A Domain-specific Language for Gabriel- Zisman

Abstract

In this thesis, a domain-specific language (DSL) in the functional programming language Haskell is being developed for representing the mathematical structure of simplicial sets, which are collections of n-dimensional geometric objects built from points. As the central component, the Gabriel–Zisman algorithm is being implemented, a procedure operating on simplicial sets that systematically fills gaps in a certain class of composite shapes by filling their hollow constituents. This algorithm will enable researchers to explore computer-instances of simplicial sets and to automate the algorithm showing whether filling these constituent parts is sufficient to complete the composite structure. Completing this task will enable the DSL to support a broader range of algorithms and modelling tasks, potentially defining more complex fillings and other relevant mathematical structures