Search for Program Structure

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