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Unification and AntiUnification in the Calculus of Constructions
 In Sixth Annual IEEE Symposium on Logic in Computer Science
, 1991
"... We present algorithms for unification and antiunification in the Calculus of Constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higherorder patterns, a notion investigated for the simplytyped calculus by Miller. Most general unifiers and ..."
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Cited by 69 (16 self)
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We present algorithms for unification and antiunification in the Calculus of Constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higherorder patterns, a notion investigated for the simplytyped calculus by Miller. Most general unifiers and least common antiinstances are shown to exist and are unique up to a simple equivalence. The unification algorithm is used for logic program execution and type and term reconstruction in the current implementation of Elf and has shown itself to be practical. The main application of the antiunification algorithm we have in mind is that of proof generalization. 1 Introduction Higherorder logic with an embedded simplytyped  calculus has been used as the basis for a number of theorem provers (for example [1, 19]) and the programming language Prolog [16]. Central to these systems is an implementation of Huet's preunification algorithm for the simplytyped calculus [12] which has shown it...
HigherOrder and Modal Logic as a Framework for ExplanationBased Generalization
, 1989
"... Logic programming provides a uniform framework in which all aspects of explanationbased generalization and learning may be defined and carried out, but firstorder Horn logic is not well suited to application domains such as theorem proving or program synthesis where functions and predicates are th ..."
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Cited by 16 (6 self)
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Logic programming provides a uniform framework in which all aspects of explanationbased generalization and learning may be defined and carried out, but firstorder Horn logic is not well suited to application domains such as theorem proving or program synthesis where functions and predicates are the objects of computation. We explore the use of a higherorder representation language and extend EBG to a higherorder logic programming language. Variables may now range over functions and predicates, which leads to an expansion of the space of possible generalizations. We address this problem by extending the logic with the modal ⊔ ⊓ operator (indicating necessary truth) which leads to the language λ ⊔ ⊓ Prolog. We develop a metainterpreter realizing EBG for λ ⊔ ⊓ Prolog and give some examples in an expanded version of this extended abstract which is available as a technical report [2]. 1
Unification and AntiUnification in the Calculus of Constructions
"... We present algorithms for unification and antiunification in the Calculus of Constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higherorder patterns, a notion investigated for the simplytyped λcalculus by Miller. Most general unifiers and ..."
Abstract
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We present algorithms for unification and antiunification in the Calculus of Constructions, where occurrences of free variables (the variables subject to instantiation) are restricted to higherorder patterns, a notion investigated for the simplytyped λcalculus by Miller. Most general unifiers and least common antiinstances are shown to exist and are unique up to a simple equivalence. The unification algorithm is used for logic program execution and type and term reconstruction in the current implementation of Elf and has shown itself to be practical. The main application of the antiunification algorithm we have in mind is that of proof generalization. 1