Many universities have courses and projects revolving around compiler or interpreter implementation as part of their degree programmes in computer science. In such teaching activities, tool support can be highly beneficial. While there are already several tools for assisting with development of the front end of compilers, tool support tapers off towards the back end, or requires more background experience than is expected of undergraduate students. Structural operational semantics is a useful and mathematically simple formalism for specifying the behaviour of programs and a specification lends itself well to implementation; in particular big-step or natural semantics is often a useful and simple approach. However, many students struggle with learning the notation and often come up with ill-defined and meaningless attempts at defining a structural operational semantics. A survey shows that students working on programming language projects feel that tool support is lacking and would be useful. Many of these problems encountered when developing a semantic definition are similar to problems encountered in programming, in particular ones that are essentially the result of type errors. We present a pedagogical metalanguage based on natural semantics, and its implementation, as an attempt to marry two notions: a syntax similar to textbook notation for natural semantics on the one hand, and automatic verification of some correctness properties on the other by means of a strong type discipline. The metalanguage and the tool provide the facilities for writing and executing specifications as a form of programming. The user can check that the specification is not meaningless as well as execute programs, if the specification makes sense.
{"title":"A Tool for Describing and Checking Natural Semantics Definitions of Programming Languages","authors":"Georgian-Vlad Saioc, Hans Hüttel","doi":"10.4204/EPTCS.369.4","DOIUrl":"https://doi.org/10.4204/EPTCS.369.4","url":null,"abstract":"Many universities have courses and projects revolving around compiler or interpreter implementation as part of their degree programmes in computer science. In such teaching activities, tool support can be highly beneficial. While there are already several tools for assisting with development of the front end of compilers, tool support tapers off towards the back end, or requires more background experience than is expected of undergraduate students. Structural operational semantics is a useful and mathematically simple formalism for specifying the behaviour of programs and a specification lends itself well to implementation; in particular big-step or natural semantics is often a useful and simple approach. However, many students struggle with learning the notation and often come up with ill-defined and meaningless attempts at defining a structural operational semantics. A survey shows that students working on programming language projects feel that tool support is lacking and would be useful. Many of these problems encountered when developing a semantic definition are similar to problems encountered in programming, in particular ones that are essentially the result of type errors. We present a pedagogical metalanguage based on natural semantics, and its implementation, as an attempt to marry two notions: a syntax similar to textbook notation for natural semantics on the one hand, and automatic verification of some correctness properties on the other by means of a strong type discipline. The metalanguage and the tool provide the facilities for writing and executing specifications as a form of programming. The user can check that the specification is not meaningless as well as execute programs, if the specification makes sense.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"91122385","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Multi-agent systems for resource allocation (MRAs) have been introduced as a concept for modelling competitive resource allocation problems in distributed computing. An MRA is composed of a set of agents and a set of resources. Each agent has goals in terms of allocating certain resources. For MRAs it is typically of importance that they are designed in a way such that there exists a strategy that guarantees that all agents will achieve their goals. The corresponding model checking problem is to determine whether such a winning strategy exists or not, and the synthesis problem is to actually build the strategy. While winning strategies ensure that all goals will be achieved, following such strategies does not necessarily involve an optimal use of resources. In this paper, we present a technique that allows to synthesise cost-optimal solutions to distributed resource allocation problems. We consider a scenario where system components such as agents and resources involve costs. A multi-agent system shall be designed that is cost-minimal but still capable of accomplishing a given set of goals. Our approach synthesises a winning strategy that minimises the cumulative costs of the components that are required for achieving the goals. The technique is based on a propositional logic encoding and a reduction of the synthesis problem to the maximum satisfiability problem (Max-SAT). Hence, a Max-SAT solver can be used to perform the synthesis. From a truth assignment that maximises the number of satisfied clauses of the encoding a cost-optimal winning strategy as well as a cost-optimal system can be immediately derived.
{"title":"Synthesis of Cost-Optimal Multi-Agent Systems for Resource Allocation","authors":"Nils Timm, J. Botha","doi":"10.4204/EPTCS.369.5","DOIUrl":"https://doi.org/10.4204/EPTCS.369.5","url":null,"abstract":"Multi-agent systems for resource allocation (MRAs) have been introduced as a concept for modelling competitive resource allocation problems in distributed computing. An MRA is composed of a set of agents and a set of resources. Each agent has goals in terms of allocating certain resources. For MRAs it is typically of importance that they are designed in a way such that there exists a strategy that guarantees that all agents will achieve their goals. The corresponding model checking problem is to determine whether such a winning strategy exists or not, and the synthesis problem is to actually build the strategy. While winning strategies ensure that all goals will be achieved, following such strategies does not necessarily involve an optimal use of resources. In this paper, we present a technique that allows to synthesise cost-optimal solutions to distributed resource allocation problems. We consider a scenario where system components such as agents and resources involve costs. A multi-agent system shall be designed that is cost-minimal but still capable of accomplishing a given set of goals. Our approach synthesises a winning strategy that minimises the cumulative costs of the components that are required for achieving the goals. The technique is based on a propositional logic encoding and a reduction of the synthesis problem to the maximum satisfiability problem (Max-SAT). Hence, a Max-SAT solver can be used to perform the synthesis. From a truth assignment that maximises the number of satisfied clauses of the encoding a cost-optimal winning strategy as well as a cost-optimal system can be immediately derived.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76308050","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Maintaining data consistency among multiple parties requires nodes to repeatedly send data to all other nodes. For example, the nodes of a blockchain network have to disseminate the blocks they create across the whole network. The scientific literature typically takes the ideal perspective that such data distribution is performed by broadcasting to all nodes directly, while in practice data is distributed by repeated multicast. Since correctness and security of consistency maintenance protocols usually have been established for the ideal setting only, it is vital to show that these properties carry over to real-world implementations. Therefore, it is desirable to prove that the ideal and the real behavior are equivalent. In the work described in this paper, we take an important step towards such a proof by proving a simpler variant of this equivalence statement. The simplification is that we consider only a concrete pair of network topologies, which nevertheless illustrates important phenomena encountered with arbitrary topologies. For describing systems that distribute data, we use a domain-specific language of processes that corresponds to a class of Petri nets and is embedded in a general-purpose process calculus. This way, we can outline our proof using an intuitive graphical notation and leverage the rich theory of process calculi in the actual proof, which is machine-checked using the Isabelle proof assistant.
{"title":"Correctness of Broadcast via Multicast: Graphically and Formally","authors":"W. Jeltsch, Javier D'iaz","doi":"10.4204/EPTCS.369.3","DOIUrl":"https://doi.org/10.4204/EPTCS.369.3","url":null,"abstract":"Maintaining data consistency among multiple parties requires nodes to repeatedly send data to all other nodes. For example, the nodes of a blockchain network have to disseminate the blocks they create across the whole network. The scientific literature typically takes the ideal perspective that such data distribution is performed by broadcasting to all nodes directly, while in practice data is distributed by repeated multicast. Since correctness and security of consistency maintenance protocols usually have been established for the ideal setting only, it is vital to show that these properties carry over to real-world implementations. Therefore, it is desirable to prove that the ideal and the real behavior are equivalent. In the work described in this paper, we take an important step towards such a proof by proving a simpler variant of this equivalence statement. The simplification is that we consider only a concrete pair of network topologies, which nevertheless illustrates important phenomena encountered with arbitrary topologies. For describing systems that distribute data, we use a domain-specific language of processes that corresponds to a class of Petri nets and is embedded in a general-purpose process calculus. This way, we can outline our proof using an intuitive graphical notation and leverage the rich theory of process calculi in the actual proof, which is machine-checked using the Isabelle proof assistant.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79505202","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Péter Bereczky, Xiaohong Chen, D'aniel Horp'acsi, Tam'as B'alint Mizsei, Lucas Peña, Jan Tusil
Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive definitions and linear temporal logic. In addition, it serves as the logical foundation of the K semantic framework, which was used to build practical verifiers for a number of real-world languages. Despite being a fundamental formal system accommodating substantial theories, matching logic lacks a general-purpose, machine-checked formalization. Hence, we formalize matching logic using the Coq proof assistant. Specifically, we create a new representation of matching logic that uses a locally nameless encoding, and we formalize the syntax, semantics, and proof system of this representation in the Coq proof assistant. Crucially, we prove the soundness of the formalized proof system and provide a means to carry out interactive matching logic reasoning in Coq. We believe this work provides a previously unexplored avenue for reasoning about matching logic, its models, and the proof system.
{"title":"Mechanizing Matching Logic in Coq","authors":"Péter Bereczky, Xiaohong Chen, D'aniel Horp'acsi, Tam'as B'alint Mizsei, Lucas Peña, Jan Tusil","doi":"10.4204/EPTCS.369.2","DOIUrl":"https://doi.org/10.4204/EPTCS.369.2","url":null,"abstract":"Matching logic is a formalism for specifying, and reasoning about, mathematical structures, using patterns and pattern matching. Growing in popularity, it has been used to define many logical systems such as separation logic with recursive definitions and linear temporal logic. In addition, it serves as the logical foundation of the K semantic framework, which was used to build practical verifiers for a number of real-world languages. Despite being a fundamental formal system accommodating substantial theories, matching logic lacks a general-purpose, machine-checked formalization. Hence, we formalize matching logic using the Coq proof assistant. Specifically, we create a new representation of matching logic that uses a locally nameless encoding, and we formalize the syntax, semantics, and proof system of this representation in the Coq proof assistant. Crucially, we prove the soundness of the formalized proof system and provide a means to carry out interactive matching logic reasoning in Coq. We believe this work provides a previously unexplored avenue for reasoning about matching logic, its models, and the proof system.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2022-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77990537","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Symbolic execution uses various algorithms (matching, (anti)unification), whose executions are parameters for proof object generation. This paper proposes a generic method for generating proof objects for such parameters. We present in detail how our method works for the case of antiunification. The approach is accompanied by an implementation prototype, including a proof object generator and a proof object checker. In order to investigate the size of the proof objects, we generate and check proof objects for inputs inspired from the K definitions of C and Java.
{"title":"Proof-Carrying Parameters in Certified Symbolic Execution: The Case Study of Antiunification","authors":"Andrei Arusoaie, D. Lucanu","doi":"10.4204/EPTCS.369.1","DOIUrl":"https://doi.org/10.4204/EPTCS.369.1","url":null,"abstract":"Symbolic execution uses various algorithms (matching, (anti)unification), whose executions are parameters for proof object generation. This paper proposes a generic method for generating proof objects for such parameters. We present in detail how our method works for the case of antiunification. The approach is accompanied by an implementation prototype, including a proof object generator and a proof object checker. In order to investigate the size of the proof objects, we generate and check proof objects for inputs inspired from the K definitions of C and Java.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2021-10-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76176296","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we make a contribution to the computation of Grobner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we investigate what happens if we make that choice arbitrarily. It turns out not only this is possible (the fact that this produces a normal form being already known in the literature), but, for a fixed choice of reductors, the obtained normal form is the same no matter the order in which we reduce the monomials. To prove this, we introduce reduction machines, which work by reducing each monomial independently and then collecting the result. We show that such a machine can simulate any such reduction. We then discuss different implementations of these machines. Some of these implementations address inherent inefficiencies in reduction machines (repeating the same computations). We describe a first implementation and look at some experimental results.
{"title":"Gröbner Bases with Reduction Machines","authors":"Georgiana Surlea, A. Craciun","doi":"10.4204/EPTCS.303.5","DOIUrl":"https://doi.org/10.4204/EPTCS.303.5","url":null,"abstract":"In this paper, we make a contribution to the computation of Grobner bases. For polynomial reduction, instead of choosing the leading monomial of a polynomial as the monomial with respect to which the reduction process is carried out, we investigate what happens if we make that choice arbitrarily. It turns out not only this is possible (the fact that this produces a normal form being already known in the literature), but, for a fixed choice of reductors, the obtained normal form is the same no matter the order in which we reduce the monomials. To prove this, we introduce reduction machines, which work by reducing each monomial independently and then collecting the result. We show that such a machine can simulate any such reduction. We then discuss different implementations of these machines. Some of these implementations address inherent inefficiencies in reduction machines (repeating the same computations). We describe a first implementation and look at some experimental results.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81521028","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing system which extends the multiparty session types in order to deal also with probabilistic behaviours. The calculus and its typing system are motivated and illustrated by a running example.
{"title":"Probabilities in Session Types","authors":"Bogdan Aman, Gabriel Ciobanu","doi":"10.4204/EPTCS.303.7","DOIUrl":"https://doi.org/10.4204/EPTCS.303.7","url":null,"abstract":"This paper deals with the probabilistic behaviours of distributed systems described by a process calculus considering both probabilistic internal choices and nondeterministic external choices. For this calculus we define and study a typing system which extends the multiparty session types in order to deal also with probabilistic behaviours. The calculus and its typing system are motivated and illustrated by a running example.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88484815","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Graph transformation systems (GTS) have been successfully proposed as a general, theoretically sound model for concurrency. Petri nets (PN), on the other side, are a central and intuitive formalism for concurrent or distributed systems, well supported by a number of analysis techniques/tools. Some PN classes have been shown to be instances of GTS. In this paper, we change perspective presenting an operational semantics of GTS in terms of Symmetric Nets, a well-known class of Coloured Petri nets featuring a structured syntax that outlines model symmetries. Some practical exploitations of the proposed operational semantics are discussed. In particular, a recently developed structural calculus for SN is used to validate graph rewriting rules in a symbolic way.
{"title":"An Operational Semantics of Graph Transformation Systems Using Symmetric Nets","authors":"L. Capra","doi":"10.4204/EPTCS.303.8","DOIUrl":"https://doi.org/10.4204/EPTCS.303.8","url":null,"abstract":"Graph transformation systems (GTS) have been successfully proposed as a general, theoretically sound model for concurrency. Petri nets (PN), on the other side, are a central and intuitive formalism for concurrent or distributed systems, well supported by a number of analysis techniques/tools. Some PN classes have been shown to be instances of GTS. In this paper, we change perspective presenting an operational semantics of GTS in terms of Symmetric Nets, a well-known class of Coloured Petri nets featuring a structured syntax that outlines model symmetries. Some practical exploitations of the proposed operational semantics are discussed. In particular, a recently developed structural calculus for SN is used to validate graph rewriting rules in a symbolic way.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74528761","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
I. Leustean, Natalia Moanga, Traian-Florin Serbanuta
Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two approaches, which should benefit both systems.
{"title":"From Hybrid Modal Logic to Matching Logic and back","authors":"I. Leustean, Natalia Moanga, Traian-Florin Serbanuta","doi":"10.4204/EPTCS.303.2","DOIUrl":"https://doi.org/10.4204/EPTCS.303.2","url":null,"abstract":"Building on our previous work on hybrid polyadic modal logic we identify modal logic equivalents for Matching Logic, a logic for program specification and verification. This provides a rigorous way to transfer results between the two approaches, which should benefit both systems.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90659918","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and inherit the coinductive nature of the logic. The proof systems differ, however, in several aspects. First, they use induction and coinduction in different proportions. The second aspect regards compositionality, broadly meaning their ability to prove simpler formulas on smaller systems, and to reuse those formulas as lemmas for more complex formulas on larger systems. The third aspect is the difficulty of their soundness proofs. We show that the more induction a proof system uses, and the more specialised is its use of coinduction (with respect to our problem domain), the more compositional the proof system is, but the more difficult its soundness proof becomes. We also briefly present mechanisations of these results in the Isabelle/HOL and Coq proof assistants.
{"title":"(Co)inductive Proof Systems for Compositional Proofs in Reachability Logic","authors":"Vlad Rusu, David Nowak","doi":"10.4204/EPTCS.303.3","DOIUrl":"https://doi.org/10.4204/EPTCS.303.3","url":null,"abstract":"Reachability Logic is a formalism that can be used, among others, for expressing partial-correctness properties of transition systems. In this paper we present three proof systems for this formalism, all of which are sound and complete and inherit the coinductive nature of the logic. The proof systems differ, however, in several aspects. First, they use induction and coinduction in different proportions. The second aspect regards compositionality, broadly meaning their ability to prove simpler formulas on smaller systems, and to reuse those formulas as lemmas for more complex formulas on larger systems. The third aspect is the difficulty of their soundness proofs. We show that the more induction a proof system uses, and the more specialised is its use of coinduction (with respect to our problem domain), the more compositional the proof system is, but the more difficult its soundness proof becomes. We also briefly present mechanisations of these results in the Isabelle/HOL and Coq proof assistants.","PeriodicalId":9644,"journal":{"name":"Catalysis Surveys from Japan","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2019-07-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"77794871","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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