Package byte-bits: Byte to bit-list conversions
Information
| name | byte-bits |
| version | 1.79 |
| description | Byte to bit-list conversions |
| author | Joe Leslie-Hurd <joe@gilith.com> |
| license | MIT |
| provenance | HOL Light theory extracted on 2014-06-12 |
| requires | bool byte-def list natural |
| show | Data.Bool Data.Byte Data.Byte.Bits Data.List Number.Natural |
Files
- Package tarball byte-bits-1.79.tgz
- Theory source file byte-bits.thy (included in the package tarball)
Theorem
⊦ ∀b.
∃x0 x1 x2 x3 x4 x5 x6 x7.
b = toByte (x0 :: x1 :: x2 :: x3 :: x4 :: x5 :: x6 :: x7 :: [])
External Type Operators
- →
- bool
- Data
- Byte
- byte
- List
- list
- Byte
- Number
- Natural
- natural
- Natural
External Constants
- =
- Data
- Bool
- ∀
- ∧
- ⇒
- ∃
- ∨
- ¬
- ⊥
- ⊤
- Byte
- width
- Bits
- fromByte
- toByte
- List
- ::
- []
- head
- length
- tail
- Bool
- Number
- Natural
- +
- bit0
- bit1
- suc
- zero
- Natural
Assumptions
⊦ ⊤
⊦ length [] = 0
⊦ bit0 0 = 0
⊦ ∀t. t ⇒ t
⊦ ⊥ ⇔ ∀p. p
⊦ (¬) = λp. p ⇒ ⊥
⊦ ∀t. (∀x. t) ⇔ t
⊦ (∀) = λp. p = λx. ⊤
⊦ ∀t. ⊤ ∧ t ⇔ t
⊦ ∀t. ⊥ ⇒ t ⇔ ⊤
⊦ ∀w. toByte (fromByte w) = w
⊦ ∀w. length (fromByte w) = width
⊦ ∀n. ¬(suc n = 0)
⊦ ∀n. 0 + n = n
⊦ width = 8
⊦ ∀n. bit1 n = suc (bit0 n)
⊦ (⇒) = λp q. p ∧ q ⇔ p
⊦ ∀h t. head (h :: t) = h
⊦ ∀h t. tail (h :: t) = t
⊦ ∀n. bit0 (suc n) = suc (suc (bit0 n))
⊦ ∀l. length l = 0 ⇔ l = []
⊦ ∀h t. length (h :: t) = suc (length t)
⊦ (∧) = 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
⊦ ∀l. l = [] ∨ ∃h t. l = h :: t
⊦ (∨) = λp q. ∀r. (p ⇒ r) ⇒ (q ⇒ r) ⇒ r
⊦ ∀p. p 0 ∧ (∀n. p n ⇒ p (suc n)) ⇒ ∀n. p n
⊦ ∀h1 h2 t1 t2. h1 :: t1 = h2 :: t2 ⇔ h1 = h2 ∧ t1 = t2