Package char-def: Definition of Unicode characters

Information

namechar-def
version1.36
descriptionDefinition of Unicode characters
authorJoe Hurd <joe@gilith.com>
licenseMIT
provenanceHOL Light theory extracted on 2011-11-30
requiresbool
pair
natural
byte
showData.Bool
Data.Byte
Data.Char
Data.Pair
Data.Word16
Number.Natural

Files

Defined Type Operators

Defined Constants

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

Input Constants

Assumptions

T

¬F T

¬T F

bit0 0 = 0

t. t t

n. 0 n

F p. p

t. t ¬t

(¬) = λp. p F

() = 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. F t F

t. T t t

t. t T t

t. t t t

t. F t T

t. T t t

t. t T T

t. F t t

t. T t T

t. t F 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 = exp 2 width

width = 8

t. (F t) ¬t

t. (t F) ¬t

t. t F ¬t

n. bit1 n = suc (bit0 n)

m. exp m 0 = 1

m. m * 1 = m

m. 1 * m = m

() = λp q. p q p

t. (t T) (t F)

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 T T

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. exp m (suc n) = m * exp 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. exp m (n + p) = exp m n * exp 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