init commit again
This commit is contained in:
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110
IBAF-cbs/Funcons-beta/Values/Composite/Bits/Bits.cbs
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110
IBAF-cbs/Funcons-beta/Values/Composite/Bits/Bits.cbs
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### Bits and bit vectors
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[
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Type bits
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Datatype bit-vectors
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Funcon bit-vector
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Type bytes Alias octets
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Funcon bit-vector-not
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Funcon bit-vector-and
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Funcon bit-vector-or
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Funcon bit-vector-xor
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Funcon bit-vector-shift-left
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Funcon bit-vector-logical-shift-right
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Funcon bit-vector-arithmetic-shift-right
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Funcon integer-to-bit-vector
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Funcon bit-vector-to-integer
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Funcon bit-vector-to-natural
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Funcon unsigned-bit-vector-maximum
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Funcon signed-bit-vector-maximum
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Funcon signed-bit-vector-minimum
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Funcon is-in-signed-bit-vector
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Funcon is-in-unsigned-bit-vector
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]
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#### Bits
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Type
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bits ~> booleans
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/*
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`false` represents the absence of a bit, `true` its presence.
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*/
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#### Bit vectors
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Datatype
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bit-vectors(N:natural-numbers) ::= bit-vector(_:bits^N)
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Type
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bytes ~> bit-vectors(8)
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Alias
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octets = bytes
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Meta-variables
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BT <: bit-vectors(_)
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Built-in Funcon
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bit-vector-not(_:BT) : =>BT
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Built-in Funcon
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bit-vector-and(_:BT, _:BT) : =>BT
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Built-in Funcon
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bit-vector-or(_:BT, _:BT) : =>BT
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Built-in Funcon
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bit-vector-xor(_:BT, _:BT) : =>BT
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/*
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The above four funcons are the natural extensions of funcons from `booleans`
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to `bit-vectors(N)` of the same length.
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*/
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Built-in Funcon
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bit-vector-shift-left(_:BT, _:natural-numbers) : BT
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Built-in Funcon
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bit-vector-logical-shift-right(_:BT, _:natural-numbers) : BT
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Built-in Funcon
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bit-vector-arithmetic-shift-right(_:BT, _:natural-numbers) : BT
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Built-in Funcon
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integer-to-bit-vector(_:integers, N:natural-numbers) : bit-vectors(N)
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/*
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`integer-to-bit-vector(M, N)` converts an integer `M` to a bit-vector of
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length `N`, using Two's Complement representation. If the integer is out of
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range of the representation, it will wrap around (modulo 2^N).
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*/
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Built-in Funcon
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bit-vector-to-integer(_:BT) : =>integers
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/*
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`bit-vector-to-integer(B)` interprets a bit-vector `BV` as an integer
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in Two's Complement representation.
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*/
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Built-in Funcon
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bit-vector-to-natural(_:BT) : =>natural-numbers
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/*
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`bit-vector-to-natural(BV)` interprets a bit-vector `BV` as a natural number
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in unsigned representation.
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*/
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Funcon
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unsigned-bit-vector-maximum(N:natural-numbers) : =>natural-numbers
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~> integer-subtract(integer-power(2, N), 1)
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Funcon
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signed-bit-vector-maximum(N:natural-numbers) : =>integers
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~> integer-subtract(integer-power(2, integer-subtract(N, 1)), 1)
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Funcon
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signed-bit-vector-minimum(N:natural-numbers) : =>integers
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~> integer-negate(integer-power(2, integer-subtract(N, 1)))
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Funcon
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is-in-signed-bit-vector(M:integers, N:natural-numbers) : =>booleans
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~> and(integer-is-less-or-equal(M, signed-bit-vector-maximum(N)),
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integer-is-greater-or-equal(M, signed-bit-vector-minimum(N)))
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Funcon
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is-in-unsigned-bit-vector(M:integers, N:natural-numbers) : =>booleans
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~> and(integer-is-less-or-equal(M, unsigned-bit-vector-maximum(N)),
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integer-is-greater-or-equal(M, 0))
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152
IBAF-cbs/Funcons-beta/Values/Composite/Bits/index.md
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152
IBAF-cbs/Funcons-beta/Values/Composite/Bits/index.md
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@@ -0,0 +1,152 @@
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---
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layout: default
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title: "Bits"
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parent: Composite
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ancestor: Funcons-beta
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---
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[Funcons-beta] : [Bits.cbs]
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-----------------------------
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### Bits and bit vectors
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<div class="highlighter-rouge"><pre class="highlight"><code>[
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<i class="keyword">Type</i> <span class="name"><a href="#Name_bits">bits</a></span>
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<i class="keyword">Datatype</i> <span class="name"><a href="#Name_bit-vectors">bit-vectors</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector">bit-vector</a></span>
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<i class="keyword">Type</i> <span class="name"><a href="#Name_bytes">bytes</a></span> <i class="keyword">Alias</i> <span class="name"><a href="#Name_octets">octets</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-not">bit-vector-not</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-and">bit-vector-and</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-or">bit-vector-or</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-xor">bit-vector-xor</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-shift-left">bit-vector-shift-left</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-logical-shift-right">bit-vector-logical-shift-right</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-arithmetic-shift-right">bit-vector-arithmetic-shift-right</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_integer-to-bit-vector">integer-to-bit-vector</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-to-integer">bit-vector-to-integer</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_bit-vector-to-natural">bit-vector-to-natural</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_unsigned-bit-vector-maximum">unsigned-bit-vector-maximum</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_signed-bit-vector-maximum">signed-bit-vector-maximum</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_signed-bit-vector-minimum">signed-bit-vector-minimum</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_is-in-signed-bit-vector">is-in-signed-bit-vector</a></span>
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<i class="keyword">Funcon</i> <span class="name"><a href="#Name_is-in-unsigned-bit-vector">is-in-unsigned-bit-vector</a></span>
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||||
]</code></pre></div>
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#### Bits
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Type</i>
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<span class="name"><span id="Name_bits">bits</span></span> ~> <span class="name"><a href="../../Primitive/Booleans/index.html#Name_booleans">booleans</a></span></code></pre></div>
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||||
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<code><span class="name"><a href="../../Primitive/Booleans/index.html#Name_false">false</a></span></code> represents the absence of a bit, <code><span class="name"><a href="../../Primitive/Booleans/index.html#Name_true">true</a></span></code> its presence.
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||||
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#### Bit vectors
|
||||
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Datatype</i>
|
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<span class="name"><span id="Name_bit-vectors">bit-vectors</span></span>(<span id="Variable145_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) ::= <span id="Name_bit-vector">bit-vector</span>(_:<span class="name"><a href="#Name_bits">bits</a></span>^<span id="Variable166_N"><i class="var">N</i></span>)</code></pre></div>
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Type</i>
|
||||
<span class="name"><span id="Name_bytes">bytes</span></span> ~> <span class="name"><a href="#Name_bit-vectors">bit-vectors</a></span>(8)
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<i class="keyword">Alias</i>
|
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<span class="name"><span id="Name_octets">octets</span></span> = <span class="name"><a href="#Name_bytes">bytes</a></span></code></pre></div>
|
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<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Meta-variables</i>
|
||||
<span id="PartVariable_BT"><i class="var">BT</i></span> <: <span class="name"><a href="#Name_bit-vectors">bit-vectors</a></span>(_)</code></pre></div>
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
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<span class="name"><span id="Name_bit-vector-not">bit-vector-not</span></span>(_:<span id="Variable234_BT"><i class="var">BT</i></span>) : =><span id="Variable248_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-and">bit-vector-and</span></span>(_:<span id="Variable261_BT"><i class="var">BT</i></span>, _:<span id="Variable272_BT"><i class="var">BT</i></span>) : =><span id="Variable287_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-or">bit-vector-or</span></span>(_:<span id="Variable300_BT"><i class="var">BT</i></span>, _:<span id="Variable311_BT"><i class="var">BT</i></span>) : =><span id="Variable326_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-xor">bit-vector-xor</span></span>(_:<span id="Variable339_BT"><i class="var">BT</i></span>, _:<span id="Variable350_BT"><i class="var">BT</i></span>) : =><span id="Variable365_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
|
||||
The above four funcons are the natural extensions of funcons from <code><span class="name"><a href="../../Primitive/Booleans/index.html#Name_booleans">booleans</a></span></code>
|
||||
to <code><span class="name"><a href="#Name_bit-vectors">bit-vectors</a></span>(<i class="var">N</i>)</code> of the same length.
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-shift-left">bit-vector-shift-left</span></span>(_:<span id="Variable414_BT"><i class="var">BT</i></span>, _:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : <span id="Variable436_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-logical-shift-right">bit-vector-logical-shift-right</span></span>(_:<span id="Variable448_BT"><i class="var">BT</i></span>, _:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : <span id="Variable470_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-arithmetic-shift-right">bit-vector-arithmetic-shift-right</span></span>(_:<span id="Variable482_BT"><i class="var">BT</i></span>, _:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : <span id="Variable504_BT"><i class="var">BT</i></span></code></pre></div>
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_integer-to-bit-vector">integer-to-bit-vector</span></span>(_:<span class="name"><a href="../../Primitive/Integers/index.html#Name_integers">integers</a></span>, <span id="Variable521_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : <span class="name"><a href="#Name_bit-vectors">bit-vectors</a></span>(<span id="Variable537_N"><i class="var">N</i></span>)</code></pre></div>
|
||||
|
||||
<code><span class="name"><a href="#Name_integer-to-bit-vector">integer-to-bit-vector</a></span>(<i class="var">M</i>, <i class="var">N</i>)</code> converts an integer <code><i class="var">M</i></code> to a bit-vector of
|
||||
length <code><i class="var">N</i></code>, using Two's Complement representation. If the integer is out of
|
||||
range of the representation, it will wrap around (modulo 2^N).
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-to-integer">bit-vector-to-integer</span></span>(_:<span id="Variable613_BT"><i class="var">BT</i></span>) : =><span class="name"><a href="../../Primitive/Integers/index.html#Name_integers">integers</a></span></code></pre></div>
|
||||
|
||||
<code><span class="name"><a href="#Name_bit-vector-to-integer">bit-vector-to-integer</a></span>(<i class="var">B</i>)</code> interprets a bit-vector <code><i class="var">BV</i></code> as an integer
|
||||
in Two's Complement representation.
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Built-in</i> <i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_bit-vector-to-natural">bit-vector-to-natural</span></span>(_:<span id="Variable676_BT"><i class="var">BT</i></span>) : =><span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span></code></pre></div>
|
||||
|
||||
<code><span class="name"><a href="#Name_bit-vector-to-natural">bit-vector-to-natural</a></span>(<i class="var">BV</i>)</code> interprets a bit-vector <code><i class="var">BV</i></code> as a natural number
|
||||
in unsigned representation.
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_unsigned-bit-vector-maximum">unsigned-bit-vector-maximum</span></span>(<span id="Variable736_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : =><span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>
|
||||
~> <span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-subtract">integer-subtract</a></span>(<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-power">integer-power</a></span>(2, <a href="#Variable736_N"><i class="var">N</i></a>), 1)</code></pre></div>
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_signed-bit-vector-maximum">signed-bit-vector-maximum</span></span>(<span id="Variable783_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : =><span class="name"><a href="../../Primitive/Integers/index.html#Name_integers">integers</a></span>
|
||||
~> <span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-subtract">integer-subtract</a></span>(<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-power">integer-power</a></span>(2, <span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-subtract">integer-subtract</a></span>(<a href="#Variable783_N"><i class="var">N</i></a>, 1)), 1)</code></pre></div>
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_signed-bit-vector-minimum">signed-bit-vector-minimum</span></span>(<span id="Variable840_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : =><span class="name"><a href="../../Primitive/Integers/index.html#Name_integers">integers</a></span>
|
||||
~> <span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-negate">integer-negate</a></span>(<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-power">integer-power</a></span>(2, <span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-subtract">integer-subtract</a></span>(<a href="#Variable840_N"><i class="var">N</i></a>, 1)))</code></pre></div>
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_is-in-signed-bit-vector">is-in-signed-bit-vector</span></span>(<span id="Variable894_M"><i class="var">M</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_integers">integers</a></span>, <span id="Variable903_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : =><span class="name"><a href="../../Primitive/Booleans/index.html#Name_booleans">booleans</a></span>
|
||||
~> <span class="name"><a href="../../Primitive/Booleans/index.html#Name_and">and</a></span>(<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-is-less-or-equal">integer-is-less-or-equal</a></span>(<a href="#Variable894_M"><i class="var">M</i></a>, <span class="name"><a href="#Name_signed-bit-vector-maximum">signed-bit-vector-maximum</a></span>(<a href="#Variable903_N"><i class="var">N</i></a>)),
|
||||
<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-is-greater-or-equal">integer-is-greater-or-equal</a></span>(<a href="#Variable894_M"><i class="var">M</i></a>, <span class="name"><a href="#Name_signed-bit-vector-minimum">signed-bit-vector-minimum</a></span>(<a href="#Variable903_N"><i class="var">N</i></a>)))</code></pre></div>
|
||||
|
||||
|
||||
<div class="highlighter-rouge"><pre class="highlight"><code><i class="keyword">Funcon</i>
|
||||
<span class="name"><span id="Name_is-in-unsigned-bit-vector">is-in-unsigned-bit-vector</span></span>(<span id="Variable984_M"><i class="var">M</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_integers">integers</a></span>, <span id="Variable993_N"><i class="var">N</i></span>:<span class="name"><a href="../../Primitive/Integers/index.html#Name_natural-numbers">natural-numbers</a></span>) : =><span class="name"><a href="../../Primitive/Booleans/index.html#Name_booleans">booleans</a></span>
|
||||
~> <span class="name"><a href="../../Primitive/Booleans/index.html#Name_and">and</a></span>(<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-is-less-or-equal">integer-is-less-or-equal</a></span>(<a href="#Variable984_M"><i class="var">M</i></a>, <span class="name"><a href="#Name_unsigned-bit-vector-maximum">unsigned-bit-vector-maximum</a></span>(<a href="#Variable993_N"><i class="var">N</i></a>)),
|
||||
<span class="name"><a href="../../Primitive/Integers/index.html#Name_integer-is-greater-or-equal">integer-is-greater-or-equal</a></span>(<a href="#Variable984_M"><i class="var">M</i></a>, 0))</code></pre></div>
|
||||
|
||||
|
||||
|
||||
____
|
||||
|
||||
From the [PLanCompS Project] | [CBS-beta issues...] | [Suggest an improvement...]
|
||||
|
||||
[Bits.cbs]: Bits.cbs
|
||||
"CBS SOURCE FILE"
|
||||
[Funcons-beta]: /CBS-beta/docs/Funcons-beta
|
||||
"FUNCONS-BETA"
|
||||
[Unstable-Funcons-beta]: /CBS-beta/docs/Unstable-Funcons-beta
|
||||
"UNSTABLE-FUNCONS-BETA"
|
||||
[Languages-beta]: /CBS-beta/docs/Languages-beta
|
||||
"LANGUAGES-BETA"
|
||||
[Unstable-Languages-beta]: /CBS-beta/docs/Unstable-Languages-beta
|
||||
"UNSTABLE-LANGUAGES-BETA"
|
||||
[CBS-beta]: /CBS-beta "CBS-BETA"
|
||||
[PLanCompS Project]: https://plancomps.github.io
|
||||
"PROGRAMMING LANGUAGE COMPONENTS AND SPECIFICATIONS PROJECT HOME PAGE"
|
||||
[CBS-beta issues...]: https://github.com/plancomps/CBS-beta/issues
|
||||
"CBS-BETA ISSUE REPORTS ON GITHUB"
|
||||
[Suggest an improvement...]: mailto:plancomps@gmail.com?Subject=CBS-beta%20-%20comment&Body=Re%3A%20CBS-beta%20specification%20at%20Values/Composite/Bits/Bits.cbs%0A%0AComment/Query/Issue/Suggestion%3A%0A%0A%0ASignature%3A%0A
|
||||
"GENERATE AN EMAIL TEMPLATE"
|
||||
Reference in New Issue
Block a user