Logic and Computation in a Lambda Calculus with Intersection and Union Types (original) (raw)

Type Assignment for the Computational lambda-Calculus

arXiv (Cornell University), 2019

We study polymorphic type assignment systems for untyped lambda-calculi with effects. We introduce an intersection type assignment system for Moggi's computational lambda-calculus, where a generic monad T is considered, and provide a concrete model of the calculus via a filter model construction. We prove soundness and completeness of the type system, together with subject reduction and expansion properties.

Intersection Types for the Computational lambda-Calculus

ArXiv, 2019

We study polymorphic type assignment systems for untyped lambda-calculi with effects, based on Moggi's monadic approach. Moving from the abstract definition of monads, we introduce a version of the call-by-value computational lambda-calculus based on Wadler's variant with unit and bind combinators, and without let. We define a notion of reduction for the calculus and prove it confluent, and also we relate our calculus to the original work by Moggi showing that his untyped metalanguage can be interpreted and simulated in our calculus. We then introduce an intersection type system inspired to Barendregt, Coppo and Dezani system for ordinary untyped lambda-calculus, establishing type invariance under conversion, and provide models of the calculus via inverse limit and filter model constructions and relate them. We prove soundness and completeness of the type system, together with subject reduction and expansion properties. Finally, we introduce a notion of convergence, which is...

From Semantics to Types: the Case of the Imperative λ -Calculus

2021

We propose an intersection type system for an imperative λ -calculus based on a state monad and equipped with algebraic operations to read and write to the store. The system is derived by solving a suitable domain equation in the category of ω -algebraic lattices; the solution consists of a filter-model generalizing the well known construction for ordinary λ -calculus. Then the type system is obtained out of the term interpretations into the filter-model itself. The so obtained type system satisfies the “type-semantics” property, and it is sound and complete by construction.