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This repository contains a converter from Haskell code to equivalent Coq code, as part of the CoreSpec component of the DeepSpec project.

CPP'18 paper “Total Haskell is Reasonable Coq” by Antal Spector-Zabusky, Joachim Breitner, Christine Rizkallah, and Stephanie Weirich. This paper describes the following examples:

  • bag Multiset implementation from GHC's implemention
  • compiler Hutton's razor
  • base-src The sources of the base/ directory

ICFP'18 paper "Ready, set, verify! applying hs-to-coq to real-world Haskell code (experience report)" by Joachim Breitner, Antal Spector-Zabusky, Yao Li, Christine Rizkallah, John Wiegley, and Stephanie Weirich. This paper describes the verification of the containers library.

Documentation for the hs-to-coq tool is available!


hs-to-coq uses Coq 8.10.2 and ssreflect.


The recommended way of building hs-to-coq is to use stack. If you have not setup stack before, run:

stack setup

To build hs-to-coq, then run

stack build

(hs-to-coq can be built with GHC 8.4, 8.6, 8.8, and 8.10. However, the repo only contains the translation of Haskell libraries such as base from GHC 8.4. Therefore, it is advised to build hs-to-coq with GHC 8.4 if you plan to use example translations contained in this repo.)

Building the base library

This repository comes with a version of (parts of the) Haskell base library converted to Coq, which you will likely need if you want to verify Haskell code.

You must have Coq 8.10.2 and ssreflect to build the base library. To install these tools:

  1. opam repo add coq-released (for SSReflect and MathComp)
  2. opam update
  3. opam install coq.8.10.2 coq-mathcomp-ssreflect.1.10.0

Once installed, you can build the base library with

make -C base

Th directory base-thy/ contains auxillary definitions and lemmas, such as lawful type-class instances. You can build these with

make -C base-thy

Using the tool

To use the tool, run it (using stack), passing the Haskell file to be translated and an output directory to write to:

stack exec hs-to-coq -- -o output-directory/ Input/File.hs

Very likely you want to make use of the base/ library. In that case, make sure you pass -e base/edits.

Have a look at the example directories, e.g. examples/successors, for a convenient Makefile based setup.


The edits file contains directives to hs-to-coq for ignoring or transforming some Haskell constructs into proper Coq.

For example, it is common in Haskell to have the following code:

module Foo where
newtype SomeType = SomeType { someFiled :: Integer }

Coq has a single namespace for types and values hence the type name will conflict with constructor name. One can pass -e edit file containing custom directives to ensure correctness of generated code with the following directive:

rename value Foo.SomeType = Foo.MkSomeType

See the manual for documentation for the edits files.

Other directories

  • The examples/ directories contains a number of example translation and verification projects, including

    Some examples use git submodule, so run

    git submodule update --init --recursive


  • structural-isomorphism-plugin: (In progress.) A GHC plugin that connects the re-extracted converted code back into GHC, allowing us to run Haskell programs against verified/verifiable code. Currently does not work.