Dijkstra Monads for Free

Abstract : Dijkstra monads are a means by which a dependent type theory can be enhanced with support for reasoning about effectful code. These specification-level monads computing weakest preconditions, and their closely related counterparts, Hoare monads, provide the basis on which verification tools like F*, Hoare Type Theory (HTT), and Ynot are built. In this paper 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 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 both by formal proof and via a prototype implementation within F*. Besides equipping F* with a more uniform and extensible effect system, EMF* enables within F* a mixture of intrinsic and extrinsic proofs that was previously impossible.
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Contributor : Cătălin Hriţcu <>
Submitted on : Monday, January 2, 2017 - 9:32:57 PM
Last modification on : Friday, May 25, 2018 - 12:02:06 PM

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Danel Ahman, Cătălin Hriţcu, Kenji Maillard, Guido Martínez, Gordon Plotkin, et al.. Dijkstra Monads for Free. 44th ACM SIGPLAN Symposium on Principles of Programming Languages (POPL), 2017, Paris, France. pp.515-529, ⟨10.1145/3009837.3009878⟩. ⟨hal-01424794⟩

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