An Analysis of Parameter Evaluation of Recursive Procedures

A class of recursive program schemata PR is defined abstracting ALGOL-like procedures. Four generic types of parameter evaluation are considered; call by value, PRV, call by copy, PRc, call by reference, PRr, and call by name, PRj. Two other types of theoretical interest are also considered: "normal evaluation", Ffin, a non-side effect, evaluation postponement mechansim and call by ouote, PRq, an extension of call by name with all assignments to formals Uf evaluated. For evaluation method x, augmentation with global variables, PRx„, and augmentation with a finite number of markers, P^ are also considered. The results include. Rc 5 Rr s Rn R*C) " RKn < Rj s Rjq Rjn a Rq where x = v, c, r, and n. The results are correlated with the notion of fixed point computation and although call by value, copy and reference do not, in general, compute the least fixed point, for any functional an equivalent one may be found for which these three do compute the least fixed point. That call by name is stronger than the othe generic evaluation mechanisms derives not from postponing evaluation, but from repeated evaluation, i.e. side effects. The last two terms in the relation list are "universal". Additionally, its shown that if PRj ■ PRjn and if PRj they cannot be constructively equivalent. PRq, then An abstract model of parameter evaluation is developed and the constituent components of parameter evaluation are isolated. These help to characterize what impact choices of parameter evaluation have on the language in general. This understanding motivates the class PRq and binds our analysis with that of the lambdo calculus models. The question of recognizing when two parameter evaluation mechanisms coincide is studied, i.e. when two mechanisms always compute the same resrlt for the same schema. The general problem is not partially decidable for seperable evaluation mfichanisms. For free recursive schemata employing the generic mechanisms, the coincidence question is decidable. A discussion of the utility of such analysis and some thoughts on future directions for research are included.