Complete sets of transformations for general E-unification

Gallier, Jean; Snyder, Wayne

doi:10.1016/0304-3975(89)90004-2

Cited by 89 publications

(39 citation statements)

References 12 publications

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“…e.g. Gallier and Snyder, 1988). During executing such a procedure call, all terms in S are viewed as first-order as elaborated in Section 2.3, with the mechanism for viewing trivial flexible subterms as first-order free variables captured explicitly by the mapping ρ in Item 2.…”

Section: Figure 2 Heu -Transformation (E-uni)mentioning

confidence: 99%

“…(Note that the equational theories E in Wolfram (1991Wolfram ( , 1993) may be higher-order.) In the spirit of "universal unification" Gallier and Snyder (1988) and Snyder (1990) presented a transformation-based higher-order E-unification procedure, where the presentation of E itself is used in the unification process. Dougherty and Johann (1992) provided a combinatory logic approach to higher-order E-unification in the restricted case when E is convergent.…”

Section: Introductionmentioning

confidence: 99%

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Modular Higher-Order Equational Preunification

Qian

Wang

1996

Journal of Symbolic Computation

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Preunification of simply typed λ-terms with respect to the equivalence relation induced by α-, β-and η-conversion and an arbitrary first-order equational theory is useful in higher-order proof and logic programming systems. In this paper we present a procedure for such preunification, which is based on three transformations and parameterized by a first-order equational unification procedure that admits free function symbols. The procedure is proved to be sound and complete, provided that the parameterizing procedure is.

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Section: Figure 2 Heu -Transformation (E-uni)mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Modular Higher-Order Equational Preunification

Qian

Wang

1996

Journal of Symbolic Computation

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“…Proof: We define the algorithm U in the style of [GS89] by a set of transformation rules on triples (K, E, S) consisting of a kind assignment K, a set E of type equations and a set S of "solved" type equations of the form (t, τ ) such that t ∈ F T V (τ ). Let F range over functions from a finite set of labels to types.…”

Section: Theorem 2 There Is An Algorithm U Which Given Any Kinded Sementioning

confidence: 99%

A compilation method for ML-style polymorphic record calculi

Ohori

1992

Proceedings of the 19th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages - POPL '92

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Polymorphic record calculi have recently attracted much attention as a typed foundation for objectoriented programming. This is based on the fact that a function that selects a field l of a record can be given a polymorphic type that enables it to be applied to various records containing a field l. Recent studies have established techniques to develop an ML-style type inference algorithm for such a polymorphic type system. There seems to be, however, no established method to compile an ML-style polymorphic record calculus into efficient code. The purpose of this paper is to present one such method. We define a polymorphic record calculus as an extension of Damas and Milner's proof system for ML. For this calculus, we define an implementation calculus where records are represented as arrays of (references to) values and field selection is performed by direct indexing. To represent polymorphic field selection, the implementation calculus contains an abstraction mechanism over indexes. We then develop an algorithm to translate the polymorphic record calculus into the implementation calculus by refining a type inference algorithm; it simultaneously computes a principal type scheme in the polymorphic record calculus and a correct implementation term in the implementation calculus. The type inference is shown to be sound and complete in the sense of Damas-Milner's algorithm for ML. Moreover, the polymorphic type system is shown to be sound with respect to an operational semantics of the translated terms in the implementation calculus. * Appeared in Proc. ACM POPL Symposium, pages 154-165, 1992 (a few minor errors corrected.)

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“…As explained in [HDP09], the trader is based on equational unification and more particularly on the work of Gallier and Snyder [GS89]. It has a type system adapted to overloaded functions with subtyping, based on the λ&−calculus defined by Castagna [CGL92].…”

Section: Inside the Tradermentioning

confidence: 99%

Intelligent Service Trading and Brokering for Distributed Network Services in GridSolve

Hurault

YarKhan

2011

Lecture Notes in Computer Science

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Abstract. One of the great benefits of computational grids is to provide access to a wide range of scientific software and a variety of different computational resources. It is then possible to choose from this large variety of available resources the one that solves a given problem, and even to combine these resources in order to obtain the best solution. Grid service trading (searching for the best combination of software and execution platform according to the user requirements) is thus a crucial issue. Trading relies on the description of available services and computers, on the current state of the grid, and on the user requirements. Given the large amount of services that may be deployed over a Grid, this description cannot be reduced to a simple service name. In this paper, a sophisticated service specification approach similar to algebraic data types is combined with a grid middleware. This leads to a transparent solution for users: they give a mathematical expression to be solved, and the appropriate grid services will be transparently located, composed and executed on their behalf.

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Complete sets of transformations for general E-unification

Cited by 89 publications

References 12 publications

Modular Higher-Order Equational Preunification

Modular Higher-Order Equational Preunification

A compilation method for ML-style polymorphic record calculi

Intelligent Service Trading and Brokering for Distributed Network Services in GridSolve

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