We present Pirouette, a language for typed higher-order functional choreographic programming. Pirouette offers programmers the ability to write centralized program and compile it via endpoint projection into programs each node in distributed system. Moreover, is defined generically over (local) of messages, lifts guarantees about message type system its own. Message soundness also deadlock free...

We show that it is decidable whether a third order matching problem in an extension of the simply typed lambda calculus with type constructors has a solution or not We present an algorithm which given such a problem returns a solution for this problem if the problem has a solution and returns fail otherwise We also show that it is undecidable whether a third order matching problem in has a clos...

We give a new characterisation of morphisms that are definable by the interpretation of the simply typed lambda calculus with sums in any bi-Cartesian closed category. The ⊤⊤-closure operator will be used to construct the category in which the collection of definable morphisms at sum types can be characterised as the coproducts of such collections at lower types.

We propose a language design where types can be enriched by tags corresponding to predicates written by the programmer. For instance, int&positive is a type, where positive is a user-defined boolean function on integers. Expressions of type int&positive are obtained by an explicit check construct, analogous to cast, e.g., (positive) 2. In this way, the fact that the value of an expression is gu...

Abst rac t . A type is inhabited (non-empty) in a typed calculus iff there is a closed term of this type. The inhabitation (emptiness) problem is to determine if a given type is inhabited. This paper provides direct, purely syntactic proofs of the following results: the inhabitation problem is PSPACE-complete for simply typed lambda-calculus and undecidable for the polymorphic second-order and ...

Definition 2 A typed family of sets D is a collection of sets Dα indexed by types α ∈ T . A typed family of nonempty sets D is a typed family of sets such that Dα is nonempty for each α ∈ T . Given two typed families of sets D and D, a typed function f : D → D is a collection of functions fα : Dα → D α indexed by types α ∈ T . We use FT (D,D ) to denote the set of typed functions from a typed f...

In the last couple of years several dynamically-typed, object-oriented programming languages have been equipped with optional static type checkers. This typically requires these to be extended a downcast operator, which is common operator in statically-typed but not dynamically-typed languages. Our objective investigate an approach for checking that does require such additional operator. We sys...

This paper proves the fundamental theorem of uncertain calculus with respect to both canonical process and renewal process, which gives the differential of an uncertain process in the form of a function of canonical process and renewal process.