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Programming interfaces and basic topology
 Annals of Pure and Applied Logic
, 2005
"... A pattern of interaction that arises again and again in programming, is a “handshake”, in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent —the client or Angel, and concluded by the other —the server or Demon. We ..."
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A pattern of interaction that arises again and again in programming, is a “handshake”, in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent —the client or Angel, and concluded by the other —the server or Demon. We present a category in which the objects —called interaction structures in the paper — serve as descriptions of services provided across such handshaken interfaces. The morphisms —called (general) simulations— model components that provide one such service, relying on another. The morphisms are relations between the underlying sets of the interaction structures. The proof that a relation is a simulation can serve (in principle) as an executable program, whose specification is that it provides the service described by its domain, given an implementation of the service described by its codomain.
On Differential Interaction Nets and the Picalculus
 Preuves, Programmes et Systèmes
, 2006
"... We propose a translation of a finitary (that is, replicationfree) version of the picalculus into promotionfree differential interaction net structures, a linear logic version of the differential lambdacalculus (or, more precisely, of a resource lambdacalculus). For the sake of simplicity only, w ..."
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We propose a translation of a finitary (that is, replicationfree) version of the picalculus into promotionfree differential interaction net structures, a linear logic version of the differential lambdacalculus (or, more precisely, of a resource lambdacalculus). For the sake of simplicity only, we restrict our attention to a monadic version of the picalculus, so that the differential interaction net structures we consider need only to have exponential cells. We prove that the nets obtained by this translation satisfy an acyclicity criterion weaker than the standard Girard (or DanosRegnier) acyclicity criterion, and we compare the operational semantics of the picalculus, presented by means of an environment machine, and the reduction of differential interaction nets. Differential interaction net structures being of a logical nature, this work provides a CurryHoward interpretation of processes.
Predicate Transformers and Linear Logic: SecondOrder
"... In [Hyv04b] we gave a denotational model whose core was the "trivial" relational model. The structure added on top of it was that of a predicate transformer. In the presence of atoms, this gave a nontrivial denotational model of full linear logic where proofs are interpreted by postfixedpoints of ..."
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In [Hyv04b] we gave a denotational model whose core was the "trivial" relational model. The structure added on top of it was that of a predicate transformer. In the presence of atoms, this gave a nontrivial denotational model of full linear logic where proofs are interpreted by postfixedpoints of the associated predicate transformer. We extend this model to # logic and then to full secondorder. Contents 1 First order in a nutshell 2 1.1 Relations, predicate transformers and multisets . . . . . . . . . . 2 1.2 Interpreting formulas . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.3 Interpreting proofs . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.4 Main result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 (linear) logic 5 2.1 Motivations and ideas . . . . . . . . . . . . . . . . . . . . . . . . 6 2.2 The state space, permutations and renaming . . . . . . . . . . . 6 2.2.1 State space: relational interpretation . . . . . . . . . . . . 6 2.2.2 Permutations . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.3 The model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.4 Some examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.1 The empty type . . . . . . . . . . . . . . . . . . . . . . . 8 2.4.2 The singleton type . . . . . . . . . . . . . . . . . . . . . . 9 2.4.3 The booleans . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.4.4 Linear booleans . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Interpreting open formulas 11 3.1 The relational model . . . . . . . . . . . . . . . . . . . . . . . . . 11 3.1.1 Preliminaries about injections . . . . . . . . . . . . . . . . 11 3.1.2 Stable functors . . . . . . . . . . . . . . . . . . . . . . . . 12 3.1.3 Trace of a stable functor . . . . . ....
Synchronous Games, Simulations and λcalculus
, 2009
"... We refine a model for linear logic based on two wellknown ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic in this way. One particularly interesting point is that we in ..."
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We refine a model for linear logic based on two wellknown ingredients: games and simulations. We have already shown that usual simulation relations form a sound notion of morphism between games; and that we can interpret all linear logic in this way. One particularly interesting point is that we interpret multiplicative connectives by synchronous operations on games. We refine this work by giving computational contents to our simulation relations. To achieve that, we need to restrict to intuitionistic linear logic. This allows to work in a constructive setting, thus keeping a computational content to the proofs. We then extend it by showing how to interpret some of the additional structure of the exponentials. To be more precise, we first give a denotational model for the typed λcalculus; and then give a denotational model for the differential λcalculus of Ehrhard and Regnier. Both this models are proved correct constructively.
Author manuscript, published in "Annals of Pure and Applied Logic 137, 13 (2006) 189239" Programming Interfaces and Basic Topology
, 2009
"... A pattern of interaction that arises again and again in programming, is a “handshake”, in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent —the client or Angel, and concluded by the other —the server or Demon. We ..."
Abstract
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A pattern of interaction that arises again and again in programming, is a “handshake”, in which two agents exchange data. The exchange is thought of as provision of a service. Each interaction is initiated by a specific agent —the client or Angel, and concluded by the other —the server or Demon. We present a category in which the objects —called interaction structures in the paper — serve as descriptions of services provided across such handshaken interfaces. The morphisms —called (general) simulations— model components that provide one such service, relying on another. The morphisms are relations between the underlying sets of the interaction structures. The proof that a relation is a simulation can serve (in principle) as an executable program, whose specification is that it provides the service described by its domain, given an implementation of the service described by its codomain.
A LINEAR CATEGORY OF POLYNOMIAL FUNCTORS (EXTENSIONAL PART)
, 2014
"... Abstract. We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is reminiscent of Day’s convolution on presheaves. W ..."
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Abstract. We construct a symmetric monoidal closed category of polynomial endofunctors (as objects) and simulation cells (as morphisms). This structure is defined using universal properties without reference to representing polynomial diagrams and is reminiscent of Day’s convolution on presheaves. We then make this category into a model for intuitionistic linear logic by defining an additive and exponential structure.