init commit again

2023-11-01 09:29:33 +01:00
parent 448147e7da
commit d6c745207b
250 changed files with 15552 additions and 1 deletions
--- a/IBAF-cbs/Funcons-beta/Values/Composite/Bits/Bits.cbs
+++ b/IBAF-cbs/Funcons-beta/Values/Composite/Bits/Bits.cbs
@@ -0,0 +1,110 @@
+### Bits and bit vectors
+
+[
+  Type     bits
+  Datatype bit-vectors
+  Funcon   bit-vector
+  Type     bytes             Alias octets
+  Funcon   bit-vector-not
+  Funcon   bit-vector-and
+  Funcon   bit-vector-or
+  Funcon   bit-vector-xor
+  Funcon   bit-vector-shift-left
+  Funcon   bit-vector-logical-shift-right
+  Funcon   bit-vector-arithmetic-shift-right
+  Funcon   integer-to-bit-vector
+  Funcon   bit-vector-to-integer
+  Funcon   bit-vector-to-natural
+  Funcon   unsigned-bit-vector-maximum
+  Funcon   signed-bit-vector-maximum
+  Funcon   signed-bit-vector-minimum
+  Funcon   is-in-signed-bit-vector
+  Funcon   is-in-unsigned-bit-vector
+]
+
+
+#### Bits
+
+Type
+  bits ~> booleans
+/*
+  `false` represents the absence of a bit, `true` its presence.
+*/
+
+
+#### Bit vectors
+
+Datatype
+  bit-vectors(N:natural-numbers) ::= bit-vector(_:bits^N)
+
+Type
+  bytes ~> bit-vectors(8)
+Alias
+  octets = bytes
+
+Meta-variables
+  BT <: bit-vectors(_)
+
+Built-in Funcon
+  bit-vector-not(_:BT) : =>BT
+Built-in Funcon
+  bit-vector-and(_:BT, _:BT) : =>BT
+Built-in Funcon
+  bit-vector-or(_:BT, _:BT) : =>BT
+Built-in Funcon
+  bit-vector-xor(_:BT, _:BT) : =>BT
+/*
+  The above four funcons are the natural extensions of funcons from `booleans`
+  to `bit-vectors(N)` of the same length.
+*/
+
+Built-in Funcon
+  bit-vector-shift-left(_:BT, _:natural-numbers) : BT
+Built-in Funcon
+  bit-vector-logical-shift-right(_:BT, _:natural-numbers) : BT
+Built-in Funcon
+  bit-vector-arithmetic-shift-right(_:BT, _:natural-numbers) : BT
+
+Built-in Funcon
+  integer-to-bit-vector(_:integers, N:natural-numbers) : bit-vectors(N)
+/*
+  `integer-to-bit-vector(M, N)` converts an integer `M` to a bit-vector of
+  length `N`, using Two's Complement representation.  If the integer is out of
+  range of the representation, it will wrap around (modulo 2^N).
+*/
+
+Built-in Funcon
+  bit-vector-to-integer(_:BT) : =>integers
+/*
+  `bit-vector-to-integer(B)` interprets a bit-vector `BV` as an integer
+  in Two's Complement representation.
+*/
+
+Built-in Funcon
+  bit-vector-to-natural(_:BT) : =>natural-numbers
+/*
+  `bit-vector-to-natural(BV)` interprets a bit-vector `BV` as a natural number
+  in unsigned representation.
+*/
+
+Funcon
+  unsigned-bit-vector-maximum(N:natural-numbers) : =>natural-numbers
+    ~> integer-subtract(integer-power(2, N), 1)
+
+Funcon
+  signed-bit-vector-maximum(N:natural-numbers) : =>integers
+    ~> integer-subtract(integer-power(2, integer-subtract(N, 1)), 1)
+
+Funcon
+  signed-bit-vector-minimum(N:natural-numbers) : =>integers
+    ~> integer-negate(integer-power(2, integer-subtract(N, 1)))
+
+Funcon
+  is-in-signed-bit-vector(M:integers, N:natural-numbers) : =>booleans
+    ~> and(integer-is-less-or-equal(M, signed-bit-vector-maximum(N)),
+           integer-is-greater-or-equal(M, signed-bit-vector-minimum(N)))
+
+Funcon
+  is-in-unsigned-bit-vector(M:integers, N:natural-numbers) : =>booleans
+    ~> and(integer-is-less-or-equal(M, unsigned-bit-vector-maximum(N)),
+           integer-is-greater-or-equal(M, 0))