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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.
Saturated Semantics for Coalgebraic Logic Programming
"... Abstract. A series of recent papers introduces a coalgebraic semantics for logic programming, where the behavior of a goal is represented by a parallel model of computation called coinductive tree. This semantics fails to be compositional, in the sense that the coalgebra formalizing such behavior do ..."
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Abstract. A series of recent papers introduces a coalgebraic semantics for logic programming, where the behavior of a goal is represented by a parallel model of computation called coinductive tree. This semantics fails to be compositional, in the sense that the coalgebra formalizing such behavior does not commute with the substitutions that may apply to a goal. We suggest that this is an instance of a more general phenomenon, occurring in the setting of interactive systems (in particular, nominal process calculi), when one tries to model their semantics with coalgebrae on presheaves. In those cases, compositionality can be obtained through saturation. We apply the same approach to logic programming: the resulting semantics is compositional and enjoys an elegant formulation in terms of coalgebrae on presheaves and their right Kan extensions. 1
Coalgebraic Logic Programming: implicit versus explicit resource handling
"... Abstract. We compare approaches to implicit and explicit resource handling in coinductive and concurrent logic programming. We show various effects that implicit and explicit handling of resources have on implementation and semantics. In particular, we show that recently introduced coalgebraic logi ..."
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Abstract. We compare approaches to implicit and explicit resource handling in coinductive and concurrent logic programming. We show various effects that implicit and explicit handling of resources have on implementation and semantics. In particular, we show that recently introduced coalgebraic logic programming [17] is a paradigm in which, in contrast to many other alternative systems, the aspects of logic and control are intertwined, and computational resources are handled implicitly.
Automated Proof Pattern Recognition: the Manual
"... This Documents is a Manual supporting the project Machinelearning coalgebraic automated proofs. Several experiments on patternrecognition of proofpatterns are given here. We provide a method to convert automatically produced prooftrees into ..."
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This Documents is a Manual supporting the project Machinelearning coalgebraic automated proofs. Several experiments on patternrecognition of proofpatterns are given here. We provide a method to convert automatically produced prooftrees into
Coinductive Proofs over Streams as CHR Confluence Proofs ⋆
"... Abstract. Coinduction is an important theoretical tool for defining and reasoning about unbounded data structures (such as streams, infinite trees, rational numbers...), and infinitebehavior systems. Confluence is a fundamental property of Constraint Handling Rules (CHR) since, as in other rewritin ..."
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Abstract. Coinduction is an important theoretical tool for defining and reasoning about unbounded data structures (such as streams, infinite trees, rational numbers...), and infinitebehavior systems. Confluence is a fundamental property of Constraint Handling Rules (CHR) since, as in other rewriting formalisms, it guarantees that the computations are not dependent on rule application order, and also because it implies the logical consistency of the program’s declarative view. In this paper, we illustrate how the confluence of CHR can be used to prove universal coinductive properties. In particular we give several examples of bisimulation proofs over streams. 1
An algebraic presentation of predicate logic (extended abstract)
"... Abstract. We present an algebraic theory for a fragment of predicate logic. The fragment has disjunction, existential quantification and equality. It is not an algebraic theory in the classical sense, but rather within a new framework that we call ‘parameterized algebraic theories’. We demonstrate t ..."
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Abstract. We present an algebraic theory for a fragment of predicate logic. The fragment has disjunction, existential quantification and equality. It is not an algebraic theory in the classical sense, but rather within a new framework that we call ‘parameterized algebraic theories’. We demonstrate the relevance of this algebraic presentation to computer science by identifying a programming language in which every type carries a model of the algebraic theory. The result is a simple functional logic programming language. We provide a syntaxfree representation theorem which places terms in bijection with sieves, a concept from category theory. We study presentationinvariance for general parameterized algebraic theories by providing a theory of clones. We show that parameterized algebraic theories characterize a class of enriched monads. 1