A simple library implementation of binary sessions

2016 ◽  
Vol 27 ◽  
Author(s):  
LUCA PADOVANI
Keyword(s):  
Programming Language ◽  
Protocol Analysis ◽  
Simple Approach ◽  
Type Inference ◽  
Hybrid Form ◽  
Type Checking ◽  
Session Types ◽  
Parametric Polymorphism ◽  
Session Type

AbstractInspired by the continuation-passing encoding of binary sessions, we describe a simple approach to embed a hybrid form of session type checking into any programming language that supports parametric polymorphism. The approach combines static protocol analysis with dynamic linearity checks. To demonstrate the effectiveness of the technique, we implement a well-integrated OCaml module for session communications. For free, OCaml provides us with equirecursive session types, parametric behavioural polymorphism, complete session type inference, and session subtyping.

scholarly journals Nested Session Types

2021 ◽  
pp. 178-206
Author(s):  
Ankush Das ◽  
Henry DeYoung ◽  
Andreia Mordido ◽  
Frank Pfenning
Keyword(s):  
Programming Language ◽  
Message Passing ◽  
Communication Protocols ◽  
Type System ◽  
First Order ◽  
Session Types ◽  
Parametric Polymorphism ◽  
Trace Equivalence

AbstractSession types statically describe communication protocols between concurrent message-passing processes. Unfortunately, parametric polymorphism even in its restricted prenex form is not fully understood in the context of session types. In this paper, we present the metatheory of session types extended with prenex polymorphism and, as a result, nested recursive datatypes. Remarkably, we prove that type equality is decidable by exhibiting a reduction to trace equivalence of deterministic first-order grammars. Recognizing the high theoretical complexity of the latter, we also propose a novel type equality algorithm and prove its soundness. We observe that the algorithm is surprisingly efficient and, despite its incompleteness, sufficient for all our examples. We have implemented our ideas by extending the Rast programming language with nested session types. We conclude with several examples illustrating the expressivity of our enhanced type system.

Cubical Agda: A dependently typed programming language with univalence and higher inductive types

2021 ◽  
Vol 31 ◽  
Author(s):  
ANDREA VEZZOSI ◽  
ANDERS MÖRTBERG ◽  
ANDREAS ABEL
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Type Checking ◽  
Dependent Type Theory ◽  
Wide Range ◽  
General Schema ◽  
Direct Definition ◽  
Inductive Types ◽  
Definition Of ◽  
Cubical Type Theory

Abstract Proof assistants based on dependent type theory provide expressive languages for both programming and proving within the same system. However, all of the major implementations lack powerful extensionality principles for reasoning about equality, such as function and propositional extensionality. These principles are typically added axiomatically which disrupts the constructive properties of these systems. Cubical type theory provides a solution by giving computational meaning to Homotopy Type Theory and Univalent Foundations, in particular to the univalence axiom and higher inductive types (HITs). This paper describes an extension of the dependently typed functional programming language Agda with cubical primitives, making it into a full-blown proof assistant with native support for univalence and a general schema of HITs. These new primitives allow the direct definition of function and propositional extensionality as well as quotient types, all with computational content. Additionally, thanks also to copatterns, bisimilarity is equivalent to equality for coinductive types. The adoption of cubical type theory extends Agda with support for a wide range of extensionality principles, without sacrificing type checking and constructivity.

scholarly journals Bidirectional Typing

2021 ◽  
Vol 54 (5) ◽  
pp. 1-38
Author(s):  
Jana Dunfield ◽  
Neel Krishnaswami
Keyword(s):  
Type Systems ◽  
Design Principles ◽  
Type Inference ◽  
Type Synthesis ◽  
Type Checking ◽  
Local Type ◽  
Typed Languages

Bidirectional typing combines two modes of typing: type checking, which checks that a program satisfies a known type, and type synthesis, which determines a type from the program. Using checking enables bidirectional typing to support features for which inference is undecidable; using synthesis enables bidirectional typing to avoid the large annotation burden of explicitly typed languages. In addition, bidirectional typing improves error locality. We highlight the design principles that underlie bidirectional type systems, survey the development of bidirectional typing from the prehistoric period before Pierce and Turner’s local type inference to the present day, and provide guidance for future investigations.

scholarly journals Session Type Inference in Haskell

2011 ◽  
Vol 69 ◽  
pp. 74-91 ◽  
Author(s):  
Keigo Imai ◽  
Shoji Yuen ◽  
Kiyoshi Agusa
Keyword(s):  
Type Inference ◽  
Session Type

FIRST-CLASS CONTEXTS IN ML

2000 ◽  
Vol 11 (01) ◽  
pp. 65-87
Author(s):  
MASATOMO HASHIMOTO
Keyword(s):  
Programming Language ◽  
Operational Semantics ◽  
Type System ◽  
Type Inference ◽  
Inference Algorithm ◽  
Hole Filling ◽  
Dynamic Binding ◽  
Polymorphic Type ◽  
Open Program ◽  
Program Modules

This paper develops an ML-style programming language with first-class contexts i.e. expressions with holes. The crucial operation for contexts is hole-filling. Filling a hole with an expression has the effect of dynamic binding or macro expansion which provides the advanced feature of manipulating open program fragments. Such mechanisms are useful in many systems including distributed/mobile programming and program modules. If we can treat a context as a first-class citizen in a programming language, then we can manipulate open program fragments in a flexible and seamless manner. A possibility of such a programming language was shown by the theory of simply typed context calculus developed by Hashimoto and Ohori. This paper extends the simply typed system of the context calculus to an ML-style polymorphic type system, and gives an operational semantics and a sound and complete type inference algorithm.

Type Inference for Session Types in the $$\pi $$ -calculus

2016 ◽  
pp. 103-121 ◽  
Author(s):  
Eva Fajstrup Graversen ◽  
Jacob Buchreitz Harbo ◽  
Hans Hüttel ◽  
Mathias Ormstrup Bjerregaard ◽  
Niels Sonnich Poulsen ◽  
...  
Keyword(s):  
Type Inference ◽  
Session Types ◽  
Pi Calculus

Idris, a general-purpose dependently typed programming language: Design and implementation

2013 ◽  
Vol 23 (5) ◽  
pp. 552-593 ◽  
Author(s):  
EDWIN BRADY
Keyword(s):  
Programming Language ◽  
Type Theory ◽  
Functional Programming ◽  
General Purpose ◽  
High Level Language ◽  
Type Checking ◽  
Programming Language Design ◽  
Implicit Arguments ◽  
Type Classes ◽  
High Level

AbstractMany components of a dependently typed programming language are by now well understood, for example, the underlying type theory, type checking, unification and evaluation. How to combine these components into a realistic and usable high-level language is, however, folklore, discovered anew by successive language implementors. In this paper, I describe the implementation ofIdris, a new dependently typed functional programming language.Idrisis intended to be ageneral-purposeprogramming language and as such provides high-level concepts such as implicit syntax, type classes anddonotation. I describe the high-level language and the underlying type theory, and present a tactic-based method forelaboratingconcrete high-level syntax with implicit arguments and type classes into a fully explicit type theory. Furthermore, I show how this method facilitates the implementation of new high-level language constructs.

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