A -model with ∞-groupoid structure based in the Scott’s -model D∞ - MARTÍNEZ RIVILLAS, Daniel Orlando (2020)
The lambda calculus is a universal programming language that represents the functions computable from the point of view of the functions as a rule, that allow the evaluation of a function on any other function. This language can be seen as a theory, with certain pre-established axioms and inference rules, which can be represented by models. Dana Scott proposed the first non-trivial model of the extensional lambda calculus, known as ∞, in order to represent the -terms as the typical functions of set theory, where it is not allowed to evaluate a function about itself. This thesis propose a construction of an ∞-groupoid from any lambda model endowed with a topology. We apply this construction for the particular case ∞ and we observe that the Scott topology does not provide relevant information about of the relation between higher equivalences. This motivates the search for a new line of research focused on the exploration of -models with the structure of a non-trivial ∞-groupoid to generalize the proofs of term conversion (e.g., -equality, -equality) to higher proof in -calculus.