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Parameterised multiparty session types
 In FOSSACS, LNCS
, 2010
"... Abstract. For many applicationlevel distributed protocols and parallel algorithms, the set of participants, the number of messages or the interaction structure are only known at runtime. This paper proposes a dependent type theory for multiparty sessions which can statically guarantee typesafe, d ..."
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Cited by 15 (9 self)
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Abstract. For many applicationlevel distributed protocols and parallel algorithms, the set of participants, the number of messages or the interaction structure are only known at runtime. This paper proposes a dependent type theory for multiparty sessions which can statically guarantee typesafe, deadlockfree multiparty interactions among processes whose specifications are parameterised by indices. We use the primitive recursion operator from Gödel’s System T to express a wide range of communication patterns while keeping type checking decidable. We illustrate our type theory through nontrivial programming and verification examples taken from parallel algorithms and Web services usecases. 1
Inductive Definitions and Type Theory: An Introduction
"... MartinLof's type theory can be described as an intuitionistic theory of iterated inductive definitions developed in a framework of dependent types. It was originally intended to be a fullscale system for the formalization of constructive mathematics, but has also proved to be a powerful framewo ..."
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Cited by 6 (0 self)
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MartinLof's type theory can be described as an intuitionistic theory of iterated inductive definitions developed in a framework of dependent types. It was originally intended to be a fullscale system for the formalization of constructive mathematics, but has also proved to be a powerful framework for programming. The theory integrates an expressive specification language (its type system) and a functional programming language (where all programs terminate). There now exist several proofassistants based on type theory, and many nontrivial examples from programming, computer science, logic, and mathematics have been implemented using these. In this series of lectures we shall describe type theory as a theory of inductive definitions. We emphasize its open nature: much like in a standard functional language such as ML or Haskell the user can add new types whenever there is a need for them. We discuss the syntax and semantics of the theory. Moreover, we present some examples ...
Ordinals and Interactive Programs
, 2000
"... The work reported in this thesis arises from the old idea, going back to the origins of constructive logic, that a proof is fundamentally a kind of program. If proofs can be ..."
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Cited by 5 (2 self)
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The work reported in this thesis arises from the old idea, going back to the origins of constructive logic, that a proof is fundamentally a kind of program. If proofs can be
Type Inference and Reconstruction for First Order Dependent Types
, 1995
"... x 1 Introduction 1 1.1 Dependent Types : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Dependent Type Inference and Reconstruction : : : : : : : : : : : : : : : : 8 2 Primitive Recursive Functionals with Dependent Types 17 2.1 A Dependent Type System for T : : : : : : : : : ..."
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Cited by 3 (1 self)
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x 1 Introduction 1 1.1 Dependent Types : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 1 1.2 Dependent Type Inference and Reconstruction : : : : : : : : : : : : : : : : 8 2 Primitive Recursive Functionals with Dependent Types 17 2.1 A Dependent Type System for T : : : : : : : : : : : : : : : : : : : : : : : 17 2.1.1 Terms : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 17 2.1.2 Types : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 19 2.1.3 Typing Rules : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : : 24 2.1.4 Strong Normalization of T Terms : : : : : : : : : : : : : : : : : : : 28 2.2 Dependent Typing Examples : : : : : : : : : : : : : : : : : : : : : : : : : : 29 2.3 A Term Model Semantics for T : : : : : : : : : : : : : : : : : : : : : : : : 34 3 Principal Types and Dependent Type Reconstruction 58 3.1 Type Subsumption and Unification : : : : : : : : : : : : : : : : : : : : : : : 58 3.2 Matching : : : : : :...
The AMEN architecture.
, 1999
"... There are many combinatorially complete sets of combinators, or `instruction sets' to which the calculus can be compiled. The most famous are perhaps fS; K g and fB;C;K;W g. Several authors have observed that there is a set of `arithmetical' combinators fA; M;E;N g arising from the Church numer ..."
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There are many combinatorially complete sets of combinators, or `instruction sets' to which the calculus can be compiled. The most famous are perhaps fS; K g and fB;C;K;W g. Several authors have observed that there is a set of `arithmetical' combinators fA; M;E;N g arising from the Church numerals, which is also combinatorially complete. However their sets of combinators are not absolutely perfect. The perfect set of combinators ( f(+); (); (^); 0g in sectionnotation) is defined herein. There is
Dependent Session Types for Evolving Multiparty Communication Topologies
"... Many applicationlevel distributed protocols and parallel algorithms are dynamic in nature: the number of participants, messages or repetitions is only known at runtime, and the communication topology may be altered during the execution. This paper proposes a dependent type theory for multiparty se ..."
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Many applicationlevel distributed protocols and parallel algorithms are dynamic in nature: the number of participants, messages or repetitions is only known at runtime, and the communication topology may be altered during the execution. This paper proposes a dependent type theory for multiparty sessions which can statically guarantee typesafe, deadlockfree multiparty interactions among processes with dynamically evolving communication topologies. We use the primitive recursion operator from Gödel’s System T along with dependent product types to express a wide range of topologies where the structure of the multiparty communications depend on numerical parameters that are instantiated at runtime. To type individual distributed processes, a parameterised global type is projected onto a generic generator which represents a class of all possible endpoint types. Termination of the typechecking algorithm is proved with the full multiparty session types including recursive types. The expressiveness of our type theory is demonstrated through nontrivial programming and verification examples with complex communication topologies taken from distributed parallel algorithms and Web services usecases. 1.