By M. Alpuente, M. Falaschi, G. Moreno, G. Vidal (auth.), Michael Hanus, Jan Heering, Karl Meinke (eds.)

ISBN-10: 3540634592

ISBN-13: 9783540634591

This publication constitutes the refereed complaints of the sixth overseas convention on Algebraic and good judgment Programming, ALP '97 and the third foreign Workshop on Higher-Order Algebra, common sense and time period Rewriting, HOA '97, held together in Southampton, united kingdom, in September 1997.

The 18 revised complete papers offered within the publication have been chosen from 31 submissions. the quantity is split in sections on sensible and good judgment programming, higher-order tools, time period rewriting, varieties, lambda-calculus, and theorem proving methods.

**Read or Download Algebraic and Logic Programming: 6th International Joint Conference ALP '97 — HOA '97 Southampton, UK, September 3–5, 1997 Proceedings PDF**

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**Additional info for Algebraic and Logic Programming: 6th International Joint Conference ALP '97 — HOA '97 Southampton, UK, September 3–5, 1997 Proceedings**

**Example text**

The calls-to relation contains the infinite chain p(X, b) p(a, b) ~ p(a, b) ~ p(a, b) ~ ... which can be observed in the binary unfoldings through the clause p( a, b) *-- p( a, b). 37 5 Abstract Interpretation Termination analysis is based on descriptions of the binary unfoldings of a program called abstract binary unfoldings. To determine that a goal G does not have an infinite computation with bin_unf(P), the analysis derives a (finite) set of abstract binary unfoldings which approximates the (possibly infinite) set of binary unfoldings which can occur in the computations with G.

For a term t containing a variable X with size X + 1, it means that the size of any instance of t is 1 plus the size of the term bound to X. Definltionl0. (symbolic norm) A symbolic norm is a function If"II: T(,U, I)) ~ T(,U', 12) such that c + ~=o Iltll = adltdl t if t = f ( t l , . , . , tn) if t is a variable where c and a l , . . , a~ are constants depending only on f / n . Symbolic norms can be applied to an arbitrary syntactic object s simply by replacing the terms occurring in s by their sizes.

Namely, t9 is a ground substitution which satisfies the constraint It. A syntactic CLP(SN) object sl is less instantiated than an object s2, denoted Sl -~ s~ if [sl] ~ [s2] and st = s2 if s~ _ s2 and s2 _ sl. The sets of CLP(SN) binary clauses and CLP(SN) atoms modulo this notion of equivalence are denoted ~SN and AtomsN respectively. Intuitively, an abstract (constrained) object lr describes the set of concrete objects with terms, the sizes of which, satisfy the constraints in ~r. For example a constrained atom of the form p(A, B, C) ~-- {A < B, C = B "4- 1} describes a concrete atom p(tl, t2, t3) if the size of tl is less than the size of t2 and the size of t3 is equal to the size of t2 plus 1.

### Algebraic and Logic Programming: 6th International Joint Conference ALP '97 — HOA '97 Southampton, UK, September 3–5, 1997 Proceedings by M. Alpuente, M. Falaschi, G. Moreno, G. Vidal (auth.), Michael Hanus, Jan Heering, Karl Meinke (eds.)

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