mirror of
https://github.com/GaloisInc/cryptol.git
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114 lines
3.3 KiB
Markdown
114 lines
3.3 KiB
Markdown
Comparisons and Ordering
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------------------------
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(==) : {a} (Cmp a) => a -> a -> Bit
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(!=) : {a} (Cmp a) => a -> a -> Bit
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(===) : {a,b} (Cmp b) => (a -> b) -> (a -> b) -> a -> Bit
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(!==) : {a,b} (Cmp b) => (a -> b) -> (a -> b) -> a -> Bit
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(<) : {a} (Cmp a) => a -> a -> Bit
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(>) : {a} (Cmp a) => a -> a -> Bit
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(<=) : {a} (Cmp a) => a -> a -> Bit
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(>=) : {a} (Cmp a) => a -> a -> Bit
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min : {a} (Cmp a) => a -> a -> a
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max : {a} (Cmp a) => a -> a -> a
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instance Cmp Bit
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// No instance for functions.
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instance (Cmp a, fin n) => Cmp [n] a
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instance (Cmp a, Cmp b) => Cmp (a,b)
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instance (Cmp a, Cmp b) => Cmp { x : a, y : b }
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Arithmetic
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----------
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(+) : {a} (Arith a) => a -> a -> a
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(-) : {a} (Arith a) => a -> a -> a
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(*) : {a} (Arith a) => a -> a -> a
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(/) : {a} (Arith a) => a -> a -> a
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(%) : {a} (Arith a) => a -> a -> a
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(^^) : {a} (Arith a) => a -> a -> a
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// No instance for `Bit`.
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instance (fin n) => Arith ( [n] Bit)
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instance (Arith a) => Arith ( [n] a)
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instance (Arith b) => Arith (a -> b)
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instance (Arith a, Arith b) => Arith (a,b)
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instance (Arith a, Arith b) => Arith { x : a, y : b }
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Note that because there is no instances for `Arith Bit`
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the top two instances do not actually overlap.
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Boolean
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-------
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False : Bit
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True : Bit
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zero : a
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(&&) : a -> a -> a
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(||) : a -> a -> a
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(^) : a -> a -> a
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(~) : a -> a
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Sequences
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---------
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length : {n,a,m} (m >= width n) => [n]a -> [m]
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join : {parts,ench,a} (fin each) => [parts][each]a -> [parts * each]a
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split : {parts,each,a} (fin each) => [parts * each]a -> [parts][each]a
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(#) : {front,back,a} (fin front) => [front]a -> [back]a -> [front + back]a
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splitAt : {front,back,a} (fin front) => [from + back] a -> ([front] a, [back] a)
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reverse : {n,a} (fin n) => [n]a -> [n]a
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transpose : {n,m,a} [n][m]a -> [m][n]a
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(@) : {n,a,m} [n]a -> [m] -> a
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(@@) : {n,a,m,i} [n]a -> [m][i] -> [m]a
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(!) : {n,a,m} (fin n) => [n]a -> [m] -> a
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(!!) : {n,a,m,i} (fin n) => [n]a -> [m][i] -> [m]a
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update : {n,a,m} (fin m) => [n]a -> [m] -> a -> [n]a
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updateEnd : {n,a,m} (fin n, fin m) => [n]a -> [m] -> a -> [n]a
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updates : {n,a,m,d} (fin m, fin d) => [n]a -> [d][m] -> [d]a -> [n]a
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updatesEnd : {n,a,m,d} (fin n, fin m, fin d) => [n]a -> [d][m] -> [d]a -> [n]a
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// Abbreviations
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groupBy n = split`{each = n}
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tail n = splitAt`{front = 1}.1
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take n = splitAt`{front = n}.0
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drop n = splitAt`{front = n}.1
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/* Also, `length` is not really needed:
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length : {n,a,m} (m >= width n) => [n]a -> [m]
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length _ = `n
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*/
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Shift And Rotate
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----------------
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New types:
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(<<) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a
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(>>) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a
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(<<<) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a
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(>>>) : {n,a,m} (fin n) => [n]a -> [m] -> [n]a
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Random Values
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-------------
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random : {a} => [256] -> a
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Debugging
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---------
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undefined : {a} a
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error : {n a} [n][8] -> a
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trace : {n, a, b} [n][8] -> a -> b -> b
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traceVal : {n, a} [n][8] -> a -> a
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