Agda2hs is a program which compiles a subset of Agda to Haskell. In this paper, an implementation of the Haskell library QuadTree is created and verified in this subset of Agda, such that Agda2hs can then produce a verified Haskell implementation. To aid with this verification, a number of techniques have been proposed which are used to prove invariants, preconditions and post-conditions of the QuadTree library. Using these techniques, the properties of the library have been proven. Additionally, recommendations are made to reduce the time needed for verification.

Static type systems can greatly enhance the quality of programs, but implementing a type checker for them is challenging and error-prone. The Statix meta-language (part of the Spoofax language workbench) aims to make this task easier by automatically deriving a type checker from a declarative specification of the type system. However, so far Statix has not been used to implement a type system with dependent types, an expressive class of type systems which require evaluation of terms during type checking. In this thesis, we present a specification of a simple dependently typed language in Statix, and discuss how to extend it with several common features such as inductive data types, universes, and inference of implicit arguments. While we encountered some challenges in the implementation, our conclusion is that Statix is already usable as a tool for implementing dependent types.