# 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} }

## Figures from this paper

## 747 Citations

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## References

SHOWING 1-10 OF 60 REFERENCES

### Specifying Theorem Provers in a Higher-Order Logic Programming Language

- Computer ScienceCADE
- 1988

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

- Computer Science
- 1988

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

- Computer ScienceSLP
- 1987

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

- Computer ScienceJ. Log. Program.
- 1987

### Some Uses of Higher-Order Logic in Computational Linguistics

- Computer ScienceACL
- 1986

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.

### Lexical Scoping as Universal Quantification

- Computer ScienceICLP
- 1989

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

- Computer ScienceJACM
- 1990

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

- PhilosophyJ. Symb. Log.
- 1950

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.