Mauro Piccolo

Ludics is a model for the finitary linear pi-calculus

We analyze in game-semantical terms the finitary fragment of the linear π-calculus. This calculus was introduced by Yoshida, Honda, and Berger [NYB01], and then refined by Honda and Laurent [LH06]. The features of this calculus - asynchrony and locality in particular - have a precise correspondence in Game Semantics. Building on work by Varacca and Yoshida [VY06], we interpret p-processes in linear strategies, that is the strategies introduced by Girard within the setting of Ludics [Gir01]. We prove that the model is fully complete and fully abstract w.r.t. the calculus.

Partial Orders, Event Structures and Linear Strategies

We introduce a Game Semantics where strategies are partial orders, and composition is a generalization of the merging of orders. Building on this, to bridge between Game Semantics and Concurrency, we explore the relation between Event Structures and Linear Strategies. The former are a true concurrency model introduced by Nielsen, Plotkin, Winskel, the latter a family of linear innocent strategies developed starting from Girards work in the setting of Ludics. We extend our construction on partial orders to classes of event structures, showing how to reduce composition of event structures to the simple definition of merging of orders. Finally, we introduce a compact closed category of event structures which embeds Linear Strategies.

Semantically linear programming languages

We propose a paradigmatic programming language (called SlPCF) which is linear in a semantic sense. SlPCF is not syntactically linear, namely its programs can contain more than one occurrencies of the same variable. We give an interpretation of SlPCF into a model of linear coherence spaces and we show that such semantics is fully abstract with respect to our language. Furthermore, we discuss the independence of new syntactical operators and we address the universality problem.

Linearity and PCF: a semantic insight!

Linearity is a multi-faceted and ubiquitous notion in the analysis and the development of programming language concepts. We study linearity in a denotational perspective by picking out programs that correspond to linear functions between coherence spaces. We introduce a language, named SlPCF*, that increases the higher-order expressivity of a linear core of PCF by means of new operators related to exception handling and parallel evaluation. SlPCF* allows us to program all the finite elements of the model and, consequently, it entails a full abstraction result that makes the reasoning on the equivalence between programs simpler. Denotational linearity provides also crucial information for the operational evaluation of programs. We formalize two evaluation machineries for the language. The first one is an abstract and concise operational semantics designed with the aim of explaining the new operators, and is based on an infinite-branching search of the evaluation space. The second one is more concrete and it prunes such a space, by exploiting the linear assumptions. This can also be regarded as a base for an implementation.

A Class of Reversible Primitive Recursive Functions

Reversible computing is bi-deterministic which means that its execution is both forward and backward deterministic, i.e. next/previous computational step is uniquely determined. Various approaches exist to catch its extensional or intensional aspects and properties. We present a class RPRF of reversible functions which holds at bay intensional aspects and emphasizes the extensional side of the reversible computation by following the style of Dedekind-Robinson Primitive Recursive Functions. The class RPRF is closed by inversion, can only express bijections on integers - not only natural numbers -, and it is expressive enough to simulate Primitive Recursive Functions, of course, in an effective way.

A Process-Model for Linear Programs

We use lin Proc (i.e. a typed process calculus based on the calculus of solos) in order to express computational processes generated by Sl PCF***, namely a simple programming language conceived in order to program only linear functions. We define a faithful translation of Sl PCF*** on lin Proc which enables us to process redexes of Sl PCF*** in a parallel way. Afterward, we prove that a suitable observational equivalence between processes is correct w.r.t the operational semantics of Sl PCF***, via our interpretation.

On a Class of Reversible Primitive Recursive Functions and Its Turing-Complete Extensions

Reversible computing is both forward and backward deterministic. This means that a uniquely determined step exists from the previous computational configuration (backward determinism) to the next one (forward determinism) and vice versa. We present the reversible primitive recursive functions (RPRF), a class of reversible (endo-)functions over natural numbers which allows to capture interesting extensional aspects of reversible computation in a formalism quite close to that of classical primitive recursive functions. The class RPRF can express bijections over integers (not only natural numbers), is expressive enough to admit an embedding of the primitive recursive functions and, of course, its evaluation is effective. We also extend RPRF to obtain a new class of functions which are effective and Turing complete, and represent all Kleene’s

Strong Normalization in the π-calculus with Intersection and Union Types

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