊦ ∀a s. length (cons a s) = suc (length s)
⊦ ∀e b f. case e b f eof = b
⊦ ∀e b f. case e b f error = e
⊦ ∀s s'. isSuffix s s' ⇔ s = s' ∨ isProperSuffix s s'
⊦ ∀h t s. append (h :: t) s = cons h (append t s)
⊦ ∀a s.
toList (cons a s) =
case toList s of none → none | some l → some (a :: l)
⊦ ∀f a s. map f (cons a s) = cons (f a) (map f s)
⊦ ∀s a s'. isProperSuffix s (cons a s') ⇔ s = s' ∨ isProperSuffix s s'
⊦ ∀e b f a s. case e b f (cons a s) = f a s
⊦ ∀P. P error ∧ P eof ∧ (∀a0 a1. P a1 ⇒ P (cons a0 a1)) ⇒ ∀x. P x
⊦ ∀f0 f1 f2.
∃fn.
fn error = f0 ∧ fn eof = f1 ∧
∀a0 a1. fn (cons a0 a1) = f2 a0 a1 (fn a1)
⊦ ∀d r.
fromRandom d r =
let (l, r') ← Geometric.fromRandom d r in
let (b, r'') ← bit r' in
(append l (if b then error else eof), r'')
External Type Operators
- →
- bool
- Data
- List
- list
- Option
- option
- Pair
- ×
- List
- Number
- Natural
- natural
- Natural
- Probability
- Random
- random
- Random
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∃!
- ∨
- ¬
- cond
- ⊥
- ⊤
- List
- ::
- []
- Geometric
- Geometric.fromRandom
- Option
- case
- none
- some
- Pair
- ,
- Bool
- Number
- Natural
- *
- +
- <
- ≤
- ↑
- bit0
- bit1
- even
- suc
- zero
- Natural
- Probability
- Random
- bit
- Random
Assumptions
⊦ ⊤
⊦ ¬⊥ ⇔ ⊤
⊦ ¬⊤ ⇔ ⊥
⊦ bit0 0 = 0
⊦ ∀t. t ⇒ t
⊦ ∀n. 0 ≤ n
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ (∃) = λp. p ((select) p)
⊦ ∀a. ∃!x. x = a
⊦ ∀t. (∀x. t) ⇔ t
⊦ ∀t. (∃x. t) ⇔ t
⊦ ∀t. (λx. t x) = t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. ¬¬t ⇔ t
⊦ ∀t. (⊤ ⇔ t) ⇔ t
⊦ ∀t. (t ⇔ ⊤) ⇔ t
⊦ ∀t. ⊥ ∧ t ⇔ ⊥
⊦ ∀t. ⊤ ∧ t ⇔ t
⊦ ∀t. t ∧ ⊤ ⇔ t
⊦ ∀t. ⊥ ⇒ t ⇔ ⊤
⊦ ∀t. ⊤ ⇒ t ⇔ t
⊦ ∀t. t ⇒ ⊤ ⇔ ⊤
⊦ ∀t. ⊥ ∨ t ⇔ t
⊦ ∀t. ⊤ ∨ t ⇔ ⊤
⊦ ∀t. t ∨ ⊥ ⇔ t
⊦ ∀n. ¬(suc n = 0)
⊦ ∀n. 0 + n = n
⊦ ∀t. (⊥ ⇔ t) ⇔ ¬t
⊦ ∀t. (t ⇔ ⊥) ⇔ ¬t
⊦ ∀t. t ⇒ ⊥ ⇔ ¬t
⊦ ∀n. even (2 * n)
⊦ ∀n. bit1 n = suc (bit0 n)
⊦ ∀m. m ↑ 0 = 1
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀t. (t ⇔ ⊤) ∨ (t ⇔ ⊥)
⊦ ∀n. even (suc n) ⇔ ¬even n
⊦ ∀m. m ≤ 0 ⇔ m = 0
⊦ ∀t1 t2. (if ⊥ then t1 else t2) = t2
⊦ ∀t1 t2. (if ⊤ then t1 else t2) = t1
⊦ ∀n. bit0 (suc n) = suc (suc (bit0 n))
⊦ ∀f y. (let x ← y in f x) = f y
⊦ ∀x y. x = y ⇔ y = x
⊦ ∀t1 t2. t1 ∨ t2 ⇔ t2 ∨ t1
⊦ ∀n. 2 * n = n + n
⊦ ∀m n. ¬(m < n ∧ n ≤ m)
⊦ ∀m n. ¬(m ≤ n ∧ n < m)
⊦ ∀m n. suc m ≤ n ⇔ m < n
⊦ (∧) = λp q. (λf. f p q) = λf. f ⊤ ⊤
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀m n. m + suc n = suc (m + n)
⊦ ∀m n. suc m + n = suc (m + n)
⊦ ∀m n. suc m = suc n ⇔ m = n
⊦ ∀m n. even (m * n) ⇔ even m ∨ even n
⊦ ∀m n. even (m + n) ⇔ even m ⇔ even n
⊦ ∀m n. m ↑ suc n = m * m ↑ n
⊦ ∀f g. (∀x. f x = g x) ⇔ f = g
⊦ ∀p a. (∃x. a = x ∧ p x) ⇔ p a
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀m n. m ≤ n ⇔ m < n ∨ m = n
⊦ ∀m n. m ≤ n ∧ n ≤ m ⇔ m = n
⊦ ∀p q. (∃x. p ∧ q x) ⇔ p ∧ ∃x. q x
⊦ ∀t1 t2 t3. (t1 ∧ t2) ∧ t3 ⇔ t1 ∧ t2 ∧ t3
⊦ ∀m n p. m * (n * p) = m * n * p
⊦ ∀p m n. m + p = n + p ⇔ m = n
⊦ ∀p x. (∀y. p y ⇔ y = x) ⇒ (select) p = x
⊦ ∀r. (∀x. ∃y. r x y) ⇔ ∃f. ∀x. r x (f x)
⊦ ∀m n. m ≤ suc n ⇔ m = suc n ∨ m ≤ n
⊦ ∀m n. m * n = 0 ⇔ m = 0 ∨ n = 0
⊦ ∀p. p 0 ∧ (∀n. p n ⇒ p (suc n)) ⇒ ∀n. p n
⊦ ∀m n. m ↑ n = 0 ⇔ m = 0 ∧ ¬(n = 0)
⊦ (∃!) = λp. (∃) p ∧ ∀x y. p x ∧ p y ⇒ x = y
⊦ ∀p q. (∀x. p x ∧ q x) ⇔ (∀x. p x) ∧ ∀x. q x
⊦ ∀p q. (∀x. p x ⇒ q x) ⇒ (∀x. p x) ⇒ ∀x. q x
⊦ ∀p q. (∀x. p x ⇒ q x) ⇒ (∃x. p x) ⇒ ∃x. q x
⊦ ∀p q. (∀x. p x) ∧ (∀x. q x) ⇔ ∀x. p x ∧ q x
⊦ ∀e f. ∃!fn. fn 0 = e ∧ ∀n. fn (suc n) = f (fn n) n
⊦ ∀m n p. m * n = m * p ⇔ m = 0 ∨ n = p
⊦ ∀m n p. m * n ≤ m * p ⇔ m = 0 ∨ n ≤ p
⊦ ∀m n p. m * n < m * p ⇔ ¬(m = 0) ∧ n < p
⊦ ∀p1 p2 q1 q2. (p1 ⇒ p2) ∧ (q1 ⇒ q2) ⇒ p1 ∧ q1 ⇒ p2 ∧ q2
⊦ ∀p1 p2 q1 q2. (p1 ⇒ p2) ∧ (q1 ⇒ q2) ⇒ p1 ∨ q1 ⇒ p2 ∨ q2
⊦ ∀p. (∀x. ∃!y. p x y) ⇔ ∃f. ∀x y. p x y ⇔ f x = y
⊦ ∀p c x y. p (if c then x else y) ⇔ (c ⇒ p x) ∧ (¬c ⇒ p y)
⊦ ∀b f. ∃fn. fn [] = b ∧ ∀h t. fn (h :: t) = f h t (fn t)
⊦ ∀p. (∃!x. p x) ⇔ (∃x. p x) ∧ ∀x x'. p x ∧ p x' ⇒ x = x'