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...

Speeding up program synthesis using specification discovery

How convenient would it be to have an AI that relieves us programmers from the burden of coding? Program synthesis is a technique that achieves exactly that: it automatically generates simple programs that meet a given set of examples or adhere to a provided specification. This is often done by enumerating all programs in the search space and...

Bringing Formal Verification into Widespread Programming Language Ecosystems

Formal verification is a powerful tool for ensuring program correctness but is often hard to learn to use and has not yet spread into the commercial world. This thesis focuses on finding an easy-to-use solution to make formal verification available in popular programming language ecosystems. We propose a solution where users can write code in an...

Tactics in Agda using reflection

In this thesis, we develop a new library for Agda named Attic, which allows us to create and compose proof tactics that can be used to generate terms through reflection. Such tactics can be converted to Agda macros, allowing them to be used in term positions where they can generate term solutions of the expected type. Tactics can make the...