Package char-def: Definition of Unicode characters
Information
| name | char-def |
| version | 1.98 |
| description | Definition of Unicode characters |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-11-17 |
| checksum | edcc12c6c0579822d2d462c18848d542615a88a2 |
| requires | bool byte natural pair word16 |
| show | Data.Bool Data.Byte Data.Char Data.Pair Data.Word16 Number.Natural Probability.Random |
Files
- Package tarball char-def-1.98.tgz
- Theory source file char-def.thy (included in the package tarball)
Defined Type Operators
- Data
- Char
- char
- plane
- position
- Char
Defined Constants
- Data
- Char
- destChar
- destPlane
- destPosition
- fromRandom
- isChar
- isPlane
- isPosition
- mkChar
- mkPlane
- mkPosition
- planeFromRandom
- positionFromRandom
- Char
Theorems
⊦ ∀p. isPosition p
⊦ ∀a. mkChar (destChar a) = a
⊦ ∀a. mkPlane (destPlane a) = a
⊦ ∀a. mkPosition (destPosition a) = a
⊦ ∀r. destPosition (mkPosition r) = r
⊦ ∀r. isPlane r ⇔ destPlane (mkPlane r) = r
⊦ ∀r. isChar r ⇔ destChar (mkChar r) = r
⊦ ∀p. isPlane p ⇔ p < 17
⊦ ∀r.
positionFromRandom r = let (w, r') ← fromRandom r in (mkPosition w, r')
⊦ ∀r.
planeFromRandom r =
let (n, r') ← Uniform.fromRandom 17 r in (mkPlane (fromNatural n), r')
⊦ ∀pl pos.
isChar (pl, pos) ⇔
let pli ← destPlane pl in
let posi ← destPosition pos in
¬(pli = 0) ∨ posi < 55296 ∨ 57343 < posi ∧ posi < 65534
⊦ ∀r.
fromRandom r =
let (pl, r') ← planeFromRandom r in
let pli ← destPlane pl in
let (pos, r'') ←
if ¬(pli = 0) then positionFromRandom r'
else
let (n, r''') ← Uniform.fromRandom 63486 r' in
let n' ← if n < 55296 then n else n + 2048 in
(mkPosition (fromNatural n'), r''') in
(mkChar (pl, pos), r'')
External Type Operators
- →
- bool
- Data
- Byte
- byte
- Pair
- ×
- Word16
- word16
- Byte
- Number
- Natural
- natural
- Natural
- Probability
- Random
- random
- Random
External Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- cond
- ⊥
- ⊤
- Byte
- <
- fromNatural
- modulus
- toNatural
- width
- Pair
- ,
- fst
- snd
- Word16
- <
- fromNatural
- fromRandom
- Bool
- Number
- Natural
- *
- +
- <
- ≤
- ↑
- bit0
- bit1
- div
- even
- mod
- suc
- zero
- Uniform
- Uniform.fromRandom
- Natural
Assumptions
⊦ ⊤
⊦ ¬⊥ ⇔ ⊤
⊦ ¬⊤ ⇔ ⊥
⊦ bit0 0 = 0
⊦ ∀t. t ⇒ t
⊦ ∀n. 0 ≤ n
⊦ ⊥ ⇔ ∀p. p
⊦ ∀t. t ∨ ¬t
⊦ (¬) = λp. p ⇒ ⊥
⊦ (∃) = λp. p ((select) p)
⊦ ∀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. ⊤ ∨ t ⇔ ⊤
⊦ ∀t. t ∨ ⊥ ⇔ t
⊦ ∀t. t ∨ ⊤ ⇔ ⊤
⊦ ∀n. ¬(suc n = 0)
⊦ ∀n. 0 * n = 0
⊦ ∀m. m * 0 = 0
⊦ ∀n. 0 + n = n
⊦ ∀m. m + 0 = m
⊦ modulus = 2 ↑ width
⊦ width = 8
⊦ ∀t. (⊥ ⇔ t) ⇔ ¬t
⊦ ∀t. (t ⇔ ⊥) ⇔ ¬t
⊦ ∀t. t ⇒ ⊥ ⇔ ¬t
⊦ ∀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
⊦ ∀n. toNatural (fromNatural n) = n mod modulus
⊦ ∀a b. fst (a, b) = a
⊦ ∀a b. snd (a, b) = b
⊦ ∀n. bit0 (suc n) = suc (suc (bit0 n))
⊦ ∀x y. x = y ⇒ y = x
⊦ ∀t1 t2. t1 ∨ t2 ⇔ t2 ∨ t1
⊦ ∀m n. m * n = n * m
⊦ ∀m n. m + n = n + m
⊦ ∀n. n ↑ 2 = n * n
⊦ ∀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 ⊤ ⊤
⊦ ∀p. ¬(∀x. p x) ⇔ ∃x. ¬p x
⊦ ∀p. ¬(∃x. p x) ⇔ ∀x. ¬p x
⊦ (∃) = λp. ∀q. (∀x. p x ⇒ q) ⇒ q
⊦ ∀x y. x < y ⇔ toNatural x < toNatural y
⊦ ∀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
⊦ ∀m n. m ↑ suc n = m * m ↑ n
⊦ ∀m n. suc m * n = m * n + n
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀m n. m ≤ n ⇔ m < n ∨ m = n
⊦ ∀m n. m ≤ n ∧ n ≤ m ⇔ m = n
⊦ ∀m n. m < n ⇔ ∃d. n = m + suc d
⊦ ∀p q. p ∨ (∃x. q x) ⇔ ∃x. p ∨ q x
⊦ ∀t1 t2 t3. (t1 ∨ t2) ∨ t3 ⇔ t1 ∨ t2 ∨ t3
⊦ ∀m n p. m * (n * p) = n * (m * p)
⊦ ∀m n p. m * (n * p) = m * n * p
⊦ ∀m n p. m + (n + p) = m + n + p
⊦ ∀m n. m ≤ suc n ⇔ m = suc n ∨ m ≤ n
⊦ ∀x y. fromNatural x = fromNatural y ⇔ x mod modulus = y mod modulus
⊦ ∀m n. m * n = 0 ⇔ m = 0 ∨ n = 0
⊦ ∀p. p 0 ∧ (∀n. p n ⇒ p (suc n)) ⇒ ∀n. p n
⊦ ∀m n p. m * (n + p) = m * n + m * p
⊦ ∀m n p. m ↑ (n + p) = m ↑ n * m ↑ p
⊦ ∀m n p. (m + n) * p = m * p + n * p
⊦ ∀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
⊦ ∀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
⊦ ∀m n q r. m = q * n + r ∧ r < n ⇒ m div n = q
⊦ ∀m n q r. m = q * n + r ∧ r < n ⇒ m mod n = r