A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification

@article{Miller1991ALP,
  title={A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification},
  author={Dale A. Miller},
  journal={J. Log. Comput.},
  year={1991},
  volume={1},
  pages={497-536}
}
  • Dale A. Miller
  • Published 1991
  • Mathematics, Computer Science
  • J. Log. Comput.
by containing implementations of higher-order unification. In this paper, we present a logic programming language, called L),, that also contains both function variables and A-abstractions, but certain restriction are placed on occurrences of function variables. As a result, an implementation of LA does not need to implement full higher-order unification. Instead, an extension to first-order unification that respects bound variable names and scopes is all that is required. Such unification… Expand
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References

SHOWING 1-10 OF 83 REFERENCES
A Logic Programming Language with Lambda-Abstraction, Function Variables, and Simple Unification
TLDR
This paper presents a logic programming language, called Lλ, that also contains both function variables and λ-abstractions, but certain restriction are placed on occurrences of function variables, so that an implementation of Lλ does not need to implement full higher-order unification. Expand
A Logic Programming Approach to Manipulating Formulas and Programs
TLDR
This paper shows how a simple natural deduction theorem prover may be implemented in $\lambda$Prolog, and how some simple program transformers for a functional programming language may be written in this language. Expand
Unification of Simply Typed Lamda-Terms as Logic Programming
TLDR
This paper shows that the unification of simply typed ‚-terms modulo the rules of fl- and ·-conversions can be coded as a query of the logic programming language L‚ in a natural and clear fashion. Expand
Specifying Theorem Provers in a Higher-Order Logic Programming Language
TLDR
An extended logic programming language where first-order terms are replaced with simply-typed λ-terms, higher-order unification replaces first- order unification, and implication and universal quantification are allowed in queries and the bodies of clauses is presented. Expand
Uses of Higher-Order Unification for Implementing Program Transformers
TLDR
This paper details some properties of higher-order unification that make it suitable for analyzing program structures and presents (in λProlog) the specification of several simple program transformers together with a more involved partial evaluator. Expand
Elf: a language for logic definition and verified metaprogramming
  • F. Pfenning
  • Mathematics, Computer Science
  • [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science
  • 1989
TLDR
Novel features of Elf include: the Elf search process automatically constructs terms that can represent object-logic proofs, and thus a program need not construct them explicitly; and the partial correctness of metaprograms with respect to a given logic can be expressed and proved in Elf itself. Expand
Uniform Proofs as a Foundation for Logic Programming
TLDR
A proof-theoretic characterization of logical languages that form suitable bases for Prolog-like programming languages is provided and it is shown that first-order and higher-order Horn clauses with classical provability are examples of such a language. Expand
AN OVERVIEW OF PROLOG
λProlog is a logic programming language that extends Prolog by incorporating notions of higher-order functions, λ-terms, higher-order unification, polymorphic types, and mechanisms for buildingExpand
A Logical Analysis of Modules in Logic Programming
TLDR
A logical language which extends the syntax of positive Horn clauses by permitting implications in goals and in the bodies of clauses is presented and it is shown how to build a Kripke-like model for programs by a fixed-point construction and shown that the operational meaning of implication is sound and complete for intuitionistic logic. Expand
Extensions and applications of higher-order unification
This dissertation explores the problem of unification in various typed $\lambda$-calculi, developing and proving the correctness and completeness of unification algorithms for various calculi withinExpand
...
1
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3
4
5
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