Dependent Types and Multi-monadic Effects in F⭑

Nikhil Swamy¹    Cătălin Hriţcu²    Chantal Keller^1,3    Aseem Rastogi⁴
Antoine Delignat-Lavaud^2,5    Simon Forest^2,5    Karthikeyan Bhargavan²    Cédric Fournet^1,3
Pierre-Yves Strub⁶    Markulf Kohlweiss¹    Jean-Karim Zinzindohoue^2,5    Santiago Zanella-Béguelin¹

¹Microsoft Research    ²Inria    ³MSR-Inria    ⁴UMD    ⁵ENS Paris    ⁶IMDEA Software Institute

Symposium on Principles of Programming Languages, POPL 2016

Abstract

We present a new, completely redesigned, version of F⭑, a language that works both as a proof assistant as well as a general-purpose, verification-oriented, effectful programming language.

In support of these complementary roles, F⭑ is a dependently typed, higher-order, call-by-value language with primitive effects including state, exceptions, divergence and IO. Although primitive, programmers choose the granularity at which to specify effects by equipping each effect with a monadic, predicate transformer semantics. F⭑ uses this to efficiently compute weakest preconditions and discharges the resulting proof obligations using a combination of SMT solving and manual proofs. Isolated from the effects, the core of F⭑ is a language of pure functions used to write specifications and proof terms---its consistency is maintained by a semantic termination check based on a well-founded order.

We evaluate our design on more than 55,000 lines of F⭑ we have authored in the last year, focusing on three main case studies. Showcasing its use as a general-purpose programming language, F⭑ is programmed (but not verified) in F⭑, and bootstraps in both OCaml and F#. Our experience confirms F⭑'s pay-as-you-go cost model: writing idiomatic ML-like code with no finer specifications imposes no user burden. As a verification-oriented language, our most significant evaluation of F⭑ is in verifying several key modules in an implementation of the TLS-1.2 protocol standard. For the modules we considered, we are able to prove more properties, with fewer annotations using F⭑ than in a prior verified implementation of TLS-1.2. Finally, as a proof assistant, we discuss our use of F⭑ in mechanizing the metatheory of a range of lambda calculi, starting from the simply typed lambda calculus to System F-omega and even micro-F⭑, a sizeable fragment of F⭑ itself---these proofs make essential use of F⭑'s flexible combination of SMT automation and constructive proofs, enabling a tactic-free style of programming and proving at a relatively large scale.