A symbolic version of an operation on values is a corresponding operation on program texts. For example, symbolic composition of two programs p, q yields a program whose meaning is the (mathematical) composition of the meanings of p and q. Another example is symbolic specialization of a function to a known first argument value. This operation, given the first argument, transforms a two-input program into an equivalent one-input program. Computability of both of these symbolic operations has long been established in recursive function theory [12,16]; the latter is known as Kleene's "s-m-n" theorem, also known as partial evaluation. In addition to computability we are concerned with efficient symbolic operations, in particular applications of the two just mentioned to compiling and compiler generation. Several examples of symbolic composition are given, culminating in nontrivial applications to compiler generation [14], [18]. Partial evaluation has recently become the subject of conside...

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