Dijkstra monads for free

Ahman, Danel; HriţcuCătălin,; MaillardKenji,; MartínezGuido,; PlotkinGordon,; ProtzenkoJonathan,; RastogiAseem,; SwamyNikhil,

doi:10.1145/3093333.3009878

Cited by 11 publications

(10 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Functions can also be annotated with other effects, e.g., to indicate stateful operations affecting the heap, or a function that handles program IO. F relies on SMT-based automation to prove properties about programs using a weakest-precondition calculus [8], and it also includes a tactic system [55] to allow the programmer greater control over how proofs are discharged.…”

Section: A Background On Evercryptmentioning

confidence: 99%

EverCrypt: A Fast, Verified, Cross-Platform Cryptographic Provider

Protzenko

Parno

Fromherz

et al. 2020

2020 IEEE Symposium on Security and Privacy (SP)

Self Cite

View full text Add to dashboard Cite

We present EverCrypt: a comprehensive collection of verified, high-performance cryptographic functionalities available via a carefully designed API. The API provably supports agility (choosing between multiple algorithms for the same functionality) and multiplexing (choosing between multiple implementations of the same algorithm). Through abstraction and zero-cost generic programming, we show how agility can simplify verification without sacrificing performance, and we demonstrate how C and assembly can be composed and verified against shared specifications. We substantiate the effectiveness of these techniques with new verified implementations (including hashes, Curve25519, and AES-GCM) whose performance matches or exceeds the best unverified implementations. We validate the API design with two high-performance verified case studies built atop EverCrypt, resulting in line-rate performance for a secure network protocol and a Merkle-tree library, used in a production blockchain, that supports 2.7 million insertions/sec. Altogether, EverCrypt consists of over 124K verified lines of specs, code, and proofs, and it produces over 29K lines of C and 14K lines of assembly code. SpecificationsImplementations Spec.Hash val compress (a:alg) (st:words a) (b:block a) : words_state a val init val finish val compress_many val hash EverCrypt.Hash val compress (st:state alg) (b:larr uint8 alg) : Stack unit (requires fun h0 -> ...) (ensures fun h0 _ h1 -> ... /\ repr s h1 == Spec.Hash.compress alg (repr s h0) (as_seq h0 b))val init, finish, compress_many, hash Refines Spec.MD5 val compress: ... val init: ...

show abstract

Section: A Background On Evercryptmentioning

confidence: 99%

EverCrypt: A Fast, Verified, Cross-Platform Cryptographic Provider

Protzenko

Parno

Fromherz

et al. 2020

2020 IEEE Symposium on Security and Privacy (SP)

Self Cite

View full text Add to dashboard Cite

show abstract

“…Rule Lam places the abstract variable in the context with the declared erasure annotation , while McBride [2016] and QTT [Atkey 2018] would place : ∧ in the context here. We use a different application and substitution rule instead.…”

Section: Typing Rulesmentioning

confidence: 99%

“…'. Like EPTS [Mishra-Linger 2008] and TT ★ , McBride's calculus [2016] introduces quantities on binders. Unlike TT ★ , the calculus allows an extra łlinearž quantity in addition to łerasedž and łunerasedž, thus unifying erasure and linear types in a single dependently typed framework.…”

Section: Related Workmentioning

confidence: 99%

See 1 more Smart Citation

A dependently typed calculus with pattern matching and erasure inference

Tejiščák

2020

Proc. ACM Program. Lang.

View full text Add to dashboard Cite

Some parts of dependently typed programs constitute evidence of their type-correctness and, once checked, are unnecessary for execution. These parts can easily become asymptotically larger than the remaining runtime-useful computation, which can cause normally linear-time programs run in exponential time, or worse. We should not make programs run slower by just describing them more precisely. Current dependently typed systems do not erase such computation satisfactorily. By modelling erasure indirectly through type universes or irrelevance, they impose the limitations of these means to erasure. Some useless computation then cannot be erased and idiomatic programs remain asymptotically sub-optimal. In this paper, we explain why we need erasure, that it is different from other concepts like irrelevance, and propose a dependently typed calculus with pattern matching with erasure annotations to model it. We show that erasure in well-typed programs is sound in that it commutes with reduction. Assuming the Church-Rosser property, erasure furthermore preserves convertibility in general. We also give an erasure inference algorithm for erasure-unannotated or partially annotated programs and prove it sound, complete, and optimal with respect to the typing rules of the calculus. Finally, we show that this erasure method is effective in that it can not only recover the expected asymptotic complexity in compiled programs at run time, but it can also shorten compilation times.

show abstract

“…Specifically, in a total correctness setting, being able to assign the type T A wp to a stateful computation M guarantees that if M is executed in a state V S that satisfies wp V Q V S (for some postcondition V Q ), then the execution of M produces a value V and a state V ′ S that satisfy V Q V V ′ S . In a recent joint work by the author and Hrit ¸cu et al [10], F* has been extended with a means for representing computational effects and their combinations using monads defined in a simply typed definition language, with the corresponding predicate transformers and Dijkstra monads derived automatically using a selective CPS-transformation; this includes global state, exceptions, and continuations, but currently excludes I/O and probability.…”

Section: F*mentioning

confidence: 99%

Fibred Computational Effects

Ahman

2017

Preprint

Self Cite

View full text Add to dashboard Cite

We study the interplay between dependent types and computational effects, two important areas of modern programming language research. On the one hand, dependent types underlie proof assistants such as Coq and functional programming languages such as Agda, Idris, and F*, providing programmers a means for encoding detailed specifications of program behaviour using types. On the other hand, computational effects, such as exceptions, nondeterminism, state, I/O, probability, etc., are integral to all widely-used programming languages, ranging from imperative languages, such as C, to functional languages, such as ML and Haskell. Separately, dependent types and computational effects both come with rigorous mathematical foundations, dependent types in the effect-free setting and computational effects in the simply typed setting.Their combination, however, has received much less attention and no similarly exhaustive theory has been developed. In this thesis we address this shortcoming by providing a comprehensive treatment of the combination of these two fields, and demonstrating that they admit a mathematically elegant and natural combination.Specifically, we develop a core effectful dependently typed language, eMLTT, based on Martin-Löf's intensional type theory and a clear separation between (effectfree) values and (possibly effectful) computations familiar from simply typed languages such as Levy's Call-By-Push-Value and Egger et al.'s Enriched Effect Calculus.A novel feature of our language is the computational Σ-type, which we use to give a uniform treatment of type-dependency in sequential composition. In addition, we define and study a class of category-theoretic models, called fibred adjunction models, that are suitable for defining a sound and complete interpretation of eMLTT. Specifically, fibred adjunction models naturally combine standard category-theoretic models of dependent types (split closed comprehension categories) with those of computational effects (adjunctions). We discuss and study various examples of these models, including a domain-theoretic model so as to extend eMLTT with general recursion.We also investigate a dependently typed generalisation of the algebraic treatment of computational effects by showing how to extend eMLTT with fibred algebraic effects and their handlers. In particular, we specify fibred algebraic effects using a dependently typed generalisation of Plotkin and Pretnar's effect theories, enabling us to capture precise notions of computation such as state with location-dependent store types and dependently typed update monads. For handlers, we observe that their conventional term-level definition leads to unsound program equivalences becoming derivable in languages that include a notion of homomorphism, such as eMLTT. To solve this iii I would like to thank the many people who have been important to my PhD studies. This long journey would not have been possible without their support and guidance.First and foremost, I would like to express my sincerest gratitude to my superviso...

show abstract

Dijkstra monads for free

Cited by 11 publications

References 41 publications

EverCrypt: A Fast, Verified, Cross-Platform Cryptographic Provider

EverCrypt: A Fast, Verified, Cross-Platform Cryptographic Provider

A dependently typed calculus with pattern matching and erasure inference

Fibred Computational Effects

Contact Info

Product

Resources

About