Pub Date : 2018-07-01DOI: 10.4230/LIPIcs.FSCD.2018.2
Grigore Roşu
This invited paper describes recent, ongoing and planned work on the use of the rewrite-based semantic framework K to formally design, implement and verify blockchain languages and virtual machines. Both academic and commercial endeavors are discussed, as well as thoughts and directions for future research and development.
{"title":"Formal Design, Implementation and Verification of Blockchain Languages (Invited Talk)","authors":"Grigore Roşu","doi":"10.4230/LIPIcs.FSCD.2018.2","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.2","url":null,"abstract":"This invited paper describes recent, ongoing and planned work on the use of the rewrite-based semantic framework K to formally design, implement and verify blockchain languages and virtual machines. Both academic and commercial endeavors are discussed, as well as thoughts and directions for future research and development.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125721322","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}
Pub Date : 2018-07-01DOI: 10.4230/LIPIcs.FSCD.2018.14
J. Endrullis, J. Klop, R. Overbeek
Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be used to obtain such a hierarchy. The decreasing diagrams technique is one of the strongest and most versatile methods for proving confluence of abstract reduction systems, it is complete for countable systems, and it has many well-known confluence criteria as corollaries. So what makes decreasing diagrams so powerful? In contrast to other confluence techniques, decreasing diagrams employ a labelling of the steps ? with labels from a well-founded order in order to conclude confluence of the underlying unlabelled relation. Hence it is natural to ask how the size of the label set influences the strength of the technique. In particular, what class of abstract reduction systems can be proven confluent using decreasing diagrams restricted to 1 label, 2 labels, 3 labels, and so on? Surprisingly, we find that two labels su ce for proving confluence for every abstract rewrite system having the cofinality property, thus in particular for every confluent, countable system. We also show that this result stands in sharp contrast to the situation for commutation of rewrite relations, where the hierarchy does not collapse. Finally, as a background theme, we discuss the logical issue of first-order definability of the notion of confluence.
{"title":"Decreasing Diagrams with Two Labels Are Complete for Confluence of Countable Systems","authors":"J. Endrullis, J. Klop, R. Overbeek","doi":"10.4230/LIPIcs.FSCD.2018.14","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.14","url":null,"abstract":"Like termination, confluence is a central property of rewrite systems. Unlike for termination, however, there exists no known complexity hierarchy for confluence. In this paper we investigate whether the decreasing diagrams technique can be used to obtain such a hierarchy. The decreasing diagrams technique is one of the strongest and most versatile methods for proving confluence of abstract reduction systems, it is complete for countable systems, and it has many well-known confluence criteria as corollaries. So what makes decreasing diagrams so powerful? In contrast to other confluence techniques, decreasing diagrams employ a labelling of the steps ? with labels from a well-founded order in order to conclude confluence of the underlying unlabelled relation. Hence it is natural to ask how the size of the label set influences the strength of the technique. In particular, what class of abstract reduction systems can be proven confluent using decreasing diagrams restricted to 1 label, 2 labels, 3 labels, and so on? Surprisingly, we find that two labels su ce for proving confluence for every abstract rewrite system having the cofinality property, thus in particular for every confluent, countable system. We also show that this result stands in sharp contrast to the situation for commutation of rewrite relations, where the hierarchy does not collapse. Finally, as a background theme, we discuss the logical issue of first-order definability of the notion of confluence.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124698306","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}
Pub Date : 2018-05-17DOI: 10.4230/LIPIcs.FSCD.2018.8
P. Bahr
The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. To obtain infinitary normalisation and infinitary confluence properties for these calculi, Kennaway et al. extend $beta$-reduction with infinitely many `$bot$-rules', which contract meaningless terms directly to $bot$. Three of the resulting B"ohm reduction calculi have unique infinitary normal forms corresponding to B"ohm-like trees. In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion. We show that each of our calculi conservatively extends the corresponding metric-based calculus. Three of our calculi are infinitarily normalising and confluent; their unique infinitary normal forms are exactly the B"ohm-like trees of the corresponding metric-based calculi. Our calculi dispense with the infinitely many $bot$-rules of the metric-based calculi. The fully non-strict calculus (called $111$) consists of only $beta$-reduction, while the other two calculi (called $001$ and $101$) require two additional rules that precisely state their strictness properties: $lambda x.bot to bot$ (for $001$) and $bot,M to bot$ (for $001$ and $101$).
Kennaway等人开创的无限λ演算将基本λ演算通过度量补全扩展到无限项和约简。根据所选择的度量，所得到的无穷微积分表现出不同的严格性概念。为了获得这些微积分的无穷归一化和无穷合流性质，Kennaway等人将$beta$ -约简扩展为无穷多个“$bot$ -规则”，这些规则将无意义的项直接压缩到$bot$。所得的三个Böhm约简演算具有对应于Böhm-like树的唯一无穷范式。本文提出了基于理想补全而不是度量补全的无限λ演算的相应理论。我们证明了我们的每个演算都保守地扩展了相应的基于度量的演算。我们的演算中有三个是无限归一化和汇合的;它们独特的无穷范式正是相应的基于度量的演算的Böhm-like树。我们的演算省去了基于度量的演算的无穷多$bot$规则。完全非严格演算(称为$111$)只包括$beta$ -reduction，而其他两个演算(称为$001$和$101$)需要两个额外的规则来精确地声明它们的严格属性:$lambda x.bot to bot$(用于$001$)和$bot,M to bot$(用于$001$和$101$)。
{"title":"Strict Ideal Completions of the Lambda Calculus","authors":"P. Bahr","doi":"10.4230/LIPIcs.FSCD.2018.8","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.8","url":null,"abstract":"The infinitary lambda calculi pioneered by Kennaway et al. extend the basic lambda calculus by metric completion to infinite terms and reductions. Depending on the chosen metric, the resulting infinitary calculi exhibit different notions of strictness. To obtain infinitary normalisation and infinitary confluence properties for these calculi, Kennaway et al. extend $beta$-reduction with infinitely many `$bot$-rules', which contract meaningless terms directly to $bot$. Three of the resulting B\"ohm reduction calculi have unique infinitary normal forms corresponding to B\"ohm-like trees. \u0000In this paper we develop a corresponding theory of infinitary lambda calculi based on ideal completion instead of metric completion. We show that each of our calculi conservatively extends the corresponding metric-based calculus. Three of our calculi are infinitarily normalising and confluent; their unique infinitary normal forms are exactly the B\"ohm-like trees of the corresponding metric-based calculi. Our calculi dispense with the infinitely many $bot$-rules of the metric-based calculi. The fully non-strict calculus (called $111$) consists of only $beta$-reduction, while the other two calculi (called $001$ and $101$) require two additional rules that precisely state their strictness properties: $lambda x.bot to bot$ (for $001$) and $bot,M to bot$ (for $001$ and $101$).","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-05-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133273711","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}
Pub Date : 2018-04-18DOI: 10.4230/LIPIcs.FSCD.2018.23
B. Mannaa, Rasmus Ejlers Møgelberg
Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of type checking. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. The main challenge for constructing this model is to model the notion of ticks used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion, but in this category there is no object of ticks, so tick-assumptions in a context can not be modelled using standard tools. Instead we show how ticks can be modelled using adjoint functors, and how to model the tick constant using a semantic substitution.
{"title":"The clocks they are adjunctions: Denotational semantics for Clocked Type Theory","authors":"B. Mannaa, Rasmus Ejlers Møgelberg","doi":"10.4230/LIPIcs.FSCD.2018.23","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.23","url":null,"abstract":"Clocked Type Theory (CloTT) is a type theory for guarded recursion useful for programming with coinductive types, allowing productivity to be encoded in types, and for reasoning about advanced programming language features using an abstract form of step-indexing. CloTT has previously been shown to enjoy a number of syntactic properties including strong normalisation, canonicity and decidability of type checking. In this paper we present a denotational semantics for CloTT useful, e.g., for studying future extensions of CloTT with constructions such as path types. \u0000The main challenge for constructing this model is to model the notion of ticks used in CloTT for coinductive reasoning about coinductive types. We build on a category previously used to model guarded recursion, but in this category there is no object of ticks, so tick-assumptions in a context can not be modelled using standard tools. Instead we show how ticks can be modelled using adjoint functors, and how to model the tick constant using a semantic substitution.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"204 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-04-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115307209","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}
Pub Date : 2018-03-26DOI: 10.4230/LIPIcs.FSCD.2019.28
L. Liquori, C. Stolze
We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the Coppo-Dezani-Salle', the Coppo-Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related intersection type systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization, decidability of type checking and type reconstruction. We state the relationship between the intersection type assignment systems a` la Curry and the corresponding intersection type systems a` la Church by means of an essence function translating an explicitly typed Delta-term into a pure lambda-term one. We finally translate a Delta-term with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic Delta-calculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.
我们提出了delta演算，一个具有强对、投影和显式类型强制的显式类型λ演算。该微积分可以用Coppo-Dezani、Coppo-Dezani- salle’、Coppo-Dezani- venneri和Barendregt-Coppo-Dezani等不同的交型理论进行参数化，从而产生具有相关交型系统的δ微积分。证明了其主要性质如Church-Rosser、类型唯一性、主体约简、强归一化、类型检验的可判定性和类型重构。我们通过一个本质函数将显式类型的delta项转换为纯lambda项，描述了交集类型分配系统a ' la Curry与相应的交集类型系统a ' la Church之间的关系。最后，我们将带强制类型的项转换为不带强制类型的项;翻译的本质是同一性，因此翻译是连贯的。一般的delta微积分可以被参数化，以考虑其他的交集类型理论，如Barendregt等人的书中的理论。
{"title":"The Delta-calculus: syntax and types","authors":"L. Liquori, C. Stolze","doi":"10.4230/LIPIcs.FSCD.2019.28","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2019.28","url":null,"abstract":"We present the Delta-calculus, an explicitly typed lambda-calculus with strong pairs, projections and explicit type coercions. The calculus can be parametrized with different intersection type theories T, e.g. the Coppo-Dezani, the Coppo-Dezani-Salle', the Coppo-Dezani-Venneri and the Barendregt-Coppo-Dezani ones, producing a family of Delta-calculi with related intersection type systems. We prove the main properties like Church-Rosser, unicity of type, subject reduction, strong normalization, decidability of type checking and type reconstruction. We state the relationship between the intersection type assignment systems a` la Curry and the corresponding intersection type systems a` la Church by means of an essence function translating an explicitly typed Delta-term into a pure lambda-term one. We finally translate a Delta-term with type coercions into an equivalent one without them; the translation is proved to be coherent because its essence is the identity. The generic Delta-calculus can be parametrized to take into account other intersection type theories as the ones in the Barendregt et al. book.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"52 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132953223","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}
Pub Date : 2018-02-02DOI: 10.4230/LIPIcs.FSCD.2018.11
Maciej Bendkowski, P. Lescanne
Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures.
{"title":"Counting Environments and Closures","authors":"Maciej Bendkowski, P. Lescanne","doi":"10.4230/LIPIcs.FSCD.2018.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.11","url":null,"abstract":"Environments and closures are two of the main ingredients of evaluation in lambda-calculus. A closure is a pair consisting of a lambda-term and an environment, whereas an environment is a list of lambda-terms assigned to free variables. In this paper we investigate some dynamic aspects of evaluation in lambda-calculus considering the quantitative, combinatorial properties of environments and closures. Focusing on two classes of environments and closures, namely the so-called plain and closed ones, we consider the problem of their asymptotic counting and effective random generation. We provide an asymptotic approximation of the number of both plain environments and closures of size $n$. Using the associated generating functions, we construct effective samplers for both classes of combinatorial structures. Finally, we discuss the related problem of asymptotic counting and random generation of closed environemnts and closures.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"20 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121179899","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}
Pub Date : 2018-01-31DOI: 10.23638/LMCS-16(1:7)2020
Max S. New, Daniel R. Licata
We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism, which were developed in blame calculi and to state the "gradual guarantee" theorem of gradual typing. Combined with the ordinary extensionality ($eta$) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs, which is a semantic analogue of Findler and Felleisen's definitions of contracts, and use it to build some concrete domain-theoretic models of gradual typing.
{"title":"Call-by-name Gradual Type Theory","authors":"Max S. New, Daniel R. Licata","doi":"10.23638/LMCS-16(1:7)2020","DOIUrl":"https://doi.org/10.23638/LMCS-16(1:7)2020","url":null,"abstract":"We present gradual type theory, a logic and type theory for call-by-name gradual typing. We define the central constructions of gradual typing (the dynamic type, type casts and type error) in a novel way, by universal properties relative to new judgments for gradual type and term dynamism, which were developed in blame calculi and to state the \"gradual guarantee\" theorem of gradual typing. Combined with the ordinary extensionality ($eta$) principles that type theory provides, we show that most of the standard operational behavior of casts is uniquely determined by the gradual guarantee. This provides a semantic justification for the definitions of casts, and shows that non-standard definitions of casts must violate these principles. Our type theory is the internal language of a certain class of preorder categories called equipments. We give a general construction of an equipment interpreting gradual type theory from a 2-category representing non-gradual types and programs, which is a semantic analogue of Findler and Felleisen's definitions of contracts, and use it to build some concrete domain-theoretic models of gradual typing.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"35 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114426196","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}
Pub Date : 2018-01-23DOI: 10.4230/LIPIcs.FSCD.2018.12
David M. Cerna, Temur Kutsia
We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time.
{"title":"Higher-Order Equational Pattern Anti-Unification [Preprint]","authors":"David M. Cerna, Temur Kutsia","doi":"10.4230/LIPIcs.FSCD.2018.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.12","url":null,"abstract":"We consider anti-unification for simply typed lambda terms in associative, commutative, and associative-commutative theories and develop a sound and complete algorithm which takes two lambda terms and computes their generalizations in the form of higher-order patterns. The problem is finitary: the minimal complete set of generalizations contains finitely many elements. We define the notion of optimal solution and investigate special fragments of the problem for which the optimal solution can be computed in linear or polynomial time.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"44 3","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-01-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133071729","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}
Pub Date : 2017-09-10DOI: 10.23638/LMCS-15(1:9)2019
N. Zeilberger
We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$.
{"title":"A Sequent Calculus for a Semi-Associative Law","authors":"N. Zeilberger","doi":"10.23638/LMCS-15(1:9)2019","DOIUrl":"https://doi.org/10.23638/LMCS-15(1:9)2019","url":null,"abstract":"We introduce a sequent calculus with a simple restriction of Lambek's product rules that precisely captures the classical Tamari order, i.e., the partial order on fully-bracketed words (equivalently, binary trees) induced by a semi-associative law (equivalently, right rotation). We establish a focusing property for this sequent calculus (a strengthening of cut-elimination), which yields the following coherence theorem: every valid entailment in the Tamari order has exactly one focused derivation. We then describe two main applications of the coherence theorem, including: 1. A new proof of the lattice property for the Tamari order, and 2. A new proof of the Tutte-Chapoton formula for the number of intervals in the Tamari lattice $Y_n$.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"37 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115278785","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}
Pub Date : 2017-09-03DOI: 10.4230/LIPIcs.FSCD.2017.12
Simon Castellan, P. Clairambault, G. Winskel
Although Plotkin's parallel-or is inherently deterministic, it has a non-deterministic interpretation in games based on (prime) event structures-in which an event has a unique causal history-because they do not directly support disjunctive causality. General event structures can express disjunctive causality and have a more permissive notion of determinism, but do not support hiding. We show that (structures equivalent to) deterministic general event structures do support hiding, and construct a new category of games based on them with a deterministic interpretation of aPCFpor, an affine variant of PCF extended with parallel-or. We then exploit this deterministic interpretation to give a relaxed notion of determinism (observable determinism) on the plain event structures model. Putting this together with our previously introduced concurrent notions of well-bracketing and innocence, we obtain an intensionally fully abstract model of aPCFpor.
{"title":"Observably Deterministic Concurrent Strategies and Intensional Full Abstraction for Parallel-or","authors":"Simon Castellan, P. Clairambault, G. Winskel","doi":"10.4230/LIPIcs.FSCD.2017.12","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2017.12","url":null,"abstract":"Although Plotkin's parallel-or is inherently deterministic, it has a non-deterministic interpretation in games based on (prime) event structures-in which an event has a unique causal history-because they do not directly support disjunctive causality. General event structures can express disjunctive causality and have a more permissive notion of determinism, but do not support hiding. We show that (structures equivalent to) deterministic general event structures do support hiding, and construct a new category of games based on them with a deterministic interpretation of aPCFpor, an affine variant of PCF extended with parallel-or. We then exploit this deterministic interpretation to give a relaxed notion of determinism (observable determinism) on the plain event structures model. Putting this together with our previously introduced concurrent notions of well-bracketing and innocence, we obtain an intensionally fully abstract model of aPCFpor.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2017-09-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114984084","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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