Agda’s standard library struggles in various places with n-ary functions and relations. It introduces congruence and substitution operators for functions of arities one and two, and provides users with convenient combinators for manipulating indexed families of arity exactly one.
After a careful analysis of the kinds of problems the unifier can easily solve, we design a unifier-friendly representation of n-ary functions. This allows us to write generic programs acting on n-ary functions which automatically reconstruct the representation of their inputs’ types by unification. In particular, we can define fully level polymorphic n-ary versions of congruence, substitution and the combinators for indexed families, all requiring minimal user input.
Sun 18 AugDisplayed time zone: Amsterdam, Berlin, Bern, Rome, Stockholm, Vienna change
15:20 - 16:40
Cas van der Rest Utrecht University, Wouter Swierstra Utrecht University, Netherlands, Manuel Chakravarty Tweag I/O & IOHKPre-print
|Generic Level Polymorphic N-ary Functions
Guillaume Allais University of StrathclydeLink to publication
|Augmenting Type Signatures for Program Synthesis
|Constraint-based Type-directed Program Synthesis
Peter-Michael Osera Grinnell CollegeLink to publication