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Title: Second-order algebraic theories
Author: Mahmoud, Ola
ISNI:       0000 0004 2712 2825
Awarding Body: University of Cambridge
Current Institution: University of Cambridge
Date of Award: 2011
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Second-order universal algebra and second-order equational logic respectively provide a model theory and a formal deductive system for languages with variable binding and parameterised metavariables. This workcompletes the foundations of the subject from the viewpoint of categorical algebra. Specifically, this thesis introduces the notion of second-order algebraic theory and develops its basic theory. Two categorical equivalences are established: at the syntactic level, that of second-order equational presentations and second-order algebraic theories; at the semanticlevel, that of second-order algebras and second-order functorial models. The development includes a mathematical definition of syntactic translation between second-order equational presentations. This gives the first formalisation of notions such as encodings and transforms in the context of languages with variable binding.
Supervisor: Fiore, Marcelo Sponsor: Not available
Qualification Name: Thesis (Ph.D.) Qualification Level: Doctoral