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Total Correctness by Local Improvement in the Transformation of Functional Programs
 ACM Transactions on Programming Languages and Systems
, 1996
"... ion. A common form of transformation, which is easily justified by appealing to reversibility, is abstraction. The abstraction transformation lifts some instances of subexpressions from the righthand sides of a set of definitions and replaces them with function calls for some new functions. The ab ..."
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Cited by 61 (6 self)
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ion. A common form of transformation, which is easily justified by appealing to reversibility, is abstraction. The abstraction transformation lifts some instances of subexpressions from the righthand sides of a set of definitions and replaces them with function calls for some new functions. The abstraction process can be used in conjunction with a callbyneed implementation to avoid repeated evaluation of subexpressions. A wellknown example is Hughes' supercombinator abstraction [Hughes 1982]. Another form of abstraction which is common in program transformation is syntactic generalization in which an expression e is replaced by a function call g e 1 : : : e n , where g is a new function defined by g x 1 : : : xn \Delta = e 0 , such that e j e 0 f e 1 : : : e n= x 1 : : : xn g. General statements about abstractions and their correctness are notationally rather complex. In practice we have found it is easier to appeal to a reversibility argument on a casebycase basis than...
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...
Perfect Model Checking via Unfold/Fold Transformations
 In Computational Logic, LNCS 1861
, 2000
"... We show how program transformation rules and strategies may be used for proving the satisfiability of first order formulas in some classes of models. In particular, we propose a technique for showing that a closed first order formula ' holds in the perfect model M(P ) of a logic program P with local ..."
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Cited by 10 (7 self)
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We show how program transformation rules and strategies may be used for proving the satisfiability of first order formulas in some classes of models. In particular, we propose a technique for showing that a closed first order formula ' holds in the perfect model M(P ) of a logic program P with locally stratified negation. This property is denoted by M(P ) j= '. For this purpose we consider a new version of the unfold/fold transformation rules and we show that this version preserves the perfect model semantics. Our proof method, called unfold/fold proof method, shows M(P ) j= ' by: (i) introducing a new predicate symbol f and constructing a conjunction F (f ; ') of clauses such that M(P ) j= ' i M(P ^ F (f ; ')) j= f , and then (ii) transforming the program P ^F (f ; ') into a new program of the form Q^f , for some conjunction Q of clauses. We also present a strategy for applying our unfold/fold rules in a semiautomatic way. Our strategy may or may not terminate, depending on t...
Automatic Derivation of Logic Programs by Transformation
 Course notes for ESSLLI
, 2000
"... We present the program transformation methodology for the automatic development of logic programs based on the rules + strategies approach. We consider both definite programs and normal programs and we present the basic transformation rules and strategies which are described in the literature. To il ..."
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Cited by 1 (0 self)
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We present the program transformation methodology for the automatic development of logic programs based on the rules + strategies approach. We consider both definite programs and normal programs and we present the basic transformation rules and strategies which are described in the literature. To illustrate the power of the program transformation approach we also give some examples of program development. Finally, we show how to use program transformations for proving properties of predicates and synthesizing programs from logical specifications.