Formal Parameter Substitution⁹

Formal parameters are block diagrams substituted where they occur in the function definition, which is then evaluated. Any unused parameters are replaced by signal inputs.

For example, given

  f(x) = x + x;

``f(2)'' gives 4, and f(_) gives ``_,_ : +,'' (not ``_ <: _,_:+'' or ``_ : *(2)''). Passing in a two-input block diagram, such as ``f(*),'' yields the four-input block diagram ``_,_,_,_ : *, * : +.'' Writing simply ``f'' compiles to a two-input adder, following the rule for unused parameters.

As another example of function structure depending on argument type, given

  f(x) = 1, 2 : _, _, x;

``process = f;'' defines the block diagram ``1,2,_,'' but ``process = f(_);'' expands to ``1,2 : _,_,_'' and fails to compile (two outputs into three inputs). Desired structure can often be enforced by adding parentheses, e.g.,

f(x) = (1, 2 : _, _), x;

To ensure that a function expansion has exactly $N$ input signals, it is good to start the function definition with a bus of size $N$ :

  f(x) = _ : (1, 2 : _, _), x; // f and f(_) compile but not f(3)

or si.bus(N) more generally. This way, when the function is used in an unintended manner, compilation is more likely to fail and alert the user.