Simone Martini - Academia.edu (original) (raw)

Papers by Simone Martini

We present natural deduction systems for fragments of intuitionistic linear logic obtained by dro... more We present natural deduction systems for fragments of intuitionistic linear logic obtained by dropping weakening and contractions also on !-prefixed formulas. The systems are based on a twodimensional generalization of the notion of sequent, which accounts for a clean formulation of the ...

this paper is a solution to the coherence problem (for restricted proof-nets, see below) obtained... more this paper is a solution to the coherence problem (for restricted proof-nets, see below) obtained by changing the way the information is coded into sharing graphs. This is achieved via two technical tools: (i) a new reduction rule (absorption) allowing a simplification of the net in some critical cases; (ii) a clear separation of the logical and control information in the representation of a net. The logical information takes the form of levels on the formulas of the proof-net; control is expressed by unifying fans and brackets into one single node (mux ). It is this separation to allow the formulation of the absorption reduction and to enforce coherence. Our results, like those of most of the literature, hold for restricted proof-nets, where weakening is not allowed. It should be clear that any approach to cutelimination based on a local graph exploration may work only on connected components. If the syntax allows, during reduction, the creation of distinct components out of a sing...

Lecture Notes in Computer Science, 1989

... We want to verify the adequacy of Higher Order Typed Functional Languages (HOTFULs), like Peb... more ... We want to verify the adequacy of Higher Order Typed Functional Languages (HOTFULs), like Pebble [Lampson&Burstal188], SOL [Mitchell&Plotkin 851 and others [Cardelli 85, Cardelli&Wegner 851, to model the configuration facilities of modern languages for system ...

The Journal of Logic Programming, 1988

Advances in Linear Logic, 1995

Applied Logic Series, 1996

SIMONE MARTINI AND ANDREA MASINI A COMPUTATIONAL INTERPRETATION OF MODAL PROOFS 1 INTRODUCTION Pr... more SIMONE MARTINI AND ANDREA MASINI A COMPUTATIONAL INTERPRETATION OF MODAL PROOFS 1 INTRODUCTION Proof theory of modal logics, though largely studied since the fifties, has always been a delicate subject, the main reason being the apparent ...

Electronic Proceedings in Theoretical Computer Science, 2010

Leivant's ramified recurrence is one of the earliest examples of an implicit characterization of ... more Leivant's ramified recurrence is one of the earliest examples of an implicit characterization of the polytime functions as a subalgebra of the primitive recursive functions. Leivant's result, however, is originally stated and proved only for word algebras, i.e. free algebras whose constructors take at most one argument. This paper presents an extension of these results to ramified functions on any free algebras, provided the underlying terms are represented as graphs rather than trees, so that sharing of identical subterms can be exploited.

Mathematical Structures in Computer Science, 2014

We show that the techniques for resource control that have been developed in the so-called "light... more We show that the techniques for resource control that have been developed in the so-called "light logics" can be fruitfully applied also to process algebras. In particular, we present a restriction of Higher-Order π-calculus inspired by Soft Linear Logic. We prove that any soft process terminates in polynomial time. We argue that the class of soft processes may be naturally enlarged so that interesting processes are expressible, still maintaining the polynomial bound on executions.

Deduction, Computation, Experiment, 2008

Logic and theory of computation have been intertwined since their first days. The formalized noti... more Logic and theory of computation have been intertwined since their first days. The formalized notion(s) of effective computation are at first technical tools for the investigation of first order systems, and only ten years later in the hands of John von Neumann become the ...

Lecture Notes in Computer Science, 2009

Theoretical Computer Science, 2003

Sharing graphs are an implementation of linear logic proof-nets in which a redex is never duplica... more Sharing graphs are an implementation of linear logic proof-nets in which a redex is never duplicated. In their usual formulation, sharing graphs present a problem of coherence: if the proof-net N reduces by standard cut-elimination to N ′ , then, by reducing the sharing graph of N we do not obtain the sharing graph of N ′ . We solve this problem by changing the way the information is coded into sharing graphs and introducing a new reduction rule (absorption). The rewriting system is confluent and terminating. The proof exploits an algebraic semantics for sharing graphs.

Theoretical Computer Science, 2001

We study the problem of local and asynchronous computation in the context of multiplicative expon... more We study the problem of local and asynchronous computation in the context of multiplicative exponential linear logic (MELL) proof nets. The main novelty is in a complete set of rewriting rules for cut-elimination in presence of weakening (which requires garbage collection). The proposed reduction system is strongly normalizing and con uent. The proof techniques are new, all based on pure syntactical reasonings.

The Journal of Symbolic Logic, 1994

Abstract. We present a sequent calculus for the modal logic S4. and building on some relevant fea... more Abstract. We present a sequent calculus for the modal logic S4. and building on some relevant features of this system (the absence of contraction rules and the confinement of weakenings into axioms and modal rules) we show how S4 can easily be translated into full ...

Logic Journal of IGPL, 1998

We apply the 2-sequents approach to the analysis of several logics derived from linear logic. In ... more We apply the 2-sequents approach to the analysis of several logics derived from linear logic. In particular, we present a uniform formal system for Linear Logic, Elementary Linear Logic and Light Linear Logic.

Information and Computation, 1994

System F is a well-known typed λ-calculus with polymorphic types, which provides a basis for poly... more System F is a well-known typed λ-calculus with polymorphic types, which provides a basis for polymorphic programming languages. We study an extension of F, called F <: (pronounced ef-sub) that combines parametric polymorphism with subtyping.

Formal Aspects of Computing, 1993

ABSTRACT We present a translation of Ada configuration constructs, in a higher order, impredicati... more ABSTRACT We present a translation of Ada configuration constructs, in a higher order, impredicatively typed, functional language (HOTFUL) with subtypes. The aim of this work is to provide an expressive executable semantics for Ada configuration constructs, and to verify the suitability of the chosen HOTFUL for such a task. In particular, we address the practicability of the approach when dealing with the development of a whole complex system, as well as the description of single modular units. After giving the detailed rules for the translation, we compare our approach with what could be obtained selecting a different typed language as target, namely the predicative type system of Standard ML.

Archive for Mathematical Logic, 1994

Abstract. The meaning of a formula built out of proof-functional connectives de-pends in an essen... more Abstract. The meaning of a formula built out of proof-functional connectives de-pends in an essential way upon the intensional aspect of the proofs of the component subformulas. We study three such connectives, strong equivalence (where the two directions of the equivalence are ...

ACM Transactions on Computational Logic, 2010

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 2004

Higher-Order Linear Ramified Recurrence (HOLRR) is a PTIME sound and complete typed lambda calucl... more Higher-Order Linear Ramified Recurrence (HOLRR) is a PTIME sound and complete typed lambda caluclus. Its terms are those of a linear (affine) λ-calculus -every variable occurs at most once -extended with a limited recursive scheme on a word algebra. Completeness for PTIME holds by embedding Leivant's ramified recurrence on words into HOLRR. Soundness is established at all types -and not only for first order terms. Type connectives are limited to tensor and linear implicaation. Moreover, typing rules are given as a simple deductive system. On one side, HOLRR allows to "program" higher-order functions, whose PTIME soundness is assured by their types. On the other, HOLRR looks like a usual recursive language.