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34
Total Correctness by Local Improvement in Program Transformation
 In Proceedings of the 22nd Annual ACM SIGPLANSIGACT Symposium on Principles of Programming Languages (POPL
, 1995
"... The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfoldfold method. Unfortunately the unfoldfold method itself guarantees neither improvement in efficiency nor totalcorrectness. The c ..."
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Cited by 20 (3 self)
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The goal of program transformation is to improve efficiency while preserving meaning. One of the best known transformation techniques is Burstall and Darlington's unfoldfold method. Unfortunately the unfoldfold method itself guarantees neither improvement in efficiency nor totalcorrectness. The correctness problem for unfoldfold is an instance of a strictly more general problem: transformation by locally equivalencepreserving steps does not necessarily preserve (global) equivalence. This paper presents a condition for the total correctness of transformations on recursive programs, which, for the first time, deals with higherorder functional languages (both strict and nonstrict) including lazy data structures. The main technical result is an improvement theorem which says that if the local transformation steps are guided by certain optimisation concerns (a fairly natural condition for a transformation), then correctness of the transformation follows. The improvement theorem make...
A Transformation System for Lazy Functional Logic Programs
, 1999
"... Needed narrowing is a complete operational principle for modern declarative languages which integrate the best features of (lazy) functional and logic programming. We define a transformation methodology for functional logic programs based on needed narrowing. We provide (strong) correctness results ..."
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Cited by 18 (12 self)
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Needed narrowing is a complete operational principle for modern declarative languages which integrate the best features of (lazy) functional and logic programming. We define a transformation methodology for functional logic programs based on needed narrowing. We provide (strong) correctness results for the transformation system w.r.t. the set of computed values and answer substitutions and show that the prominent properties of needed narrowing  namely, the optimality w.r.t. the length of derivations and the number of computed solutions  carry over to the transformation process and the transformed programs. We illustrate the power of the system by taking on in our setting two wellknown transformation strategies (composition and tupling). We also provide an implementation of the transformation system which, by means of some experimental results, highlights the benefits of our approach.
Sharing of Computations
, 1993
"... This report is a revised version of my thesis of the same title, which was accepted for the Ph.D. degree in Computer Science at University of Aarhus, Denmark, in June 1993 ..."
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Cited by 15 (3 self)
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This report is a revised version of my thesis of the same title, which was accepted for the Ph.D. degree in Computer Science at University of Aarhus, Denmark, in June 1993
Transformation Rules for Locally Stratified Constraint Logic Programs
, 2004
"... We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally strati ed and, thus, it has a unique perfect model. We give sucient conditions which ensure that the proposed set of transformation rules preserves the perfect model of ..."
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Cited by 14 (13 self)
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We propose a set of transformation rules for constraint logic programs with negation. We assume that every program is locally strati ed and, thus, it has a unique perfect model. We give sucient conditions which ensure that the proposed set of transformation rules preserves the perfect model of the programs. Our rules extend in some respects the rules for logic programs and constraint logic programs already considered in the literature and, in particular, they include a rule for unfolding a clause with respect to a negative literal.
Beyond TamakiSato Style Unfold/Fold Transformations for Normal Logic Programs
 IN ASIAN, LNCS 1742
, 1999
"... Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs allow only TamakiSato style folding using clauses from a previous program in the transformation sequence: i.e., they fold using a singl ..."
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Cited by 11 (3 self)
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Unfold/fold transformation systems for logic programs have been extensively investigated. Existing unfold/fold transformation systems for normal logic programs allow only TamakiSato style folding using clauses from a previous program in the transformation sequence: i.e., they fold using a single, nonrecursive clause. In this paper we present a transformation system that permits folding in the presence of recursion, disjunction, as well as negation. We show that the transformations are correct with respect to various semantics of negation including the wellfounded model and stable model semantics.
Simultaneous Replacement in Normal Programs
, 1993
"... The simultaneous replacement transformation operation, is here defined and studied wrt normal programs. We give applicability conditions able to ensure the correctness of the operation wrt the set of logical consequences of the completed database. We consider separately the cases in which the underl ..."
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Cited by 10 (4 self)
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The simultaneous replacement transformation operation, is here defined and studied wrt normal programs. We give applicability conditions able to ensure the correctness of the operation wrt the set of logical consequences of the completed database. We consider separately the cases in which the underlying language is infinite and finite; in this latter case we also distinguish according to the kind of domain closure axioms adopted. As corollaries we obtain results for Fitting's and Kunen's semantics. We also show how simultaneous replacement can mimic other transformation operations such as thinning, fattening and folding, thus producing applicability conditions for them too.
Unfold/fold transformations preserving termination properties. To appear as a technical report from DAIMI
, 1992
"... Abstract. The unfold/fold framework constitutes the spine of many program transformation strategies. However, by unrestricted use of folding the target program may terminate less often than the source program. Several authors have investigated the problem of setting up conditions of syntactic nature ..."
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Cited by 10 (1 self)
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Abstract. The unfold/fold framework constitutes the spine of many program transformation strategies. However, by unrestricted use of folding the target program may terminate less often than the source program. Several authors have investigated the problem of setting up conditions of syntactic nature, i.e. not based on some wellfounded ordering of the arguments, which guarantee preservation of termination properties. These conditions are typically formulated in a way which makes it hard to grasp the basic intuition why they work, and in a way which makes it hard to give elegant proofs of correctness. The aim of this paper will be to give a more unified treatment by setting up a model which enables us to reason about termination preservation in a cleaner and more algebraic fashion. The model resembles a logic language and is parametrized with respect to evaluation order, but it should not be too difficult to transfer the ideas to other languages. 1
Replacement Can Preserve Termination
"... We consider the replacement transformation operation, a very general and powerful transformation, and study under which conditions it preserves universal termination besides computed answer substitutions. With this safe replacement we can significantly extend the safe unfold/fold transformation sequ ..."
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Cited by 9 (3 self)
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We consider the replacement transformation operation, a very general and powerful transformation, and study under which conditions it preserves universal termination besides computed answer substitutions. With this safe replacement we can significantly extend the safe unfold/fold transformation sequence presented in [11]. By exploiting typing information, more useful conditions can be defined and we may deal with some special cases of replacement very common in practice, namely switching two atoms in the body of a clause and the associativity of a predicate. This is a first step in the direction of exploiting a Pre/Post specification on the intended use of the program to be transformed. Such specification can restrict the instances of queries and clauses to be considered and then relax the applicability conditions on the transformation operations.
Programs without Failures
 Proceedings LOPSTR'97, Lecture Notes in Computer Science
, 1997
"... . We try to formalize the intuitive reasoning which we normally use to get convinced that a query has successful LDderivations in a program. To this purpose we define the class of programs and queries without failures which have the property of not having finitely failing derivations. Such property ..."
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Cited by 6 (2 self)
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. We try to formalize the intuitive reasoning which we normally use to get convinced that a query has successful LDderivations in a program. To this purpose we define the class of programs and queries without failures which have the property of not having finitely failing derivations. Such property is simple to verify, it is preserved through leftmost unfolding and it can be useful both in verifying properties of logic programs and in program transformation. The class of programs without failures is very restricted but in program transformations it is sufficient that only some predicates in the program are in the class. Keywords and Phrases: finitely failing derivations, program transformation, program verification 1 Introduction Logic programming is a declarative paradigm. This pleasant characteristic allows one to ignore the computation and simply define which are its desired results. But, when queried through a Prolog interpreter, logic definitions are performed with backtracking...
Correctness of Logic Program Transformations Based on Existential Termination
 Proceedings of the 1995 International Logic Programming Symposium (ILPS '95
, 1995
"... We study the relationships between the correctness of logic program transformation and program termination. We consider definite programs and we identify some `invariants' of the program transformation process. The validity of these invariants ensures the preservation of the success set semantics, p ..."
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Cited by 5 (4 self)
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We study the relationships between the correctness of logic program transformation and program termination. We consider definite programs and we identify some `invariants' of the program transformation process. The validity of these invariants ensures the preservation of the success set semantics, provided that the existential termination of the initial program implies the existential termination of the final program. We also identify invariants for the preservation of the finite failure set semantics. We consider four very general transformation rules: definition introduction, definition elimination, iffreplacement, and finite failure. Many versions of the transformation rules proposed in the literature, including unfolding, folding, and goal replacement, are instances of the iffreplacement rule. By using our proposed invariants which are based on Clark completion, we prove, for our transformation rules, various results concerning the preservation of both the success set and finite ...