NATURAL DEDUCTION AS HIGHER-ORDER RESOLUTION
Accepted version
Peer-reviewed
Repository URI
Repository DOI
Change log
Authors
PAULSON, LC
Abstract
An interactive theorem prover, Isabelle, is under development. In LCF, each inference rule is represented by one function for forwards proof and another (a tactic) for backwards proof. In Isabelle, each inference rule is represented by a Horn clause. Resolution gives both forwards and backwards proof, supporting a large class of logics. Isabelle has been used to prove theorems in Martin-L"of's Constructive Type Theory. Quantifiers pose several difficulties: substitution, bound variables, Skolemization. Isabelle's representation of logical syntax is the typed lambda-calculus, requiring higher- order unification. It may have potential for logic programming. Depth-first subgoaling along inference rules constitutes a higher-order Prolog.
Description
Keywords
cs.LO, cs.LO, D.2.4; F.3.1; F.4.1
Journal Title
J LOGIC PROGRAM
Conference Name
Journal ISSN
0743-1066
Volume Title
3
Publisher
Elsevier BV