agda2hs Documentation

agda2hs is a tool for producing verified and readable Haskell code by extracting it from a (lightly annotated) Agda program. For example, the following Agda program encodes well-formed binary search trees:

open import Haskell.Prelude

_≤_ : {{Ord a}}  a  a  Set
x  y = (x <= y)  True

data BST (a : Set) {{@0 _ : Ord a}} (@0 lower upper : a) : Set where
  Leaf : (@0 pf : lower  upper)  BST a lower upper
  Node : (x : a) (l : BST a lower x) (r : BST a x upper)  BST a lower upper


agda2hs translates this to the following Haskell datatype:

module BST where

data BST a = Leaf
           | Node a (BST a) (BST a)

agda2hs is intended to be used together with the provided Haskell.Prelude module, which provides an Agda implementation of (a large subset of) the Haskell Prelude. It also provides proofs for reasoning about Haskell functions under the Haskell.Law namespace. agda2hs is not compatible with other Agda libraries such as the Agda standard library.


The goal of this project is not to translate arbitrary Agda code to Haskell. Rather it is to carve out a common sublanguage between Agda and Haskell, with a straightforward translation from the Agda side to the Haskell side. This lets you write your program in the Agda fragment, using full Agda to prove properties about it, and then translate it to nice looking readable Haskell code that you can show your Haskell colleagues without shame.

If you want to compile arbitrary Agda programs to runnable (but not readable) Haskell, you should instead use the built-in GHC backend of Agda (a.k.a. MAlonzo).


The documentation you are currently reading is a work in progress, so if you have been using agda2hs and want to contribute in some way, adding documentation or examples would be very welcome.

agda2hs was introduced in the Haskell Symposium ‘22 paper Reasonable Agda is Correct Haskell: Writing Verified Haskell using agda2hs.

Future work

Currently agda2hs is under active development, please take a look at the issue tracker. If you have a suggestion for a new feature that is not yet on the issue tracker, you are welcome to create a new issue or a PR. Feature requests should be of the form “Add support for Haskell feature X”, not “Add support for Agda feature Y” (see “Objective” above). If you want to compile arbitrary Agda code to Haskell, you are advised to use Agda’s built-in GHC backend instead.