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Rules of definitional reflection
 In Symposium on Logic and Computer Science
, 1993
"... This paper discusses two rules of definitional reflection: The “logical ” version of definitional reflection as used in the extended logic programming language GCLA and the “ω”version of definitional reflection as proposed by Eriksson and Girard. The logical version is a Leftintroduction rule comp ..."
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Cited by 57 (8 self)
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This paper discusses two rules of definitional reflection: The “logical ” version of definitional reflection as used in the extended logic programming language GCLA and the “ω”version of definitional reflection as proposed by Eriksson and Girard. The logical version is a Leftintroduction rule completely analogous to the Leftintroduction rules for logical operators in Gentzenstyle sequent systems, whereas the ωversion extends the logical version by a principle related to the ωrule in arithmetic. Correspondingly, the interpretation of free variables differs between the two approaches, resulting in different principles of closure of inference rules under substitution. This difference is crucial for the computational interpretation of definitional reflection. 1
A New Perspective on Integrating Functional and Logic Languages
 Languages, Proceedings of the 3rd International Conference on Fifth Generation Computer Systems
, 1992
"... Traditionally the integration of functional and logic languages is performed by attempting to integrate their semantic logics in some way. Many languages have been developed by taking this approach, but none manages to exploit fully the programming features of both functional and logic languages and ..."
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Cited by 14 (0 self)
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Traditionally the integration of functional and logic languages is performed by attempting to integrate their semantic logics in some way. Many languages have been developed by taking this approach, but none manages to exploit fully the programming features of both functional and logic languages and provide a smooth integration of the two paradigms. We propose that improved integrated systems can be constructed by taking a broader view of the underlying semantics of logic programming. A novel integrated language paradigm, Definitional Constraint Programming (DCP), is proposed. DCP generalises constraint logic programming by admitting userdefined functions via a purely functional subsystem and enhances it with the power to solve constraints over functional programs. This constraint approach to integration results in a homogeneous unified system in which functional and logic programming features are combined naturally. 1 Introduction During the past ten years the integration of funct...
Program Development Schemata as Derived Rules
, 2000
"... This paper makes several contributions towards a clarified view of schemabased program development. First, we propose that schemata can be understood, formalized, and used in a simple way: program development schemata are derived rules. We mean this in the standard sense of a derived rule of infere ..."
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Cited by 9 (2 self)
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This paper makes several contributions towards a clarified view of schemabased program development. First, we propose that schemata can be understood, formalized, and used in a simple way: program development schemata are derived rules. We mean this in the standard sense of a derived rule of inference in logic. A schema like Figure i can be formulated as a rule stating that the conclusion follows from the premises defining F, G, and the applicability conditions. By deriving the rule in an axiomatic theory, we validate a semantic statement about it: the conclusion of the rule holds in every model where both the axioms of the theory and the premises of the rule are true. Hence, by selecting a language to work in we control which development schemata are formalizable, and by selecting a theory we determine which schemata are derivable
Deriving and Applying Logic Program Transformers
 In Algorithms, 30 P. Anderson and D. Basin Concurrency and Knowledge (1995 Asian Computing Science Conference), volume 1023 of LNCS
, 1995
"... We present a methodology for logic program development based on the use of verified transformation templates. We use the Isabelle Logical Framework to formalize transformation templates as inference rules. We derive these rules in higherorder logic and afterwards use higherorder unification to app ..."
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Cited by 5 (4 self)
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We present a methodology for logic program development based on the use of verified transformation templates. We use the Isabelle Logical Framework to formalize transformation templates as inference rules. We derive these rules in higherorder logic and afterwards use higherorder unification to apply them to develop programs in a deductive synthesis style. Our work addresses the pragmatics of template formalization and application as well as which theories and semantics of programs and data we require to derive templates. Key words: program transformation, logic programs, higherorder unification, logical frameworks. 1 Introduction We investigate the transformation of logic programs based on the use of transformation templates which formalize equivalences between schemata representing logic programs. Our focus and contributions center on three problems: 1. How may we acquire and formalize useful templates? 2. What foundations are appropriate for formally demonstrating the correctn...
FALCON: Functional and Logic Language with Constraints
, 1993
"... Introduction During the past ten years, integration of functional and logic programming languages has attracted much research. An extensive survey and classification of their results can be found in [GLDD90]. Traditionally this integration is performed by attempting to integrate the respective sema ..."
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Cited by 3 (2 self)
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Introduction During the past ten years, integration of functional and logic programming languages has attracted much research. An extensive survey and classification of their results can be found in [GLDD90]. Traditionally this integration is performed by attempting to integrate the respective semantic logics of functional and logic languages in some way, resulting in a "super logic language". As we presented in Chapter ??, the conventional understanding of logic programming is that a logic program defines a logical theory and computation is attempting to prove that a query is a logical consequence of this theory. Taking this view, integration is regarded as enhancing the original logic underlying a logic programming system to cope with functional programming features and results in a new logic programming system. Most approaches take firstorder equational logic as the semantic logic of functional languages and combine it with Horn clause logic. The following
Correction et complétude des sémantiques PLC revisitée par (co)induction
, 1998
"... Ce rapport propose une reformulation de la s'emantique des programmes logiques avec contraintes en termes de s'emantique positive et s'emantique n'egative dans un cadre inductif uniforme. Dans ce cadre, les r'esultats de correction et compl'etude s'expriment de mani`ere naturelle et 'el'egante. En p ..."
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Cited by 1 (1 self)
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Ce rapport propose une reformulation de la s'emantique des programmes logiques avec contraintes en termes de s'emantique positive et s'emantique n'egative dans un cadre inductif uniforme. Dans ce cadre, les r'esultats de correction et compl'etude s'expriment de mani`ere naturelle et 'el'egante. En particulier, nous montrons un r'esultat de compl 'etude de la s'emantique n'egative en utilisant des ensembles infinis de contraintes. Ce cadre th'eorique est une extension originale de la (( vision grammaticale de la programmation logique )). Motscl'es : s'emantique, programmation logique avec contraintes, correction, compl'etude, induction, coinduction. Recherche r'ealis'ee dans le cadre du projet LOCO, commun `a l'Universit'e d'Orl'eans et l'Unit'e de Recherche de l'INRIA Rocquencourt. L'introduction des contraintes dans la programmation logique (LP) par [12], pour donner la programmation logique avec contraintes (CLP), a 'et'e une avanc'ee importante `a la fois dans le domaine des a...
Logic Programming and CoInductive Definitions
, 1998
"... This paper focuses on the assignment of meaning to infinite derivations in logic programming. Several approaches have been developped by considering infinite elements in the universe of the discourse but none are complete. By considering proofs as objects in a coinductive set, standard properties o ..."
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Cited by 1 (0 self)
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This paper focuses on the assignment of meaning to infinite derivations in logic programming. Several approaches have been developped by considering infinite elements in the universe of the discourse but none are complete. By considering proofs as objects in a coinductive set, standard properties of coinductive definitions are used both to explain this incompleteness and to define a sound and complete semantics, based on the logic program as coinductive denition paradigm, for a subclass of infinite derivations, called infinite derivations over a finite domain (i.e. derivations which do not compute infinite terms).
Coalgebraic Semantics for Parallel Derivation Strategies in Logic Programming
"... Abstract. Logic programming, a class of programming languages based on firstorder logic, provides simple and efficient tools for goaloriented proofsearch. Logic programming supports recursive computations, and some logic programs resemble the inductive or coinductive definitions written in functi ..."
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Abstract. Logic programming, a class of programming languages based on firstorder logic, provides simple and efficient tools for goaloriented proofsearch. Logic programming supports recursive computations, and some logic programs resemble the inductive or coinductive definitions written in functional programming languages. In this paper, we give a coalgebraic semantics to logic programming. We show that ground logic programs can be modelled by either Pf Pfcoalgebras or Pf Listcoalgebras on Set. We analyse different kinds of derivation strategies and derivation trees (prooftrees, SLDtrees, andor parallel trees) used in logic programming, and show how they can be modelled coalgebraically.
PhD Thesis Proposal
, 1996
"... This report reviews the current state of research in the amalgam of functional and logic languages, and proposes an area of further study. The approach proposed in this report maintains the syntax and semantics of standard Prolog, while allowing the declaration of functions in an upwardscompatible ..."
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This report reviews the current state of research in the amalgam of functional and logic languages, and proposes an area of further study. The approach proposed in this report maintains the syntax and semantics of standard Prolog, while allowing the declaration of functions in an upwardscompatible style. The research will advance the benefits of expressivity and efficiency of the extended paradigm, while maintaining compatibility with the Delphi principle ([Clo87]). ijl20@cl.cam.ac.uk Contents 1 Introduction 3 2 Summary of current research 5 2.1 Term evaluation : : : : : : : : : : : : : : : : : : : : : : : : : : 5 2.1.1 Motivation : : : : : : : : : : : : : : : : : : : : : : : : : 6 2.2 Mode and determinism declarations for relations : : : : : : : : 6 2.2.1 Motivation : : : : : : : : : : : : : : : : : : : : : : : : : 8 2.3 Predicates as setvalued functions : : : : : : : : : : : : : : : : 8 2.3.1 Motivation : : : : : : : : : : : : : : : : : : : : : : : : : 9 2.4 Predicates as Boo...
Coalgebraic Derivations in Logic Programming ∗
"... Coalgebra may be used to provide semantics for SLDderivations, both finite and infinite. We first give such semantics to classical SLDderivations, proving results such as adequacy, soundness and completeness. Then, based upon coalgebraic semantics, we propose a new sound and complete algorithm for ..."
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Coalgebra may be used to provide semantics for SLDderivations, both finite and infinite. We first give such semantics to classical SLDderivations, proving results such as adequacy, soundness and completeness. Then, based upon coalgebraic semantics, we propose a new sound and complete algorithm for parallel derivations. We analyse this new algorithm in terms of the Theory of Observables, and we prove soundness, completeness, correctness and full abstraction results.