Function Definitions

A Refal program consists of function definitions, each definition having either of the two forms:

    Fname \{ Snt₁; Snt₂; ... Snt_n; };
    Fname  { Snt₁; Snt₂; ... Snt_n; };

where Fname is the name of the function being defined, and Snt₁, Snt₂, ..., Snt_n are sentences. (Being, at present, of no importance, the subtle difference between \{ and { will be explained later.)

Each sentence Snt_j is of the form P_j R_j, with P_j being the input pattern of the sentence, and R_j the rest of the sentence. A function definition specifies the way in which the calls to the function are to be evaluated. Suppose a call

    <Fname Re>

to the function Fname is to be evaluated. Then the result expression Re is evaluated. If a ground expression Ge is returned, an attempt is made to match Ge against the input patterns P₁, P₂, ..., P_n, in order to find the first pattern P_j such that matching Ge against P succeeds. Let Env be the "first" variant of matching Ge against P. Then the rest R_j is evaluated in the environment Env. If a ground expression Ge' is returned, this expression is taken to be the result of evaluating the function call.

For the time being, for the sake of simplicity, each rest R_j will be assumed to be of the form

    = Re_j

where Re_j is a result expression. A rest of the form = Re is a special case of right hand side. Evaluating a right hand side = Re_j amounts to evaluating the result expression Re_j. If the evaluation of Re_j results in returning a ground expression Ge, then Ge is taken to be the result of the whole right hand side.

For example, let us consider a function SumSq computing the sum of the squares of two numbers. Here is the definition of this function written in traditional notation

    SumSq(X,Y) = X*X + Y*Y

which may be rewritten in Refal in the following way:

$func SumSq sX sY = sZ;

SumSq
 {
 sX sY = <Add <Mult sX sX> <Mult sY sY>>;
 };

It should be noted that the declaration of a function must precede the function's definition as well as the calls to the function, since the information provided by the declaration is necessary for compiling the function's definition as well as the calls to the function.

If the function declaration has the form

$func Fname Fin = Fout;

the compiler verifies that the input patterns P₁, P₂, ..., P_n are "instances" of the input format Fin, whereas all the rests R₁, R₂, ..., R_n are certain to return ground expressions satisfying the output format Fout.