Results 1 
2 of
2
Connectiondriven inductive theorem proving
 Studia Logica
"... Abstract. We present a method for integrating ripplingbased rewriting into matrixbased theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. ..."
Abstract

Cited by 4 (2 self)
 Add to MetaCart
(Show Context)
Abstract. We present a method for integrating ripplingbased rewriting into matrixbased theorem proving as a means for automating inductive specification proofs. The selection of connections in an inductive matrix proof is guided by symmetries between induction hypothesis and induction conclusion. Unification is extended by decision procedures and a rippling/reverserippling heuristic. Conditional substitutions are generated whenever a uniform substitution is impossible. We illustrate the integrated method by discussing several inductive proofs for the integer square root problem as well as the algorithms extracted from these proofs.
Publication/citation: A prooftheoretic approach to mathematical knowledge management
, 2005
"... There are many reallife examples of formal systems that support constructions or proofs, but that do not provide direct support for remembering them so that they can be recalled and reused in the future. In this paper we examine the operations of publication (remembering a proof) and citation (reca ..."
Abstract

Cited by 1 (1 self)
 Add to MetaCart
(Show Context)
There are many reallife examples of formal systems that support constructions or proofs, but that do not provide direct support for remembering them so that they can be recalled and reused in the future. In this paper we examine the operations of publication (remembering a proof) and citation (recalling a proof for reuse), regarding them as forms of common subexpression elimination on proof terms. We then develop this idea from a proof theoretic perspective, describing a simple complete proof system for universal Horn equational logic using three new proof rules, publish, cite and forget. These rules can provide a prooftheoretic infrastructure for proof reuse in any system. 1