Package char-def: Definition of Unicode characters
Information
| name | char-def |
| version | 1.54 |
| description | Definition of Unicode characters |
| author | Joe Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2012-03-26 |
| requires | bool byte natural pair |
| show | Data.Bool Data.Byte Data.Char Data.Pair Data.Word16 Number.Natural |
Files
- Package tarball char-def-1.54.tgz
- Theory 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
- isChar
- isPlane
- isPosition
- mkChar
- mkPlane
- mkPosition
- 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
⊦ ∀pl pos.
isChar (pl, pos) ⇔
let pli ← destPlane pl in
let posi ← destPosition pos in
¬(pli = 0) ∨ posi < 55296 ∨ 57343 < posi ∧ posi < 65534
Input Type Operators
- →
- bool
- Data
- Byte
- byte
- Pair
- ×
- Word16
- word16
- Byte
- Number
- Natural
- natural
- Natural
Input Constants
- =
- select
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- ⊥
- ⊤
- Byte
- <
- ≤
- fromNatural
- modulus
- toNatural
- width
- Pair
- ,
- fst
- snd
- Word16
- <
- fromNatural
- Bool
- Number
- Natural
- *
- +
- <
- ≤
- ↑
- bit0
- bit1
- div
- even
- mod
- suc
- zero
- 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
⊦ ∀m. m * 1 = m
⊦ ∀m. 1 * m = m
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀t. (t ⇔ ⊤) ∨ (t ⇔ ⊥)
⊦ ∀n. even (suc n) ⇔ ¬even n
⊦ ∀m. m ≤ 0 ⇔ m = 0
⊦ ∀x. toNatural (fromNatural x) = x mod modulus
⊦ ∀x y. fst (x, y) = x
⊦ ∀x y. snd (x, y) = y
⊦ ∀n. bit0 (suc n) = suc (suc (bit0 n))
⊦ ∀t1 t2. t1 ∨ t2 ⇔ t2 ∨ t1
⊦ ∀m n. m + n = n + m
⊦ ∀n. 2 * n = n + n
⊦ ∀x y. x < y ⇔ ¬(y ≤ x)
⊦ ∀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
⊦ (∃) = 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
⊦ ∀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) = 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