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94 lines
2.8 KiB
TeX
94 lines
2.8 KiB
TeX
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\chapter{Cryptol primitive functions}
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\commentout{
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\begin{code}
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primsPlaceHolder=1;
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\end{code}
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}
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\paragraph*{Bitwise operations}
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\begin{Verbatim}
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&&, ||, ^ : {a} a -> a -> a
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~ : {a} a -> a
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\end{Verbatim}
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\paragraph*{Comparisons}
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\begin{Verbatim}
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==, != : {a} (Cmp a) => a -> a -> Bit
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<, >, <=, >= : {a} (Cmp a) => [a] -> [a] -> Bit
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\end{Verbatim}
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\paragraph*{Arithmetic}
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\begin{Verbatim}
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+, -, *, /, %, ** : {a} (Arith a) => a -> a -> a
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lg2 : {a, b} (Arith a) => a -> a
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\end{Verbatim}
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% negate : {a b} (a >= 1) => [a]b -> [a]b
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\paragraph*{Polynomial arithmetic}
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\begin{Verbatim}
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pdiv : {a, b} (fin a, fin b) => [a] -> [b] -> [a]
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pmod : {a, b} (fin a, fin b) => [a] -> [1 + b] -> [b]
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pmult : {a, b} (fin a, fin b) => [a] -> [b] -> [max 1 (a + b) - 1]
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\end{Verbatim}
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\paragraph*{Sequences}
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\begin{Verbatim}
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take : {front, back, elem} (fin front)
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=> [front + back]elem -> [front]elem
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drop : {front, back, elem} (fin front)
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=> [front + back]elem -> [front]elem
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tail : {a, b} [a+1]b -> [a]b
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# : {a, b, c} (fin a) => ([a]b,[c]b) -> [a+c]b
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join : {parts, each, a} (fin each)
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=> [parts][each]a -> [parts * each]a
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groupBy : {each, parts, elem} (fin each)
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=> [parts * each]elem -> [parts][each]elem
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splitBy : {parts, each, elem}
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=> [parts * each]elem -> [parts][each]elem
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reverse : {a, b} (fin a) => [a]b -> [a]b
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@ : {a, b, c} ([a]b,[c]) -> b
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! : {a, b, c} (fin a) => ([a]b,[c]) -> b
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@@ : {a, b, c, d} ([a]b,[c][d]) -> [c]b
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!! : {a, b, c, d} (fin a) => ([a]b,[c][d]) -> [c]b
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width : {a, b, c} (c >= width a) => [a]b -> [c]
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\end{Verbatim}
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\paragraph*{Shifting, rotating}
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\begin{Verbatim}
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>>, <<, >>>, <<< : {a b c} (fin a,c >= lg2 a)
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=> ([a]b,[c]) -> [a]b
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\end{Verbatim}
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\paragraph*{Miscellaneous}
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\begin{Verbatim}
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zero : {a} a
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transpose : {a, b, c} [a][b]c -> [b][a]c
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min, max : {a} (fin a) => ([a],[a]) -> [a]
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\end{Verbatim}
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% parity : {a} (fin a) => [a] -> Bit
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\paragraph*{Representing exceptions}
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\begin{Verbatim}
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error : {a, b} [a][8] -> b
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undefined : {a} a
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\end{Verbatim}
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\todo[inline]{\texttt{error} and \texttt{undefined} are not covered in
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the book at the moment.}
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\todo[inline]{What is the state of debugging (\texttt{trace},
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\texttt{ASSERT}), randomness (\texttt{random}), and pretty-printing
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(\texttt{format}) built-ins?}
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%\paragraph*{Debugging}
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%\begin{Verbatim}
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% trace : {a b c} ([a][8],b,c) -> c
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% ASSERT : {a b} (Bit,[a][8],b) -> b
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%\end{Verbatim}
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%\paragraph*{Generating random numbers}
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%\begin{Verbatim}
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% random : {a b} (32 >= a) => [a] -> b
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%\end{Verbatim}
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%\paragraph*{Pretty printing}
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%\begin{Verbatim}
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% format
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%\end{Verbatim}
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%%% Local Variables:
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%%% mode: latex
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%%% TeX-master: "../main/Cryptol"
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%%% End:
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