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GraphBased Proof Counting and Enumeration with Applications for Program Fragment Synthesis
 in &quot;International Symposium on Logicbased Program Synthesis and Transformation 2004 (LOPSTR 2004)&quot;, S. ETALLE (editor)., Lecture Notes in Computer Science
, 2004
"... Abstract. For use in earlier approaches to automated module interface adaptation, we seek a restricted form of program synthesis. Given some typing assumptions and a desired result type, we wish to automatically build a number of program fragments of this chosen typing, using functions and values av ..."
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Abstract. For use in earlier approaches to automated module interface adaptation, we seek a restricted form of program synthesis. Given some typing assumptions and a desired result type, we wish to automatically build a number of program fragments of this chosen typing, using functions and values available in the given typing environment. We call this problem term enumeration. To solve the problem, we use the CurryHoward correspondence (propositionsastypes, proofsasprograms) to transform it into a proof enumeration problem for an intuitionistic logic calculus. We formally study proof enumeration and counting in this calculus. We prove that proof counting is solvable and give an algorithm to solve it. This in turn yields a proof enumeration algorithm. 1
Proofsearch in typetheoretic languages: an introduction
 Theoretical Computer Science
, 2000
"... We introduce the main concepts and problems in the theory of proofsearch in typetheoretic languages and survey some specific, connected topics. We do not claim to cover all of the theoretical and implementation issues in the study of proofsearch in typetheoretic languages; rather, we present som ..."
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We introduce the main concepts and problems in the theory of proofsearch in typetheoretic languages and survey some specific, connected topics. We do not claim to cover all of the theoretical and implementation issues in the study of proofsearch in typetheoretic languages; rather, we present some key ideas and problems, starting from wellmotivated points of departure such as a definition of a typetheoretic language or the relationship between languages and proofobjects. The strong connections between different proofsearch methods in logics, type theories and logical frameworks, together with their impact on programming and implementation issues, are central in this context.
A Constructive Type System to Integrate Logic and Functional Programming
 CADE Workshop on Proofsearch in Typetheoretic Languages
, 1994
"... In this work we present a type system called HH def that extends the theory of simply typed hereditary Harrop formulae [Mil90] with definitions and strong \Sigmatypes. The use of definitions permits the construction of clearer programs and of shorter proofs by using a rule (the def rule) similar ..."
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In this work we present a type system called HH def that extends the theory of simply typed hereditary Harrop formulae [Mil90] with definitions and strong \Sigmatypes. The use of definitions permits the construction of clearer programs and of shorter proofs by using a rule (the def rule) similar to Gentzen's cut rule. Proofsearch for HH def is performed in a goaldirected manner with occurrences of defined constants in a goal triggering instances of the def rule. Such a search procedure is shown to be complete for HH def . 1 Introduction The motivation for development of the calculus HH def is to provide a logical foundation on which to develop a programming language that integrates logic and functional programming. This work develops the ideas outlined in [Pin94], which are intended to be a first step towards a prooftheoretic characterisation of such programming. The central idea is that the execution mechanisms both for logic and for functional programming can be seen as ...