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## Uniform proofs as a foundation for logic programming (1991)

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### Other Repositories/Bibliography

Venue: | ANNALS OF PURE AND APPLIED LOGIC |

Citations: | 423 - 123 self |

### Citations

987 | A formulation of a simple theory of types - Church - 1940 |

801 | Predicate Logic as Programming Language - Kowalski - 1974 |

439 | A Kripke-Kleene semantics for logic programs - Fitting - 1985 |

354 | Higher-order abstract syntax
- Pfenning, Elliot
(Show Context)
Citation Context ...plemented prior to writingsthe various programs desired. If the variable-binding constructs of a language are directlysrepresented in the A-calculus (in effect using higher-order abstract syntax, see =-=[27]-=-), thesnotions of free and bound variables and the operation of substitution for such terms isspart of the meta-theory of the logic programming language itself and would not have to besreimplemented e... |

226 | The Art of Prolog: Advanced Programming Techniques - Shapiro, Sterling - 1994 |

206 | Contributions to the Theory of Logic Programming - Apt, Emden - 1982 |

167 | Proving and applying program transformations expressed with second-order patterns - Huet, Lang - 1978 |

133 | A unification algorithm for typed λ-calculus - Huet - 1975 |

117 | An overview of λProlog - Nadathur, Miller - 1988 |

108 | Intuitionistic Logic, Model Theory and Forcing - Fitting - 1969 |

96 | N-Prolog: an Extension of Prolog with Hypothetical Implications - Gabbay, Reyle - 1984 |

88 | Partial polymorphic type inference and higher-order unification - Pfenning - 1988 |

83 | Proofs in Higher-Order Logic - Miller - 1983 |

78 | Specifying theorem provers in a higherorder logic programming language - Felty, Miller - 1988 |

64 | Lexical scoping as universal quantification
- Miller
- 1989
(Show Context)
Citation Context ...sible to naturally support abstract data types in Horn clause logics. Use ofsuniversal quantifiers in goals, however, provides for a degree of security that can be usedsto support abstract data types =-=[17]-=-. Consider the following concrete example. Let Sort besa set of Horn clauses that implements a binary tree sorting algorithm and let us assumesthat it internally builds a labeled binary trees using th... |

61 | Higher-order Horn Clauses
- Nadathur, Miller
- 1990
(Show Context)
Citation Context ...edent and succedentsof each sequent occurrence is a subset of Dl and G1 U {I), respectively. The rest of thesargument in the proof of Theorem 1 would then carry over to this case as well.sIn [22] and =-=[24]-=-, it is shown that this restriction on substitutions within C-proofs insfact preserves the set of provable sequents. That is, if 'P is a set of higher-order Hornsclauses and G is a formula in G2 such ... |

61 | Natural Deduction as Higher-Order Resolution - Paulson |

56 | A logic programming approach to manipulating formulas and programs - Miller, Nadathur - 1987 |

46 | Natural Deduction, Almqvist - Prawitz - 1965 |

37 |
A Higher-Order Logic as the Basis for Logic Programming
- Nadathur
- 1987
(Show Context)
Citation Context ...the antecedent and succedentsof each sequent occurrence is a subset of Dl and G1 U {I), respectively. The rest of thesargument in the proof of Theorem 1 would then carry over to this case as well.sIn =-=[22]-=- and [24], it is shown that this restriction on substitutions within C-proofs insfact preserves the set of provable sequents. That is, if 'P is a set of higher-order Hornsclauses and G is a formula in... |

32 | Investigations into logical deduction. In The Collected Papers of Gerhard Gentzen - Gentzen - 1969 |

31 |
Hereditary Harrop Formulas and Uniform Proofs Systems
- Miller, Nadathur, et al.
- 1987
(Show Context)
Citation Context ...ov from NSF grants DMS85-01522sand CCR-87-05596 and from the University of Pennsylvania Natural Sciences AssociationsYoung Faculty Award.s9. ReferencessA preliminary version of this paper appeared as =-=[21]-=-. Theorem 3 of that paper is incorrect.sIt is corrected by the material in Sections 5 and 6 of the current paper.s[I] K. Apt and M. H. van Emden, Contributions to the Theory of Logic Programming,sJour... |

30 | Uses of higher-order unification for implementing program trans- formers - Hannan, Miller - 1988 |

26 | Some uses of higher-order logic in computational linguistics - Miller, Nadathur - 1986 |

24 |
A Logical Analysis of Modules
- Miller
- 1989
(Show Context)
Citation Context ...in this paper. This is largely because I contributes little to our understanding ofsabstractions in logic programs. This symbol is useful within logic programming to providesa notion of negation: see =-=[15]-=- for a development of this notion. In the present context it issimportant to point out that the natural tendency to read I as failure does not correspondsto the role of this symbol within logical syst... |

8 | Negation as failure, in Logic and - Clark - 1978 |

8 |
An overview of XProlog
- Nadathur, Miller
- 1988
(Show Context)
Citation Context ... aspect dealt with ins[16], and it is necessary to consider programs that change in a stack-based fashion. A pro-stotype implementation of most of hohh has, in fact, been built based on this approach =-=[23]-=-.sIt has been used in several programming experiments [4, 10, 18, 20, 261 that have providedsan understanding of the usefulness of the various abstraction mechanisms discussed in thisspaper in actual ... |

6 | Higher-order Extensions of Prolog: Are they needed?" Machine Intelligence 10 - Warren - 1982 |

5 | Hornlog: A Graph-Based Interpreter for General Horn Clauses - Gallier, Raatz - 1987 |

5 | Some Uses of Higher-Order Logic - Miller, Nadathur - 1986 |

2 | Concerning Formulas of the types A ! B . C, A ! (Ex)(B(x - Harrop - 1960 |

2 |
Hereditary Harrop Formulas and Logic
- Miller
- 1987
(Show Context)
Citation Context ...hesfollowing following mutual recursion meet these conditions:sLet V3 be the set of D-formulas and let G3 be the set of G-formulas. A formula from V3sis called a first-order hereditary Harrop formula =-=[14]-=-, and fohh is defined to be the triples(V3, G3, I- I ) .sWe have the following theorem concerning this triple.sTheorem4. fohhisanabstractlogicprogramminglanguage.sProof. Again we only outline the proo... |

2 | Solutions to λ-Term Equations Under a Mixed Prefix, submitted - Miller - 1989 |

2 |
Solutions to A-Term Equations Under a Mixed Prefix, submitted
- Miller
- 1989
(Show Context)
Citation Context ...c. Similar ideas cansbe used in implementing hohh with the following main differences: there might be a needsto solve unification problems that have mixed quantifier prefixes, an aspect dealt with ins=-=[16]-=-, and it is necessary to consider programs that change in a stack-based fashion. A pro-stotype implementation of most of hohh has, in fact, been built based on this approach [23].sIt has been used in ... |

2 | A Logic Programming Approach to Manipulating For- mulas and Programs - Miller, Nadathur - 1987 |

1 | First-Order Predicate Logic as a Common Basis for Relational and Functional - Emden - 1987 |