Dependent Type-Checking Modulo Associativity and Commutativity

Writing software that follows its specification is important for many applications. One approach to guarantee this is formal verification in a dependently-typed programming language. Formal verification in these dependently-typed languages is based on proof writing. Sadly, while proofs are easy to check for computers, writing proofs can be...

Improving Agda's module system

Agda is a language used to write computer-verified proofs. It has a module system that provides namespacing, module parameters and module aliases. These parameters and aliases can be used to write shorter and cleaner proofs. However, the current implementation of the module system has several problems, such as an exponential desugaring of module...

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...

Dependent Types and Conversion Checking: A literature survey on implementation techniques for type systems

While dependent types can allow programmers to verify properties of their programs, implementing a type checker for a dependent type theory is often difficult. This is due to the fact that, in the presence of dependent types, deciding the equality of types - conversion checking - becomes non-trivial. Due to an identified gap in literature...

Dependently Typed Languages in Statix

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...

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...

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...

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...

Describing Inter Parameter Constraints in Web APIs Using Dependent Types

Web APIs are being used for increasingly larger and complex use cases. Right now it can be hard to make sure that what is documented about an API is correct everywhere and to know if a change will have impact on the users of a web API. When details are missing in an API specification users of that API need to make assumptions about how the API...

Producing a verified implementation of sequences using agda2hs

Purely functional languages are advantageous in that it is easy to reason about the correctness of functions. Dependently typed programming languages such as Agda enable us to prove properties in the language itself. However, dependently typed programming languages have a steep learning curve and are usable only by expert programmers. The...

Dependent Types for Invariants in Session Types

Session types are a formal method to describe communication protocols between two or more actors. Protocols that type check are guaranteed to respect communication safety, linearity, progress, and session fidelity. Basic session types, however, do not in general guarantee anything about the contents of messages, while real-life applications of...