Graph-Based Proof Counting and Enumeration with Applications for Program Fragment Synthesis

  • J. B. Wells
  • Boris Yakobowski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 3573)


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 Curry-Howard correspondence (propositions-as-types, proofs-as-programs) 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.


Sequent Calculus Proof Tree Goal Typing Proof Search Program Synthesis 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2005

Authors and Affiliations

  • J. B. Wells
    • 1
  • Boris Yakobowski
    • 2
  1. 1.Heriot-Watt University 
  2. 2.ENS Lyon 

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