Pedagogical lambda-cube: the λ² case

Vincent Demange (1)

1 TYPES - Logic, Proof Theory and Programming

In pedagogical formal systems one needs to systematically give examples of hypotheses made. This main characteristic is not the only one needed, and a formal definition of pedagogical sub-systems of the Calculus of Constructions (CC) has already been stated. Here we give such a pedagogical sub-system of CC corresponding to the second-order pedagogical λ-calculus of Colson and Michel. It thus illustrates the appropriateness of the formal definition, and opens the study to stronger systems of the λ-cube, for which CC is the most expressive representative. In addition we study the type-checking problem for the formalisms of those pedagogical calculi of second-order.

Mots clés: typed lambda-calculus; calculus of constructions: pedagogical formal systems; mathematical logic; negationless mathematics; constructive mathematics

Domaines: Logique en informatique [cs.LO]; Logique [math.LO]

Vincent Demange. Pedagogical lambda-cube: the λ² case. 2014. ⟨hal-00958835⟩