Infix Notation Rewriting

For readability and convenience, infix notation such as x * y is recognized and translated to Block-Diagram Normal Form (BDNF) as x,y:*, i.e., the parallel signals x and y are fed to the two-input multiplier *. Similarly, the notation f(x) is rewritten to x:f if f is a primitive function. (More generally, f(x) is first rewritten as possible using pattern-matching (§2.23) and definition-expansion (§2.7)). Postfix operators such as ' are handled similarly. More formally, we can write

$$\begin{tabular}{rcrcl} \texttt{x * y} & $\to$\ & \texttt{x,y} &\!\texttt{:}\!& \texttt{*} \\ \texttt{x / y} & $\to$\ & \texttt{x,y} &\!\texttt{:}\!& \texttt{/} \\ \texttt{x \^{} y} & $\to$\ & \texttt{x,y} &\!\texttt{:}\!& \texttt{\^} \\ \texttt{pow(x,y)} & $\to$\ & \texttt{x,y} &\!\texttt{:}\!& \texttt{\^} \\ \texttt{x @ y} & $\to$\ & \texttt{x,y} &\!\texttt{:}\!& \texttt{@} \\ \texttt{x'} & $\to$\ & \texttt{ x} &\!\texttt{:}\!& \texttt{mem} \\ \texttt{f(x)} & $\to$\ & \texttt{ x} &\!\texttt{:}\!& \texttt{f} \\ \texttt{f(x,y)} & $\to$\ & \texttt{x,y} &\!\texttt{:}\!& \texttt{f}\\ \texttt{f(x,y,z)} & $\to$\ & \texttt{x,y,z} &\!\texttt{:}\!& \texttt{f} \end{tabular}$$

and so on.