Formally proving the correctness of the (un)currying refactoring: Using Agda with a simple Haskell-like programming language

When designing critical software, great care must be taken to guarantee its correctness. Refactoring is one of the techniques used to improve code readability, maintainability, and other factors without changing functionality. Thus, to ensure that it is properly applied, automated tools are used to perform refactoring. To ensure that the code...

Maybe a List would be better?: Correct by construction Maybe to List refactorings in a Haskell-like language

This paper concerns itself with correct by construction refactoring of Maybe values to List values in a Haskell-like language (HLL) as a case study on data-oriented refactorings. Our language makes use of intrinsically-typed syntax and de Bruijn indices for variables. Operational semantics are defined using big step semantics. We define a...

Proving correctness of refactoring tuples to records: A correct-by-construction approach on a Haskell-like language

Refactoring is a useful tool for increasing the overall quality of software without making changes to how it interacts with the environment. To verify that a refactoring operation correctly transforms an expression, one can provide a formal proof. Using Agda, a dependently-typed language, as a proof assistant, we investigate the feasibility of...

Extracting LLVM Intermediate Representation from Agda

Agda, a promising dependently typed function language, needs more mainstream adoption. By the process of code extraction, we compile proven Agda code into a popular existing language, allowing smooth integration with existing workflows. Due to Agda’s pluggable nature, this process is relatively straightforward. We implement a solution in Haskell...

Practical Verification of Lenses: Implementing Formally Verified Lenses using agda2hs

agda2hs is a tool which translates a subset of Agda to readable Haskell. Using agda2hs, programmers can implement libraries in this subset of Agda, formally verify them, and then convert them to Haskell. In this paper we present a new, verified implementation of the lens data type, which is used to access data structures in a readable yet...

Agda2Rust: A Study on an Alternative Backend for the Agda Compiler

Agda is a functional programming language with built-in support for dependent types. A dependent type depends on a value. This allows the developer to specify strict constraints for the types used in an application. Writing code with dependent types results in fewer type-related errors slipping through the compilation process. <br/>When...

Practical Verification of the Reader Monad

Agda2hs is a tool that allows developers to write verified programs using Agda and then translate these programs to Haskell while maintaining the verified properties. Previous research has shown that Agda2hs can be used to produce a verified implementation of a wide range of programs. However, monads that model effectful computations were...

Practical Verification of Infinite Structures in agda2hs

Agda allows for writing code that can be mathematically proven and verified to be correct, this type of languages is generally known as a proof assistant. The agda2hs library makes an effort to translate Agda to readable Haskell, in a way the Haskell is still consistent. In previous work it is shown that with the current agda2hs implementation,...

Code extraction from Agda to HVM

Dependently typed languages such as Agda have the potential to revolutionize the way we write software because they allow the programmer to catch more bugs at compile time than classical languages. Nonetheless, dependently typed languages are hardly used in practice. One of the reasons is the lack of mature compilers for them.<br/>This paper...

Comparing Code extraction from Agda to Java to existing Methods

Dependent programming languages such as Agda show a lot of promise in creating new ways of writing code, but currently suffer from a lack of support and features. In this paper we attempt to create a new back-end for Agda targeting Java which has a huge and thriving ecosystem.<br/><br/>We implement the new back-end for Agda in Haskell and we...

Code Extraction from a Dependently Typed Language to a Stack Based Language

Dependently typed languages such as Agda can provide users certain guarantees about the correct- ness of the code that they write, however, this comes at the cost of excess code that is not used at run time. Agda code is currently compiled to another language before it is run, there are not many target languages in popular use, so it is unclear...

Verifying correctness of Haskell programs using the programming language Agda and framework agda2hs

Equational reasoning based verification address some of the limitations of classical testing. The Curry-Howard correspondence shows a direct link between type systems and mathematical logic based proofs. Agda is a language with totality and dependent types which makes use of the CH isomorphism to support equational reasoning in its programs. ...

Practical Verification of the Inductive Graph Library

Formal verification works better than testing, since the correctness of a program is proven. It is researched if it is possible and feasible to formally verify the Inductive Graph Library. The library is an abstract class in Haskell and is ported manually to Agda. Agda is a total and dependently typed language and thus can be used as a proof...