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This can be done using the \lstinline+when+ operator, that samples a stream according to a condition, either a boolean or an enumerated value. If \texttt{x} is a stream that is always present, then \lstinline+x when c+ (resp \lstinline+x when C(y)+) is a stream equal to \texttt{x} but only present when \texttt{c} is true (resp. \lstinline{y = C}). \lstinline+x whenot c+ is a shortcut for \lstinline+x when (not c)+. The \texttt{split} operator allows to sample a stream according to all possible values, i.e. \lstinline+split c (x) = x when c, x whenot c+ if \texttt{x} is a boolean and \lstinline+split y (x) = x when C1(y), .., x when Cp(y)+ if \texttt{y} has an enumerated type defined by \lstinline+type t = C1 | ... | Cp+. + +\[ +\begin{streams}{3} + \text{\lstinline|x|} & x_1 & x_2 & x_3 \\ + \hline + \text{\lstinline|c|} & true & false & true \\ + \hline + \text{\lstinline|x when c|} & x_1 & . & x_3 \\ + \hline + \text{\lstinline|y|} & C' & C & C' \\ + \hline + \text{\lstinline|x when C(y)|} & . & x_2 & . \\ +\end{streams} +\] + +The clock of an expression (resp. a stream) is a boolean stream that defines the instants when it is present. The clock of the streams that are always present is called \texttt{base} or \texttt{.}. If \texttt{x} has clock \texttt{ck}, denoted \lstinline+x :: ck+, then \lstinline+x when c+ has clock \lstinline{ck on c}. + +The \lstinline{merge} operator joins slow streams to create a faster stream. +\[ +\begin{streams}{3} + \text{\lstinline|c|} & true & false & true \\ + \hline + \text{\lstinline|x|} & x_1 & . & x_3 \\ + \hline + \text{\lstinline|y|} & . & y_2 & . \\ + \hline + \text{\lstinline|merge c x y|} & x_1 & y_2 & x_3 \\ +\end{streams} +\] +\lstinline{merge} expects complementary streams. If \lstinline{z = merge c x y} and \lstinline+z :: ck+, then we must have \lstinline+x :: ck on c+ and \lstinline+y :: ck onot c+. It is thus different from \lstinline+if c then x else y+ that expects all its arguments to have the same clock. An analysis pass called \emph{clock calculus} checks that these conditions are met. + +Here is a first example of a bidirectional counter: +\begin{lstlisting} +type modes = Up | Down + +node two(m:modes;v:int) returns (o:int) + var x:int; + x_up:int :: . on Up(m); + x_down:int :: . on Down(m); +let + o = 0 fby x; + x_up = o when Up(m) + 1; + x_down = o when Down(m) + 1; + x = merge m (Up -> x_up) (Down -> x_down) +tel +\end{lstlisting} +Note that clocks are inferred by the compiler, so the clocking annotations are optional. + +It is important to understand the interaction between sampling and delays. The value of a delay only changes when it is activated, that is, when its clock is true. As soon as a function \texttt{f} contains some delay operator, sampling its inputs is not equivalent to sampling its outputs, that is, \lstinline+f(x when c)+ $\neq$ \lstinline+(f x) when c+. +\[ +\begin{streams}{4} + \text{\lstinline|c|} & true & false & true & false \\ + \hline + \text{\lstinline|counter(1)|} & 0 & 1 & 2 & 3 \\ + \hline + \text{\lstinline|counter(1) when c|} & 0 & . & 2 & . \\ + \hline + \text{\lstinline|counter(1 when c)|} & 0 & . & 1 & .\\ +\end{streams} +\] + \subsection{Declarations} \label{sec:declarations}