Refining and extending previous work by Retore, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz reductions in parallel. Then we derive as immediate consequences of Subject Reduction the main theorems about normalization for intersection types: for system D, strong normalization, for system Omega, the leftmost reduction termination for terms typable without Omega.
{"title":"Natural Deduction and Normalization Proofs for the Intersection Type Discipline","authors":"Federico Aschieri","doi":"10.4204/EPTCS.293.3","DOIUrl":"https://doi.org/10.4204/EPTCS.293.3","url":null,"abstract":"Refining and extending previous work by Retore, we develop a systematic approach to intersection types via natural deduction. We show how a step of beta reduction can be seen as performing, at the level of typing derivations, Prawitz reductions in parallel. Then we derive as immediate consequences of Subject Reduction the main theorems about normalization for intersection types: for system D, strong normalization, for system Omega, the leftmost reduction termination for terms typable without Omega.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"18 1","pages":"29-37"},"PeriodicalIF":0.0,"publicationDate":"2019-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"81554051","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}
We study the question of extending the BCD intersection type system with additional type constructors. On the typing side, we focus on adding the usual rules for product types. On the subtyping side, we consider a generic way of defining a subtyping relation on families of types which include intersection types. We find back the BCD subtyping relation by considering the particular case where the type constructors are intersection, omega and arrow. We obtain an extension of BCD subtyping to product types as another instance. We show how the preservation of typing by both reduction and expansion is satisfied in all the considered cases. Our approach takes benefits from a "subformula property" of the proposed presentation of the subtyping relation.
{"title":"Intersection Subtyping with Constructors","authors":"Olivier Laurent","doi":"10.4204/EPTCS.293.6","DOIUrl":"https://doi.org/10.4204/EPTCS.293.6","url":null,"abstract":"We study the question of extending the BCD intersection type system with additional type constructors. On the typing side, we focus on adding the usual rules for product types. On the subtyping side, we consider a generic way of defining a subtyping relation on families of types which include intersection types. We find back the BCD subtyping relation by considering the particular case where the type constructors are intersection, omega and arrow. We obtain an extension of BCD subtyping to product types as another instance. We show how the preservation of typing by both reduction and expansion is satisfied in all the considered cases. Our approach takes benefits from a \"subformula property\" of the proposed presentation of the subtyping relation.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"213 1","pages":"73-84"},"PeriodicalIF":0.0,"publicationDate":"2019-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89086804","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}
Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for describing quantitative properties of simply typed lambda-terms. We present two type systems. The first allows to estimate (by appropriately defined value of a derivation) the number of appearances of a fixed constant 'a' in the beta-normal form of a considered lambda-term. The second type system is more complicated, and allows to estimate the maximal number of appearances of the constant 'a' on a single branch.
{"title":"Intersection Types for Unboundedness Problems","authors":"P. Parys","doi":"10.4204/EPTCS.293.2","DOIUrl":"https://doi.org/10.4204/EPTCS.293.2","url":null,"abstract":"Intersection types have been originally developed as an extension of simple types, but they can also be used for refining simple types. In this survey we concentrate on the latter option; more precisely, on the use of intersection types for describing quantitative properties of simply typed lambda-terms. We present two type systems. The first allows to estimate (by appropriately defined value of a derivation) the number of appearances of a fixed constant 'a' in the beta-normal form of a considered lambda-term. The second type system is more complicated, and allows to estimate the maximal number of appearances of the constant 'a' on a single branch.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"5 1","pages":"7-27"},"PeriodicalIF":0.0,"publicationDate":"2019-04-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79393728","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. Cervesato, Sharjeel Khan, Giselle Reis, D. Zunic
We present a declarative and modular specification of an automated trading system (ATS) in the concurrent linear framework CLF. We implemented it in Celf, a CLF type checker which also supports executing CLF specifications. We outline the verification of two representative properties of trading systems using generative grammars, an approach to reasoning about CLF specifications.
{"title":"Formalization of Automated Trading Systems in a Concurrent Linear Framework","authors":"I. Cervesato, Sharjeel Khan, Giselle Reis, D. Zunic","doi":"10.4204/EPTCS.292.1","DOIUrl":"https://doi.org/10.4204/EPTCS.292.1","url":null,"abstract":"We present a declarative and modular specification of an automated trading system (ATS) in the concurrent linear framework CLF. We implemented it in Celf, a CLF type checker which also supports executing CLF specifications. We outline the verification of two representative properties of trading systems using generative grammars, an approach to reasoning about CLF specifications.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"33 1","pages":"1-14"},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72927742","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 introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should view this logic as composed of two logics; one sitting to the left of the other. On the left, there is intuitionistic linear logic, and on the right is a mixed commutative/non-commutative formalization of the Lambek calculus. Then both of these logics are connected via a pair of monoidal adjoint functors. An exchange modality is then derivable within the logic using the adjunction between both sides. Thus, the adjoint functors allow one to pull the exchange structural rule from the left side to the right side. We then give a categorical model in terms of a monoidal adjunction, and then a concrete model in terms of dialectica Lambek spaces.
{"title":"On the Lambek Calculus with an Exchange Modality","authors":"Jiaming Jiang, H. Eades, Valeria C V de Paiva","doi":"10.4204/EPTCS.292.4","DOIUrl":"https://doi.org/10.4204/EPTCS.292.4","url":null,"abstract":"In this paper we introduce Commutative/Non-Commutative Logic (CNC logic) and two categorical models for CNC logic. This work abstracts Benton's Linear/Non-Linear Logic by removing the existence of the exchange structural rule. One should view this logic as composed of two logics; one sitting to the left of the other. On the left, there is intuitionistic linear logic, and on the right is a mixed commutative/non-commutative formalization of the Lambek calculus. Then both of these logics are connected via a pair of monoidal adjoint functors. An exchange modality is then derivable within the logic using the adjunction between both sides. Thus, the adjoint functors allow one to pull the exchange structural rule from the left side to the right side. We then give a categorical model in terms of a monoidal adjunction, and then a concrete model in terms of dialectica Lambek spaces.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"4 1","pages":"43-89"},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79504637","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}
We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value lambda-calculi to be encoded in. We investigate how the bang calculus subsumes both call-by-name and call-by-value lambda-calculi from a syntactic and a semantic viewpoint.
{"title":"The Bang Calculus and the Two Girard's Translations","authors":"Giulio Guerrieri, Giulio Manzonetto","doi":"10.4204/EPTCS.292.2","DOIUrl":"https://doi.org/10.4204/EPTCS.292.2","url":null,"abstract":"We study the two Girard's translations of intuitionistic implication into linear logic by exploiting the bang calculus, a paradigmatic functional language with an explicit box-operator that allows both call-by-name and call-by-value lambda-calculi to be encoded in. We investigate how the bang calculus subsumes both call-by-name and call-by-value lambda-calculi from a syntactic and a semantic viewpoint.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"177 1","pages":"15-30"},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90231930","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}
Process calculi based on logic, such as $pi$DILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of the $pi$-calculus: the fundamental operator for parallel composition does not correspond to any rule of linear logic. Kokke et al. (2019) introduced Hypersequent Classical Processes (HCP), which addresses this mismatch using hypersequents (collections of sequents) to register parallelism in the typing judgements. However, the step from CP to HCP is a big one. As of yet, HCP does not have reduction semantics, and the addition of delayed actions means that CP processes interpreted as HCP processes do not behave as they would in CP. We introduce HCP-, a variant of HCP with reduction semantics and without delayed actions. We prove progress, preservation, and termination, and show that HCP- supports the same communication protocols as CP.
{"title":"Taking Linear Logic Apart","authors":"W. Kokke, F. Montesi, Marco Peressotti","doi":"10.4204/EPTCS.292.5","DOIUrl":"https://doi.org/10.4204/EPTCS.292.5","url":null,"abstract":"Process calculi based on logic, such as $pi$DILL and CP, provide a foundation for deadlock-free concurrent programming. However, in previous work, there is a mismatch between the rules for constructing proofs and the term constructors of the $pi$-calculus: the fundamental operator for parallel composition does not correspond to any rule of linear logic. Kokke et al. (2019) introduced Hypersequent Classical Processes (HCP), which addresses this mismatch using hypersequents (collections of sequents) to register parallelism in the typing judgements. However, the step from CP to HCP is a big one. As of yet, HCP does not have reduction semantics, and the addition of delayed actions means that CP processes interpreted as HCP processes do not behave as they would in CP. We introduce HCP-, a variant of HCP with reduction semantics and without delayed actions. We prove progress, preservation, and termination, and show that HCP- supports the same communication protocols as CP.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"60 1","pages":"90-103"},"PeriodicalIF":0.0,"publicationDate":"2019-04-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76000055","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 addresses a problem found within the construction of Service Oriented Architecture: the adaptation of service protocols with respect to functional redundancy and heterogeneity of global communication patterns. We utilise the theory of Multiparty Session Types (MPST). Our approach is based upon the notion of a multiparty session type isomorphism, utilising a novel constructive realisation of service adapter code to establishing equivalence. We achieve this by employing trace semantics over a collection of local types and introducing meta abstractions over the syntax of global types. We develop a corresponding equational theory for MPST isomorphisms. The main motivation for this line of work is to define a type isomorphism that affords the assessment of whether two components/services are substitutables, modulo adaptation code given software components formalised as session types.
{"title":"Service Equivalence via Multiparty Session Type Isomorphisms","authors":"A. Altayeva, N. Yoshida","doi":"10.4204/EPTCS.291.1","DOIUrl":"https://doi.org/10.4204/EPTCS.291.1","url":null,"abstract":"This paper addresses a problem found within the construction of Service Oriented Architecture: the adaptation of service protocols with respect to functional redundancy and heterogeneity of global communication patterns. We utilise the theory of Multiparty Session Types (MPST). Our approach is based upon the notion of a multiparty session type isomorphism, utilising a novel constructive realisation of service adapter code to establishing equivalence. We achieve this by employing trace semantics over a collection of local types and introducing meta abstractions over the syntax of global types. We develop a corresponding equational theory for MPST isomorphisms. The main motivation for this line of work is to define a type isomorphism that affords the assessment of whether two components/services are substitutables, modulo adaptation code given software components formalised as session types.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"6 1","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74028656","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}
Modern web applications can now offer desktop-like experiences from within the browser, thanks to technologies such as WebSockets, which enable low-latency duplex communication between the browser and the server. While these advances are great for the user experience, they represent a new responsibility for web developers who now need to manage and verify the correctness of more complex and potentially stateful interactions in their application. In this paper, we present a technique for developing interactive web applications that are statically guaranteed to communicate following a given protocol. First, the global interaction protocol is described in the Scribble protocol language -- based on multiparty session types. Scribble protocols are checked for well-formedness, and then each role is projected to a Finite State Machine representing the structure of communication from the perspective of the role. We use source code generation and a novel type-level encoding of FSMs using multi-parameter type classes to leverage the type system of the target language and guarantee only programs that communicate following the protocol will type check. Our work targets PureScript -- a functional language that compiles to JavaScript -- which crucially has an expressive enough type system to provide static linearity guarantees. We demonstrate the effectiveness of our approach through a web-based Battleship game where communication is performed through WebSocket connections.
{"title":"Multiparty Session Type-safe Web Development with Static Linearity","authors":"Jonathan King, Nicholas Ng, N. Yoshida","doi":"10.4204/EPTCS.291.4","DOIUrl":"https://doi.org/10.4204/EPTCS.291.4","url":null,"abstract":"Modern web applications can now offer desktop-like experiences from within the browser, thanks to technologies such as WebSockets, which enable low-latency duplex communication between the browser and the server. While these advances are great for the user experience, they represent a new responsibility for web developers who now need to manage and verify the correctness of more complex and potentially stateful interactions in their application. In this paper, we present a technique for developing interactive web applications that are statically guaranteed to communicate following a given protocol. First, the global interaction protocol is described in the Scribble protocol language -- based on multiparty session types. Scribble protocols are checked for well-formedness, and then each role is projected to a Finite State Machine representing the structure of communication from the perspective of the role. We use source code generation and a novel type-level encoding of FSMs using multi-parameter type classes to leverage the type system of the target language and guarantee only programs that communicate following the protocol will type check. \u0000Our work targets PureScript -- a functional language that compiles to JavaScript -- which crucially has an expressive enough type system to provide static linearity guarantees. We demonstrate the effectiveness of our approach through a web-based Battleship game where communication is performed through WebSocket connections.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"3 1","pages":"35-46"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89099210","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}
We describe a generative approach that enables concurrent typestate-oriented programming in Java and other mainstream languages. The approach allows programmers to implement objects exposing a state-sensitive interface using a high-level synchronization abstraction that synchronizes methods with the states of the receiver object in which those methods have an effect. An external tool takes care of generating all the boilerplate code that implements the synchronization logic. Behavioral types are used to specify object protocols. The tool integrates protocol conformance verification with the synchronization logic so that protocol violations are promptly detected at runtime.
{"title":"Concurrent Typestate-Oriented Programming in Java","authors":"Rosita Gerbo, L. Padovani","doi":"10.4204/EPTCS.291.3","DOIUrl":"https://doi.org/10.4204/EPTCS.291.3","url":null,"abstract":"We describe a generative approach that enables concurrent typestate-oriented programming in Java and other mainstream languages. The approach allows programmers to implement objects exposing a state-sensitive interface using a high-level synchronization abstraction that synchronizes methods with the states of the receiver object in which those methods have an effect. An external tool takes care of generating all the boilerplate code that implements the synchronization logic. Behavioral types are used to specify object protocols. The tool integrates protocol conformance verification with the synchronization logic so that protocol violations are promptly detected at runtime.","PeriodicalId":10720,"journal":{"name":"CoRR","volume":"43 1","pages":"24-34"},"PeriodicalIF":0.0,"publicationDate":"2019-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"80942104","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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