Guido Martinez | Searcharxiv

arXiv2019

Dijkstra Monads for Free

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*.

cs.PL↗

arXiv2019

Dijkstra Monads for All

This paper proposes a general semantic framework for verifying programs with arbitrary monadic side-effects using Dijkstra monads, which we define as monad-like structures indexed by a specification monad. We prove that any monad morphism between a computational monad and a specification monad gives rise to a Dijkstra monad, which provides great flexibility for obtaining Dijkstra monads tailored to the verification task at hand. We moreover show that a large variety of specification monads can be obtained by applying monad transformers to various base specification monads, including predicate transformers and Hoare-style pre- and postconditions. For defining correct monad transformers, we propose a language inspired by Moggi's monadic metalanguage that is parameterized by a dependent type theory. We also develop a notion of algebraic operations for Dijkstra monads, and start to investigate two ways of also accommodating effect handlers. We implement our framework in both Coq and F*, and illustrate that it supports a wide variety of verification styles for effects such as exceptions, nondeterminism, state, input-output, and general recursion.

cs.PL↗