Espírito Santo, José and Matthes, Ralph and Pinto, Luís A Coinductive Approach to Proof Search. (2013) In: Fixed Points in Computer Science (FICS 2013), 1 September 2013 (Turin, Italy).

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Official URL: http://dx.doi.org/10.4204/EPTCS.126.3
Abstract
We propose to study proof search from a coinductive point of view. In this paper, we consider intuitionistic logic and a focused system based on Herbelin's LJT for the implicational fragment. We introduce a variant of lambda calculus with potentially infinitely deep terms and a means of expressing alternatives for the description of the "solution spaces" (called Böhm forests), which are a representation of all (not necessarily wellfounded but still locally wellformed) proofs of a given formula (more generally: of a given sequent). <p> As main result we obtain, for each given formula, the reduction of a coinductive definition of the solution space to a effective coinductive description in a finitary term calculus with a formal greatest fixedpoint operator. This reduction works in a quite direct manner for the case of Horn formulas. For the general case, the naive extension would not even be true. We need to study "cocontraction" of contexts (contraction bottomup) for dealing with the varying contexts needed beyond the Horn fragment, and we point out the appropriate finitary calculus, where fixedpoint variables are typed with sequents. Cocontraction enters the interpretation of the formal greatest fixed points  curiously in the semantic interpretation of fixedpoint variables and not of the fixedpoint operator.
Item Type:  Conference or Workshop Item (Paper) 

HAL Id:  hal01226485 
Audience (conference):  National conference proceedings 
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Institution:  French research institutions > Centre National de la Recherche Scientifique  CNRS (FRANCE) Université de Toulouse > Institut National Polytechnique de Toulouse  Toulouse INP (FRANCE) Université de Toulouse > Université Toulouse III  Paul Sabatier  UT3 (FRANCE) Université de Toulouse > Université Toulouse  Jean Jaurès  UT2J (FRANCE) Université de Toulouse > Université Toulouse 1 Capitole  UT1 (FRANCE) Other partners > Universidade do Minho (PORTUGAL) 
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Deposited On:  16 Oct 2015 09:24 
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