Dijkstra Monads for Free

TL;DR

This paper introduces a method to automatically derive Dijkstra monads for effectful computations using CPS translation, enhancing dependent type theories with verified effect reasoning.

Contribution

It presents a novel approach to derive Dijkstra monads automatically, improving effect reasoning in dependent type theories and implementing it in EMF* for practical validation.

Findings

Automatic derivation of Dijkstra monads is correct and efficient.

EMF* extends F* with a more uniform effect system.

Supports intrinsic and extrinsic proofs within F*.

Abstract

Dijkstra monads enable a dependent type theory to be enhanced with support for specifying and verifying effectful code via weakest preconditions. Together with their closely related counterparts, Hoare monads, they provide the basis on which verification tools like F*, Hoare Type Theory (HTT), and Ynot are built. We show that Dijkstra monads can be derived "for free" by applying a continuation-passing style (CPS) translation to the standard monadic definitions of the underlying computational effects. Automatically deriving Dijkstra monads in this way provides a correct-by-construction and efficient way of reasoning about user-defined effects in dependent type theories. We demonstrate these ideas in EMF*, a new dependently typed calculus, validating it via both formal proof and a prototype implementation within F*. Besides equipping F* with a more uniform and extensible effect system, EMF* enables a novel mixture of intrinsic and extrinsic proofs within F*.