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...

A computer-checked library of category theory: Formally verifying currying via the product-exponential adjunction

Existing implementations of category theory for proof assistants aim to be as generic as possible in order to be reusable and extensible, often at the expense of readability and clarity. We present a (partial) formalisation of category theory in the proof assistant Lean limited in purpose to explaining currying, intended to be faithful to the...

A computer-checked library of category theory: Defining functors and their algebras

Category theory is a branch of abstract mathematics that aims to give a high-level overview of relations between objects. Proof assistants are tools that aid in verifying the correctness of mathematical proofs. To reason about category theory using such assistants, fundamental notions have to be defined. Computer-checked libraries contain all...

A Computer-Checked Library of Category Theory: Functors and F-Coalgebras

This research project aims to develop a computer-checked library of category theory within the Lean proof assistant, with a specific emphasis on concepts and examples relevant to functional programming. Category theory offers a robust mathematical framework that allows for the abstraction and comprehension of concepts across diverse fields,...

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,...

Programming With Effects: Improving the quality of code in IO intensive applications through effect handlers

Effect handler orient programming (EHOP) is a recently proposed programming paradigm that aims to provide a high-level abstraction in code. Using this paradigm, programmers are able to define operations as an effect, which are implemented by an effect handler. Functions can then use effects, allowing the effect operations to be used in this...

Exploring Program Equivalence as a Means of Comparing Definitional Interpreters

Grading and giving feedback to student submissions automatically is becoming more and more necessary with an increasing amount of students. To verify the correctness of student-written definitional interpreters, a program equivalence approach has been implemented, improved, and extended with new rules to make it more suited specifically for...