Modelling cyclic structures in Agda
Evaluating Agda's coinduction through modelling graphs
F. Mangroe (TU Delft - Electrical Engineering, Mathematics and Computer Science)
Jesper Cockx – Mentor (TU Delft - Programming Languages)
B. Liesnikov – Mentor (TU Delft - Programming Languages)
Diomidis Spinellis – Graduation committee member (TU Delft - Software Engineering)
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Abstract
Graphs are a widely used concept within computer science. Modelling graphs can be done in various ways, but the most popular approach is doing so inductively. When graphs contain cycles modelling them becomes less intuitive. A solution for this is using the dual of induction called coinduction, which has not been as well researched as induction. In this paper I explored the possibilities and limitations of coinduction in Agda by modelling graphs using coinduction. I looked at the struggles I encountered while coding in Agda. I also provide implementations of the graphs encodings. Suitability of the encodings is determined through experiments, in which properties about graphs are proven. Both guarded coinduction and musical coinduction were successful in all of the experiments. Creating an implementation using sized types was not successful. The main improvements I identified are concerning the ease of use for a new user of Agda. I recommend improving the documentation as well as the clarity of the error messages.