Logic programming, functional programming, and inductive definitions

Paulson, Lawrence C.; Smith, Andrew W.

doi:10.1007/bfb0038699

Cited by 12 publications

(7 citation statements)

References 31 publications

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“…The fact that logic programs can be naturally represented via fixed point semantics has led to the development of logic programs as inductive definitions, [22,14], as opposed to the view of logic programs as first-order logic.…”

Section: Remarkmentioning

confidence: 99%

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Coalgebraic Semantics for Parallel Derivation Strategies in Logic Programming

Komendantskaya

McCusker

Power

2011

Algebraic Methodology and Software Technology

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Abstract. Logic programming, a class of programming languages based on first-order logic, provides simple and efficient tools for goal-oriented proof-search. 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 P f P f -coalgebras or P f Listcoalgebras on Set. We analyse different kinds of derivation strategies and derivation trees (proof-trees, SLD-trees, and-or parallel trees) used in logic programming, and show how they can be modelled coalgebraically.

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Section: Remarkmentioning

confidence: 99%

“…There have been numerous attempts to resolve the mismatch between infinite derivations and greatest fixed point semantics, [14,19,22,24]. But, the infinite SLD derivations of both finite and infinite objects have not yet received a uniform semantics, see Figure 2.…”

Section: Finite and Infinite Computations By Logic Programsmentioning

confidence: 99%

Coalgebraic Semantics for Parallel Derivation Strategies in Logic Programming

Komendantskaya

McCusker

Power

2011

Algebraic Methodology and Software Technology

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“…First-order logic cannot characterize this model, but it can be directly expressed in higher-order logic by an inductive definition. The view of logic programs as inductive definitions has been explored (primarily in the context of negation-as-failure) by a number of authors including Hagiya and Sakurai (1984), Aronsson et al (1991), and Paulson and Smith (1991). Here we adopt this view and use it to establish the correctness of another way of formalizing development schemata.…”

Section: Relational Inductionmentioning

confidence: 99%

“…With respect to the formalization based on inductive definitions, equivalence means provable equivalence in higher-order logic in a theory where the program schemata are formalized as inductively defined relations. This approach, of viewing pure logic programs as defining not a first-order theory, but rather a set of inductive definitions, has been also taken by Paulson and Smith (1991), Aronsson et al (1991) and Hagiya and Sakurai (1984).…”

Section: Logic Program Developmentmentioning

confidence: 99%

Program Development Schemata as Derived Rules

Anderson

Basin

2000

Journal of Symbolic Computation

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We show how the formalization and application of schemata for program development can be reduced to the formalization and application of derived rules of inference. We formalize and derive schemata as rules in theories that axiomatize program data and programs themselves. We reduce schema-based program development to ordinary theorem proving, where higher-order unification is used to apply rules. Conceptually, our formalization is simple and unifies divergent views of schemata, program synthesis, and program transformation. Practically, our formalization yields a simple methodology for carrying out development using existing logical frameworks; we illustrate this in the domain of logic program synthesis and transformation using the Isabelle logical framework.

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“…If C is sufficiently restricted (e.g., to Horn clauses or hereditary Harrop formulas), this principle is the basis of logic programming understood proof-theoretically (see [10,15]). It can also be viewed as reading the database as an inductive definition (see [9,16]), expressing what it means to establish an atom by reference to its defining conditions. If that way one regards ( D) as introducing an atom on the right side of the turnstile, one may look for a corresponding rule (D ) introducing an atom on the left side of the turnstile, in accordance with the symmetry of Gentzen-style sequent systems.…”

Section: Introductionmentioning

confidence: 99%

Rules of definitional reflection

Schroeder‐Heister

[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science

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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 Left-introduction rule completely analogous to the Left-introduction rules for logical operators in Gentzen-style sequent systems, whereas the ω-version extends the logical version by a principle related to the ω-rule 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.

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Logic programming, functional programming, and inductive definitions

Cited by 12 publications

References 31 publications

Coalgebraic Semantics for Parallel Derivation Strategies in Logic Programming

Coalgebraic Semantics for Parallel Derivation Strategies in Logic Programming

Program Development Schemata as Derived Rules

Rules of definitional reflection

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