This tutorial will go through these steps in detail:
#COQ TACTICS INSTALL#
It also contains additional setup information, in particular instructions to install Coq and details of software versions. The complete files produced in this tutorial can be found in this repository. To start, create the following directories and clone the hs-to-coq repository: mkdir src src-coq theories This tutorial can be followed by just reading along or by replaying the examples on your own.
#COQ TACTICS VERIFICATION#
In this tutorial, we will walk through the verification of a simple data structure: a purely functional queue.įamiliarity with basic concepts of functional programming is assumed (algebraic data types, pattern-matching, and recursive functions) and some determination to decipher the explanations of Coq code is recommended. A verified version of containers is available on Hackage. Hs-to-coq has already been used to verify subsets of the libraries base (Haskell’s standard library) and containers (in particular, Map, Set, and IntSet). The hs-to-coq project leverages that similarity to translate Haskell programs into Coq, so they can then be subjected to mechanized formal specification and proof. Haskell to CoqĬoq and Haskell are both pure functional languages, and thus closely related both syntactically and semantically. It is a skill you can pick up like another programming language, and you can start to apply it to verify libraries and programs. This tutorial shows a glimpse of interactive theorem proving in practice. You may already be curious about interactive theorem proving and its close ties to functional programming. This post is a practical introduction to using the hs-to-coq tool to verify Haskell programs in Coq. Projects such as VST (for C) and hs-to-coq aim to bring down that barrier, allowing programs in widely used programming languages to be the actual objects of study. One of perhaps many barriers to the adoption of proof assistants is that they are most commonly used to formalize models that are nevertheless disconnected from the programs that eventually run. Rather than tools for experts, they can be vessels to teach formal methods, and bridges to bring cutting-edge knowledge into the hands of non-specialists.
Proof assistants such as Isabelle, Coq, Agda, and Lean are already available, and they are here to stay. Much work remains to be done to realize that vision practically, but there are good reasons to be hopeful. Proof assistants mechanize reasoning like compilers mechanize programming, translating high-level programs to execute on machines which understand low-level instructions.
Even a relatively untrained programmer must have some intuitive idea of why their program is correct a proof assistant helps users fill the gaps in their reasoning, and point out parts where more attention is required. The objective is to codify reasoning that people are already doing in their heads. Proof assistants create an objective standard of rigor: if a proof type-checks, it is correct. Even with the necessary skills in hand, applying them requires sustained effort and perseverance to succeed.Īutomating logic can reduce the cost of formal reasoning. Writing a rigorous proof requires knowledge and discipline which take years of expensive training and experience to acquire. Proving programs correct is possible, but it is also very hard. Many solutions have been devised to reduce the likelihood and impact of human error in programming, testing and type systems being prominent examples. A program can also fail, over and over, billions of instructions per second.
And with great power comes great responsibility. A task, a program, can be run over and over, billions of instructions per second. Programming is the power of automation at our fingertips.
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