Uniform Proofs as a Foundation for Logic Programming

@article{Miller1991UniformPA,
  title={Uniform Proofs as a Foundation for Logic Programming},
  author={Dale A. Miller and Gopalan Nadathur and Frank Pfenning and Andre Scedrov},
  journal={Ann. Pure Appl. Log.},
  year={1991},
  volume={51},
  pages={125-157}
}

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References

SHOWING 1-10 OF 60 REFERENCES

A Logical Analysis of Modules in Logic Programming

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.

AN OVERVIEW OF PROLOG

TLDR
The correspondence between each extension to Prolog and the new features in the stronger logical theory is discussed and various aspects of an experimental implementation of λProlog are discussed.

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.

Hornlog: A Graph-Based Interpreter for General Horn Clauses

Some Uses of Higher-Order Logic in Computational Linguistics

TLDR
A higher-order logic programming language is described, called λProlog, which represents programs as higher- order definite clauses and interprets them using a depth-first interpreter and claims that its use makes the task of providing formal justifications for the computations specified much more direct.

Natural Deduction as Higher-Order Resolution

Lexical Scoping as Universal Quantification

TLDR
An interpreter for a logic programming language containing both universal quantifiers and implications in goals and the body of clauses is described, and how such scoping can be used to provide a Prolog-like language with facilities for local definition of programs, local declarations in modules, abstract data types, and encapsulation of state is presented.

Higher-order Horn clauses

TLDR
A generalization of Horn clauses to a higher-order logic is described and examined as a basis for logic programming and proof-theoretic results concerning these extended clauses show that although the substitutions for predicate variables can be quite complex in general, the substitution necessary in the context of higher- order Horn clauses are tightly constrained.

On Natural Deduction

TLDR
The object of this paper is to present and justify a simplification of Gentzen's natural deduction method, to the end of enhancing the advantages just claimed.
...