Paolo Torrini - Academia.edu (original) (raw)
Papers by Paolo Torrini
We present partial translations of Haskell programs to Is- abelle that have been implemented as p... more We present partial translations of Haskell programs to Is- abelle that have been implemented as part of the Heterogenous Tool Set. The the target logic is Isabelle/HOLCF, and the translation is based on a shallow embedding approach.
Electronic Proceedings in Theoretical Computer Science, 2009
Linear logics have been shown to be able to embed both rewriting-based approaches and process cal... more Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs / transformations and formulas / proof terms. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs / transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties.
Proceedings of the 2015 Workshop on Partial Evaluation and Program Manipulation - PEPM '15, 2015
Dealing with polymorphism in the presence of imperative features is a long-standing open problem ... more Dealing with polymorphism in the presence of imperative features is a long-standing open problem for Hindley-Milner type systems. A widely adopted approach is the value restriction, which inhibits polymorphic generalisation and unfairly rejects various programs that cannot go wrong. We consider abstract interpretation as a tool for constructing safe and precise type systems, and investigate how to derive store-based types by abstract interpretation. We propose store-based types as a type discipline that holds potential for interesting and flexible alternatives to the value restriction.
Lecture Notes in Computer Science, 2010
Electronic Proceedings in Theoretical Computer Science, 2010
Graph transformation has been used to model concurrent systems in software engineering, as well a... more Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems.
Lecture Notes in Computer Science, 2010
Distributed systems with mobile components are naturally modelled by graph transformations. To fo... more Distributed systems with mobile components are naturally modelled by graph transformations. To formalise and predict properties such as performance or reliability of such systems, stochastic methods are required. Stochastic graph transformations allow the integrated modelling of these two concerns by associating with each rule and match a probability distribution governing the delay of its application. Depending on the nature of these distributions, different techniques for analysis are available, ranging from stochastic model checking for exponential distributions to simulation for systems with general distributions.
Graph transformation is being increasingly used to express the semantics of domain specific visua... more Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time to accurately represent the behaviour of a real system and to obtain useful simulation metrics in order to measure throughputs, utilization times and average delays.
Lecture Notes in Computer Science, 2010
Graph transformation is being increasingly used to express the semantics of domain specific visua... more Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time in order to represent accurately the behaviour of the real system and to obtain useful simulation metrics. Inspired by the vast knowledge and experience accumulated by the discrete event simulation community, we propose a novel way of adding explicit time to graph transformation rules. In particular, we take the event scheduling discrete simulation world view and incorporate to the rules the ability of scheduling the occurrence of other rules in the future. Hence, our work combines standard, efficient techniques for discrete event simulation (based on the handling of a future event set) and the intuitive, visual nature of graph transformation. Moreover, we show how our formalism can be used to give semantics to other timed approaches.
Semantic specifications of programming languages typically have poor modularity. This hinders reu... more Semantic specifications of programming languages typically have poor modularity. This hinders reuse of parts of the semantics of one language when specifying a different language -even when the two languages have many constructs in common -and evolution of a language may require major reformulation of its semantics. Such drawbacks have discouraged language developers from using formal semantics to document their designs. In the PLanCompS project, we have developed a component-based approach to semantics. Here, we explain its modularity aspects, and present an illustrative case study: a component-based semantics for Caml Light. We have tested the correctness of the semantics by running programs on an interpreter generated from the semantics, comparing the output with that produced on the standard implementation of the language. Our approach provides good modularity, facilitates reuse, and should support co-evolution of languages and their formal semantics. It could be particularly useful in connection with domain-specific languages and language-driven software development.
Software & Systems Modeling, 2014
Graph transformation is being increasingly used to express the semantics of domain specific visua... more Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time to accurately represent the behaviour of a real system and to obtain useful simulation metrics in order to measure throughputs, utilization times and average delays.
Journal of Applied Non-Classical Logics, 2002
Imagine two sets, M and T . M is a set of machines partially ordered by cost or simplicity. T is ... more Imagine two sets, M and T . M is a set of machines partially ordered by cost or simplicity. T is a set of sets of tasks partially ordered by inclusion. There is a function g : M → T , taking each machine to the set of tasks it performs. This function is assumed to be orderpreserving, that is m 1 m 2 ⇒ gm 1 gm 2 for all m 1 , m 1 ∈ M .
Pattern matching plays a central role in graph transformations as a key technology for computing ... more Pattern matching plays a central role in graph transformations as a key technology for computing local contexts in which transformation rules are to be applied. Incremental matching techniques offer a performance advantage over the search-based approach, in a number of scenarios including on-the-fly model synchronization, model simulation, view maintenance, well-formedness checking and state space traversal . However, the incremental computation of transitive closure in graph pattern matching has started to be investigated only recently . In this paper, we propose multiple algorithms for the efficient computation of generalized transitive closures. As such, our solutions are capable of computing reachability regions defined by simple graph edges as well as complex binary relationships defined by graph patterns, that may be used in a wide spectrum of modeling problems. We also report on experimental evaluation of our prototypical implementation, carried out within the context of a stochastic system simulation case study.
We present a highly expressive logical language for describing qualitative con gurations of spati... more We present a highly expressive logical language for describing qualitative con gurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We show that our theory is categorical: all models are isomorphic to a classical interpretation in terms of Cartesian spaces over R.
We explore the expressive power of a recently developed qualitative region-based geometry and app... more We explore the expressive power of a recently developed qualitative region-based geometry and apply it to the problem of representing and reasoning about the motion of rigid bodies within a confining environment.
We present a highly expressive logical language for describing qualitative configurations of spat... more We present a highly expressive logical language for describing qualitative configurations of spatial regions, based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We give a categorical axiom system, whose models can be interpreted classically in terms of Cartesian spaces over Ê.We show that within this system the concept of sphere and the congruence relation are interdefinable. We investigate the 2nd-order character of the theory and prove incompleteness of some weaker 1st-order variants.
We present partial translations of Haskell programs to Is- abelle that have been implemented as p... more We present partial translations of Haskell programs to Is- abelle that have been implemented as part of the Heterogenous Tool Set. The the target logic is Isabelle/HOLCF, and the translation is based on a shallow embedding approach.
Electronic Proceedings in Theoretical Computer Science, 2009
Linear logics have been shown to be able to embed both rewriting-based approaches and process cal... more Linear logics have been shown to be able to embed both rewriting-based approaches and process calculi in a single, declarative framework. In this paper we are exploring the embedding of double-pushout graph transformations into quantified linear logic, leading to a Curry-Howard style isomorphism between graphs / transformations and formulas / proof terms. With linear implication representing rules and reachability of graphs, and the tensor modelling parallel composition of graphs / transformations, we obtain a language able to encode graph transformation systems and their computations as well as reason about their properties.
Proceedings of the 2015 Workshop on Partial Evaluation and Program Manipulation - PEPM '15, 2015
Dealing with polymorphism in the presence of imperative features is a long-standing open problem ... more Dealing with polymorphism in the presence of imperative features is a long-standing open problem for Hindley-Milner type systems. A widely adopted approach is the value restriction, which inhibits polymorphic generalisation and unfairly rejects various programs that cannot go wrong. We consider abstract interpretation as a tool for constructing safe and precise type systems, and investigate how to derive store-based types by abstract interpretation. We propose store-based types as a type discipline that holds potential for interesting and flexible alternatives to the value restriction.
Lecture Notes in Computer Science, 2010
Electronic Proceedings in Theoretical Computer Science, 2010
Graph transformation has been used to model concurrent systems in software engineering, as well a... more Graph transformation has been used to model concurrent systems in software engineering, as well as in biochemistry and life sciences. The application of a transformation rule can be characterised algebraically as construction of a double-pushout (DPO) diagram in the category of graphs. We show how intuitionistic linear logic can be extended with resource-bound quantification, allowing for an implicit handling of the DPO conditions, and how resource logic can be used to reason about graph transformation systems.
Lecture Notes in Computer Science, 2010
Distributed systems with mobile components are naturally modelled by graph transformations. To fo... more Distributed systems with mobile components are naturally modelled by graph transformations. To formalise and predict properties such as performance or reliability of such systems, stochastic methods are required. Stochastic graph transformations allow the integrated modelling of these two concerns by associating with each rule and match a probability distribution governing the delay of its application. Depending on the nature of these distributions, different techniques for analysis are available, ranging from stochastic model checking for exponential distributions to simulation for systems with general distributions.
Graph transformation is being increasingly used to express the semantics of domain specific visua... more Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time to accurately represent the behaviour of a real system and to obtain useful simulation metrics in order to measure throughputs, utilization times and average delays.
Lecture Notes in Computer Science, 2010
Graph transformation is being increasingly used to express the semantics of domain specific visua... more Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time in order to represent accurately the behaviour of the real system and to obtain useful simulation metrics. Inspired by the vast knowledge and experience accumulated by the discrete event simulation community, we propose a novel way of adding explicit time to graph transformation rules. In particular, we take the event scheduling discrete simulation world view and incorporate to the rules the ability of scheduling the occurrence of other rules in the future. Hence, our work combines standard, efficient techniques for discrete event simulation (based on the handling of a future event set) and the intuitive, visual nature of graph transformation. Moreover, we show how our formalism can be used to give semantics to other timed approaches.
Semantic specifications of programming languages typically have poor modularity. This hinders reu... more Semantic specifications of programming languages typically have poor modularity. This hinders reuse of parts of the semantics of one language when specifying a different language -even when the two languages have many constructs in common -and evolution of a language may require major reformulation of its semantics. Such drawbacks have discouraged language developers from using formal semantics to document their designs. In the PLanCompS project, we have developed a component-based approach to semantics. Here, we explain its modularity aspects, and present an illustrative case study: a component-based semantics for Caml Light. We have tested the correctness of the semantics by running programs on an interpreter generated from the semantics, comparing the output with that produced on the standard implementation of the language. Our approach provides good modularity, facilitates reuse, and should support co-evolution of languages and their formal semantics. It could be particularly useful in connection with domain-specific languages and language-driven software development.
Software & Systems Modeling, 2014
Graph transformation is being increasingly used to express the semantics of domain specific visua... more Graph transformation is being increasingly used to express the semantics of domain specific visual languages since its graphical nature makes rules intuitive. However, many application domains require an explicit handling of time to accurately represent the behaviour of a real system and to obtain useful simulation metrics in order to measure throughputs, utilization times and average delays.
Journal of Applied Non-Classical Logics, 2002
Imagine two sets, M and T . M is a set of machines partially ordered by cost or simplicity. T is ... more Imagine two sets, M and T . M is a set of machines partially ordered by cost or simplicity. T is a set of sets of tasks partially ordered by inclusion. There is a function g : M → T , taking each machine to the set of tasks it performs. This function is assumed to be orderpreserving, that is m 1 m 2 ⇒ gm 1 gm 2 for all m 1 , m 1 ∈ M .
Pattern matching plays a central role in graph transformations as a key technology for computing ... more Pattern matching plays a central role in graph transformations as a key technology for computing local contexts in which transformation rules are to be applied. Incremental matching techniques offer a performance advantage over the search-based approach, in a number of scenarios including on-the-fly model synchronization, model simulation, view maintenance, well-formedness checking and state space traversal . However, the incremental computation of transitive closure in graph pattern matching has started to be investigated only recently . In this paper, we propose multiple algorithms for the efficient computation of generalized transitive closures. As such, our solutions are capable of computing reachability regions defined by simple graph edges as well as complex binary relationships defined by graph patterns, that may be used in a wide spectrum of modeling problems. We also report on experimental evaluation of our prototypical implementation, carried out within the context of a stochastic system simulation case study.
We present a highly expressive logical language for describing qualitative con gurations of spati... more We present a highly expressive logical language for describing qualitative con gurations of spatial regions. We call the theory Region Based Geometry (RBG). Our axiomatisation is based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We show that our theory is categorical: all models are isomorphic to a classical interpretation in terms of Cartesian spaces over R.
We explore the expressive power of a recently developed qualitative region-based geometry and app... more We explore the expressive power of a recently developed qualitative region-based geometry and apply it to the problem of representing and reasoning about the motion of rigid bodies within a confining environment.
We present a highly expressive logical language for describing qualitative configurations of spat... more We present a highly expressive logical language for describing qualitative configurations of spatial regions, based on Tarski's Geometry of Solids, in which the parthood relation and the concept of sphere are taken as primitive. We give a categorical axiom system, whose models can be interpreted classically in terms of Cartesian spaces over Ê.We show that within this system the concept of sphere and the congruence relation are interdefinable. We investigate the 2nd-order character of the theory and prove incompleteness of some weaker 1st-order variants.