May 7-10, 2017 Asilomar, California
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 the logical technique of focusing to study the canonical structure of simply-typed λ-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.