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Search for Program Structure

Author Gabriel Scherer

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Gabriel Scherer

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Gabriel Scherer. Search for Program Structure. In 2nd Summit on Advances in Programming Languages (SNAPL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 71, pp. 15:1-15:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)
https://doi.org/10.4230/LIPIcs.SNAPL.2017.15

Abstract

The community of programming language research loves the Curry-Howard correspondence between proofs and programs. Cut-elimination as computation, theorems for free, 'call/cc' as excluded middle, dependently typed languages as proof assistants, etc. Yet we have, for all these years, missed an obvious observation: "the structure of programs corresponds to the structure of proof search". For pure programs and intuitionistic logic, more is known about the latter than the former. We think we know what programs are, but logicians know better! To motivate the study of proof search for program structure, we retrace recent research on applying focusing to study the canonical structure of simply-typed lambda-terms. We then motivate the open problem of extending canonical forms to support richer type systems, such as polymorphism, by discussing a few enticing applications of more canonical program representations.
Keywords
  • programs
  • proofs
  • focusing
  • canonicity

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