MPhil in Advanced Computer Science Advanced

SYLLABUS A range of topics for the course follows. 1. Algebraic theories: universal algebra; equational logic; soundness and completeness; theory translations and constructions. 2. Algebras: initial algebras; induction principle; recursive domain equations; free algebras. 3. Presheaves: cartesian closure; essential geometric morphisms; free cocompletions; Kan extensions; coends. 4. Simply typed lambda calculus: λ-definability; Kripke logical relations; glueing; normalisation by evaluation; conservative extensions. 5. Monoidal categories: Day’s convolution tensor product; substitution tensor products; operads. 6. Second-order algebraic theories: variable binding and α-equivalence; captureavoiding substitution; metavariables; meta-substitution. 7. Joyal’s species of structures: calculus of combinatorial constructions; analytic functors; the Schanuel topos.