Sequent Calculus and Equational Programming

Sequent Calculus and Equational Programming

Blog Article

Proof assistants and programming languages based on type theories usually come in two flavours: one The Slacker Jean is based on the standard natural deduction presentation of type theory and involves eliminators, while the other provides a syntax in equational style.We show here that the equational approach corresponds to the use of a focused presentation of a type theory expressed as a sequent calculus.A typed functional language is presented, based on a HR Handlebar sequent calculus, that we relate to the syntax and internal language of Agda.In particular, we discuss the use of patterns and case splittings, as well as rules implementing inductive reasoning and dependent products and sums.