A Hoare logic style refinement types formalisation

Abstract

Refinement types is a lightweight yet expressive tool for specifying and reasoning about programs. The connection between refinement types and Hoare logic has long been recognised but the discussion remains largely informal. In this paper, we present a Hoare triple style Agda formalisation of a refinement type system on a simply-typed λ-calculus restricted to first-order functions. In our formalisation, we interpret the object language as shallow Agda terms and use Agda’s type system as the underlying logic for the type refinement. To deterministically typecheck a program with refinement types, we reduce it to the computation of the weakest precondition and define a verification condition generator which aggregates all the proof obligations that need to be fulfilled to witness the well-typedness of the program.