The next meeting of the Algebra and Logic Seminar will be held

on

**August 30, 2019**(Friday) at**1:00 p.m.**in**Room 578**of the Institute of Mathematics and Informatics.A talk on

## TYPE-THEORY OF ACYCLIC RECURSION AND ITS REDUCTION CALCULUS

will be delivered by

**Rusanka LUKANOVA**.Everybody is invited.

**Abstract**. In this talk, I will introduce Moschovakis typed-theory of algorithms. I shall present its formal language and original reduction calculus, which reduces the terms to their canonical forms. Distinctively, the reduction calculus associates the formal theory with denotational and algorithmic semantics. The canonical forms determine the relation of algorithmic equivalence between terms.

If time allows, I will extend the formal system by gamma-reduction and algorithmic gamma-equivalence. The gamma-calculus reduces the algorithmic complexity, by simplifying recursion terms that have superfluous lambda-abstraction and corresponding functional applications.