research-article

Well-typed narrowing with extra variables in functional-logic programming

Authors:

Francisco López-Fraguas,

Enrique Martin-Martin,

Juan Rodríguez-HortaláAuthors Info & Claims

PEPM '12: Proceedings of the ACM SIGPLAN 2012 workshop on Partial evaluation and program manipulation

Pages 83 - 92

https://doi.org/10.1145/2103746.2103763

Published: 23 January 2012 Publication History

Abstract

Narrowing is the usual computation mechanism in functional-logic programming (FLP), where bindings for free variables are found at the same time that expressions are reduced. These free variables may be already present in the goal expression, but they can also be introduced during computations by the use of program rules with extra variables. However, it is known that narrowing in FLP generates problems from the point of view of types, problems that can only be avoided using type information at run-time. Nevertheless, most FLP systems use static typing based on Damas-Milner type system and they do not carry any type information in execution, thus ill-typed reductions may be performed in these systems. In this paper we prove, using the let-narrowing relation as the operational mechanism, that types are preserved in narrowing reductions provided the substitutions used preserve types. Based on this result, we prove that types are also preserved in narrowing reductions without type checks at run-time when higher order (HO) variable bindings are not performed and most general unifiers are used in unifications, for programs with transparent patterns. Then we characterize a restricted class of programs for which no binding of HO variables happens in reductions, identifying some problems encountered in the definition of this class. To conclude, we use the previous results to show that a simulation of needed narrowing via program transformation also preserves types.

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Cited By

López-Fraguas FMartin-Martin EAlbert EMu S(2013)Typing as functional-logic evaluationProceedings of the ACM SIGPLAN 2013 workshop on Partial evaluation and program manipulation10.1145/2426890.2426896(23-32)Online publication date: 21-Jan-2013
https://dl.acm.org/doi/10.1145/2426890.2426896
Martin-Martin ERodríguez-Hortalá JDe Schreye DJanssens GKing A(2012)Transparent function typesProceedings of the 14th symposium on Principles and practice of declarative programming10.1145/2370776.2370793(127-138)Online publication date: 19-Sep-2012
https://dl.acm.org/doi/10.1145/2370776.2370793

Index Terms

Well-typed narrowing with extra variables in functional-logic programming
1. Software and its engineering
  1. Software notations and tools
    1. General programming languages
      1. Language types
        Multiparadigm languages
2. Theory of computation
  1. Semantics and reasoning
    1. Program constructs
      1. Type structures

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cover image ACM Conferences

PEPM '12: Proceedings of the ACM SIGPLAN 2012 workshop on Partial evaluation and program manipulation

January 2012

172 pages

ISBN:9781450311182

DOI:10.1145/2103746

Program Chairs:
Oleg Kiselyov
Monterey, CA., USA
,
Simon Thompson
University of Kent, UK

Copyright © 2012 ACM.

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Published: 23 January 2012

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POPL '12

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POPL '12: The 39th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 23 - 24, 2012

Pennsylvania, Philadelphia, USA

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Cited By

López-Fraguas FMartin-Martin EAlbert EMu S(2013)Typing as functional-logic evaluationProceedings of the ACM SIGPLAN 2013 workshop on Partial evaluation and program manipulation10.1145/2426890.2426896(23-32)Online publication date: 21-Jan-2013
https://dl.acm.org/doi/10.1145/2426890.2426896
Martin-Martin ERodríguez-Hortalá JDe Schreye DJanssens GKing A(2012)Transparent function typesProceedings of the 14th symposium on Principles and practice of declarative programming10.1145/2370776.2370793(127-138)Online publication date: 19-Sep-2012
https://dl.acm.org/doi/10.1145/2370776.2370793

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