Higher-Order Logic Programming Languages with Constraints: A Semantics

Lipton, James; Nieva, Susana

doi:10.1007/978-3-540-73228-0_20

Cited by 4 publications

(2 citation statements)

References 21 publications

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“…Whilst first-order constraint logic programming is a very well developed area (an old, but good survey is (Jaffar and Maher, 1994)), there is very little existing work on the higher-order extension. Lipton and Nieva (2007) give a Kripke semantics for a λProlog-like language extended with a generic framework for constraints. In contrast to our work, the underlying higher-order logic is intuitionistic and the precise notion of model is bespoke to the paper.…”

Section: Related Workmentioning

confidence: 99%

Higher-order constrained horn clauses for verification

Burn

Ong

Ramsay

2017

Proc. ACM Program. Lang.

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Motivated by applications in automated verification of higher-order functional programs, we develop a notion of constrained Horn clauses in higher-order logic and a decision problem concerning their satisfiability. We show that, although satisfiable systems of higher-order clauses do not generally have least models, there is a notion of canonical model obtained through a reduction to a problem concerning a kind of monotone logic program. Following work in higher-order program verification, we develop a refinement type system in order to reason about and automate the search for models. This provides a sound but incomplete method for solving the decision problem. Finally, we show that there is a sense in which we can use refinement types to express properties of terms whilst staying within the higher-order constrained Horn clause framework.

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Section: Related Workmentioning

confidence: 99%

Higher-order constrained horn clauses for verification

Burn

Ong

Ramsay

2017

Proc. ACM Program. Lang.

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“…Several kinds of semantics have been defined for HH(C) without negation, including proof theoretic, operational [10] and fixed point semantics [7], as well as for its higher-order version [11]. The simplest way for explaining the meaning of programs and goals in the present framework is by using a proof theoretic semantics.…”

Section: Sequent Calculusmentioning

confidence: 99%

Formalizing a Constraint Deductive Database Language Based on Hereditary Harrop Formulas with Negation

Nieva¹,

Sánchez-Hernández²,

Sáenz-Pérez³

Functional and Logic Programming

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Abstract. In this paper, we present an extension of the scheme HH(C) (Hereditary Harrop formulas with Constraints) with a suitable formulation of negation in order to obtain a constraint deductive database query language. In addition to constraints, our proposal includes logical connectives (implication and quantifiers) for defining databases and queries, which altogether are unavailable in current database query languages.We define a proof theoretic semantic framework based on a sequent calculus, that allows to represent the meaning of a database query by means of a derived constraint answer in the sense of CLP. We also introduce an appropriate notion of stratification, which provides a starting point for suitable operational semantics dealing with recursion and negation. We formalize a fixed point semantics for stratifiable databases, whose fixpoint operator is applied stratum by stratum. This semantics is proved to be sound and complete with respect to derivability in the sequent calculus, and it provides the required support for actual implementations, as the prototype we have developed already and introduce in this paper.

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