Horn clause programs with polymorphic types: Semantics and resolution

Hanus, Michael

doi:10.1007/3-540-50940-2_38

Cited by 24 publications

(7 citation statements)

References 20 publications

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“…αProlog permits type variables in declarations, which are treated polymorphically, following previous work on polymorphic typing in logic programming [Mycroft and O'Keefe 1984;Hanus 1991]. Polymorphic type checking is performed in the standard way by generating equational constraints and solving them using unification.…”

Section: Syntaxmentioning

confidence: 99%

Nominal logic programming

Cheney

Urban

2008

ACM Trans. Program. Lang. Syst.

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Nominal logic is an extension of first-order logic which provides a simple foundation for formalizing and reasoning about abstract syntax modulo consistent renaming of bound names (that is, α-equivalence). This article investigates logic programming based on nominal logic. This technique is especially well-suited for prototyping type systems, proof theories, operational semantics rules, and other formal systems in which bound names are present. In many cases, nominal logic programs are essentially literal translations of "paper" specifications. As such, nominal logic programming provides an executable specification language for prototyping, communicating, and experimenting with formal systems.We describe some typical nominal logic programs, and develop the model-theoretic, prooftheoretic, and operational semantics of such programs. Besides being of interest for ensuring the correct behavior of implementations, these results provide a rigorous foundation for techniques for analysis and reasoning about nominal logic programs, as we illustrate via two examples.

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Section: Syntaxmentioning

confidence: 99%

Nominal logic programming

Cheney

Urban

2008

ACM Trans. Program. Lang. Syst.

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“…The reader may wonder whether function indexing can be avoided and thus reconstructed. Interestingly enough, the dual of the property of transparency [11], for which the type declaration of every (internal) function is such that every type variable occurring in the domain also occurs in the range, ensures, in the absence of overloading, index reconstruction. Space prevents us from providing a formal proof.…”

Section: Now Given the Ground Instance P([3]) ← Q([ ])mentioning

confidence: 99%

“…The introduction of polymorphism in logic programming has required some care: there are predicate definitions that are semantically non-problematic, yet may lead to runtime errors [15,11]. A sufficient condition is definitional genericity, which requires that the type of a defining occurrence of a predicate must be a renaming of the assigned type signature of the predicate.…”

Section: Related Work and Conclusionmentioning

confidence: 99%

Towards a Type Discipline for Answer Set Programming

Fiorentini

Momigliano

Ornaghi

2009

Lecture Notes in Computer Science

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Abstract. We argue that it is high time that types had a beneficial impact in the field of Answer Set Programming and in particular Disjunctive Datalog as exemplified by the DLV system. Things become immediately more challenging, as we wish to present a type system for DLV-Complex, an extension of DLV with uninterpreted function symbols, external implemented predicates and types. Our type system owes to the seminal polymorphic type system for Prolog introduced by Mycroft and O'Keefe, in the formulation by Lakshman and Reddy. The most innovative part of the paper is developing a declarative grounding procedure which is at the same time appropriate for the operational semantics of ASP and able to handle the new features provided by DLV-Complex. We discuss the soundness of the procedure and evaluate informally its success in reducing, as expected, the set of ground terms. This yields an automatic reduction in size and numbers of (non isomorphic) models. Similar results could have only been achieved in the current untyped version by careful use of generator predicates in lieu of types.

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“…In a programming-language setting, logical consistency is not a concern: programs that do not terminate are considered acceptable. Hanus [1988;1989] designed a typed logic programming language where "functions" (data constructors, in our terminology) are introduced by declarations of the form (4). (In fact, in Hanus' system, it is even possible for the result type to be a type variable; it does not have to be an application of a data constructor ε.)…”

Section: An Alternative Formmentioning

confidence: 99%

A constraint-based approach to guarded algebraic data types

Simonet

Pottier

2007

ACM Trans. Program. Lang. Syst.

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We study HMG(X), an extension of the constraint-based type system HM(X) with deep pattern matching, polymorphic recursion, and guarded algebraic data types. Guarded algebraic data types subsume the concepts known in the literature as indexed types, guarded recursive datatype constructors, (first-class) phantom types, and equality qualified types, and are closely related to inductive types. Their characteristic property is to allow every branch of a case construct to be typechecked under different assumptions about the type variables in scope. We prove that HMG(X) is sound and that, provided recursive definitions carry a type annotation, type inference can be reduced to constraint solving. Constraint solving is decidable, at least for some instances of X, but prohibitively expensive. Effective type inference for guarded algebraic data types is left as an issue for future research. INTRODUCTIONMembers of the ML family of programming languages offer type inference in the style of Hindley [1969] andMilner [1978], making type annotations optional. Type inference can be decomposed into constraint generation and constraint solving phases, where constraints are, roughly speaking, systems of type equations. This remark has led to the definition of a family of constraint-based type systems, known as HM(X) [Odersky et al. 1999;Pottier and Rémy 2005], whose members exploit potentially more complex constraint languages, achieving greater expressiveness while still enjoying type inference in the style of Hindley and Milner.These programming languages also provide high-level facilities for defining and manipulating data structures, namely algebraic data types and pattern matching. In the setting of an explicitly typed calculus, Xi, Chen, and Chen [2003] have recently introduced guarded algebraic data types, an extension that offers significant new expressive power to programmers.The purpose of the present paper is to study how these two lines of research Permission to make digital/hard copy of all or part of this material without fee for personal or classroom use provided that the copies are not made or distributed for profit or commercial advantage, the ACM copyright/server notice, the title of the publication, and its date appear, and notice is given that copying is by permission of the ACM, Inc. To copy otherwise, to republish, to post on servers, or to redistribute to lists requires prior specific permission and/or a fee. . 2005], it is necessary to study their interaction with Hindley-Milner-style type inference. Furthermore, because type inference is best understood in a constraint-based setting, and because constraint-based type systems are more general than Hindley and Milner's original type system, we believe it is worth studying an extension of HM(X) with guarded algebraic data types.We proceed as follows. First, we present an untyped call-by-value λ-calculus featuring data constructors and pattern matching ( §2). (We believe that our results could be transferred to a call-by-name calculus without difficulty.) The...

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Horn clause programs with polymorphic types: Semantics and resolution

Cited by 24 publications

References 20 publications

Nominal logic programming

Nominal logic programming

Towards a Type Discipline for Answer Set Programming

A constraint-based approach to guarded algebraic data types

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