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The computation mechanism of functional logic languages is based on narrowing, a generalization of term-rewriting where unification replaces matching: both the rewrite rule and the term to be rewritten can be instantiated.
Decreasingness is a property which exactly captures the finiteness of the recursive evaluation of functions in conditional term-rewriting systems [Dershowitz 1995] (see Appendix A.
Variants of this relation are used in termination proofs for term-rewriting systems [Dershowitz and Jouannaud 1991] and for ensuring local termination of partial deduction [Bol 1993].
Now we discuss the relation to some works of partial evaluation in functional programming, term-rewriting systems, and partial deduction of logic programs.
Earlier work on partial evaluation of term-rewriting systems has focused on self-application rather than on the termination or the correctness of the transformation [Bondorf 1988; 1989].
The work by Miniussi and Sherman [1996] aims to improve the efficiency of a term-rewriting implementation of equational programs by tackling the problems associated to the partial evaluation of an imperative, intermediate code that the implementation uses for the equations.