A Categorical Model for the Lambda Calculus with Constructors

The lambda calculus with constructors is an extension of the lambda calculus with variadic constructors. It decomposes the pattern-matching à la ML into a case analysis on constants and a commutation rule between case and application constructs. Although this commutation rule does not match with the usual computing intuitions, it makes the calculus expressive and confluent, with a rather simple syntax. In this paper we define a sound notion of categorical model for the lambda calculus with constructors. We then prove that this definition is complete for the fragment of the calculus with no match-failure, using the model of partial equivalence relations.