Pub Date : 2019-02-18DOI: 10.4230/LIPIcs.FSCD.2019.11
T. Coquand, Simon Huber, Christian Sattler
Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. In this paper we show by a sconing argument that if we remove these equations for the path lifting operation from the system, we still retain homotopy canonicity: every natural number is path equal to a numeral.
{"title":"Homotopy canonicity for cubical type theory","authors":"T. Coquand, Simon Huber, Christian Sattler","doi":"10.4230/LIPIcs.FSCD.2019.11","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2019.11","url":null,"abstract":"Cubical type theory provides a constructive justification of homotopy type theory and satisfies canonicity: every natural number is convertible to a numeral. A crucial ingredient of cubical type theory is a path lifting operation which is explained computationally by induction on the type involving several non-canonical choices. In this paper we show by a sconing argument that if we remove these equations for the path lifting operation from the system, we still retain homotopy canonicity: every natural number is path equal to a numeral.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-18","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115841593","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 : 2019-02-13DOI: 10.46298/lmcs-18(3:2)2022
T. Ehrhard
In probabilistic coherence spaces, a denotational model of probabilistic functional languages, morphisms are analytic and therefore smooth. We explore two related applications of the corresponding derivatives. First we show how derivatives allow to compute the expectation of execution time in the weak head reduction of probabilistic PCF (pPCF). Next we apply a general notion of "local" differential of morphisms to the proof of a Lipschitz property of these morphisms allowing in turn to relate the observational distance on pPCF terms to a distance the model is naturally equipped with. This suggests that extending probabilistic programming languages with derivatives, in the spirit of the differential lambda-calculus, could be quite meaningful.
{"title":"Differentials and distances in probabilistic coherence spaces","authors":"T. Ehrhard","doi":"10.46298/lmcs-18(3:2)2022","DOIUrl":"https://doi.org/10.46298/lmcs-18(3:2)2022","url":null,"abstract":"In probabilistic coherence spaces, a denotational model of probabilistic\u0000functional languages, morphisms are analytic and therefore smooth. We explore\u0000two related applications of the corresponding derivatives. First we show how\u0000derivatives allow to compute the expectation of execution time in the weak head\u0000reduction of probabilistic PCF (pPCF). Next we apply a general notion of\u0000\"local\" differential of morphisms to the proof of a Lipschitz property of these\u0000morphisms allowing in turn to relate the observational distance on pPCF terms\u0000to a distance the model is naturally equipped with. This suggests that\u0000extending probabilistic programming languages with derivatives, in the spirit\u0000of the differential lambda-calculus, could be quite meaningful.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125710840","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 : 2019-02-04DOI: 10.4230/LIPICS.FSCD.2019.25
A. Kaposi, Simon Huber, Christian Sattler
We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tier-ing is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras.
{"title":"Gluing for Type Theory","authors":"A. Kaposi, Simon Huber, Christian Sattler","doi":"10.4230/LIPICS.FSCD.2019.25","DOIUrl":"https://doi.org/10.4230/LIPICS.FSCD.2019.25","url":null,"abstract":"We translate the usual class of partial/primitive recursive functions to a pointer recursion framework, accessing actual input values via a pointer reading unit-cost function. These pointer recursive functions classes are proven equivalent to the usual partial/primitive recursive functions. Complexity-wise, this framework captures in a streamlined way most of the relevant sub-polynomial classes. Pointer recursion with the safe/normal tiering discipline of Bellantoni and Cook corresponds to polylogtime computation. We introduce a new, non-size increasing tiering discipline, called tropical tiering. Tropical tiering and pointer recursion, used with some of the most common recursion schemes, capture the classes logspace, logspace/polylogtime, ptime, and NC. Finally, in a fashion reminiscent of the safe recursive functions, tropical tier-ing is expressed directly in the syntax of the function algebras, yielding the tropical recursive function algebras.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"36 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2019-02-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124141468","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 : 2018-12-11DOI: 10.4230/LIPIcs.FSCD.2019.7
Maciej Bendkowski
Substitution resolution supports the computational character of $beta$-reduction, complementing its execution with a capture-avoiding exchange of terms for bound variables. Alas, the meta-level definition of substitution, masking a non-trivial computation, turns $beta$-reduction into an atomic rewriting rule, despite its varying operational complexity. In the current paper we propose a somewhat indirect average-case analysis of substitution resolution in the classic $lambda$-calculus, based on the quantitative analysis of substitution in $lambdaupsilon$, an extension of $lambda$-calculus internalising the $upsilon$-calculus of explicit substitutions. Within this framework, we show that for any fixed $n geq 0$, the probability that a uniformly random, conditioned on size, $lambdaupsilon$-term $upsilon$-normalises in $n$ normal-order (i.e. leftmost-outermost) reduction steps tends to a computable limit as the term size tends to infinity. For that purpose, we establish an effective hierarchy $left(mathscr{G}_nright)_n$ of regular tree grammars partitioning $upsilon$-normalisable terms into classes of terms normalising in $n$ normal-order rewriting steps. The main technical ingredient in our construction is an inductive approach to the construction of $mathscr{G}_{n+1}$ out of $mathscr{G}_n$ based, in turn, on the algorithmic construction of finite intersection partitions, inspired by Robinson's unification algorithm. Finally, we briefly discuss applications of our approach to other term rewriting systems, focusing on two closely related formalisms, i.e. the full $lambdaupsilon$-calculus and combinatory logic.
{"title":"Towards the Average-Case Analysis of Substitution Resolution in Lambda-Calculus","authors":"Maciej Bendkowski","doi":"10.4230/LIPIcs.FSCD.2019.7","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2019.7","url":null,"abstract":"Substitution resolution supports the computational character of $beta$-reduction, complementing its execution with a capture-avoiding exchange of terms for bound variables. Alas, the meta-level definition of substitution, masking a non-trivial computation, turns $beta$-reduction into an atomic rewriting rule, despite its varying operational complexity. In the current paper we propose a somewhat indirect average-case analysis of substitution resolution in the classic $lambda$-calculus, based on the quantitative analysis of substitution in $lambdaupsilon$, an extension of $lambda$-calculus internalising the $upsilon$-calculus of explicit substitutions. Within this framework, we show that for any fixed $n geq 0$, the probability that a uniformly random, conditioned on size, $lambdaupsilon$-term $upsilon$-normalises in $n$ normal-order (i.e. leftmost-outermost) reduction steps tends to a computable limit as the term size tends to infinity. For that purpose, we establish an effective hierarchy $left(mathscr{G}_nright)_n$ of regular tree grammars partitioning $upsilon$-normalisable terms into classes of terms normalising in $n$ normal-order rewriting steps. The main technical ingredient in our construction is an inductive approach to the construction of $mathscr{G}_{n+1}$ out of $mathscr{G}_n$ based, in turn, on the algorithmic construction of finite intersection partitions, inspired by Robinson's unification algorithm. Finally, we briefly discuss applications of our approach to other term rewriting systems, focusing on two closely related formalisms, i.e. the full $lambdaupsilon$-calculus and combinatory logic.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"29 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-12-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123601458","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 : 2018-07-09DOI: 10.4230/LIPIcs.FSCD.2018.15
Simon Forest, S. Mimram
We consider rewriting of a regular language with a left-linear term rewriting system. We show a completeness theorem on equational tree automata completion stating that, if there exists a regular over-approximation of the set of reachable terms, then equational completion can compute it (or safely under-approximate it). A nice corollary of this theorem is that, if the set of reachable terms is regular, then equational completion can also compute it. This was known to be true for some term rewriting system classes preserving regularity, but was still an open question in the general case. The proof is not constructive because it depends on the regularity of the set of reachable terms, which is undecidable. To carry out those proofs we generalize and improve two results of completion: the Termination and the Upper-Bound theorems. Those theoretical results provide an algorithmic way to safely explore regular approximations with completion. This has been implemented in Timbuk and used to verify safety properties, automatically and efficiently, on first-order and higher-order functional programs.
{"title":"Coherence of Gray Categories via Rewriting","authors":"Simon Forest, S. Mimram","doi":"10.4230/LIPIcs.FSCD.2018.15","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.15","url":null,"abstract":"We consider rewriting of a regular language with a left-linear term rewriting system. We show a completeness theorem on equational tree automata completion stating that, if there exists a regular over-approximation of the set of reachable terms, then equational completion can compute it (or safely under-approximate it). A nice corollary of this theorem is that, if the set of reachable terms is regular, then equational completion can also compute it. This was known to be true for some term rewriting system classes preserving regularity, but was still an open question in the general case. The proof is not constructive because it depends on the regularity of the set of reachable terms, which is undecidable. To carry out those proofs we generalize and improve two results of completion: the Termination and the Upper-Bound theorems. Those theoretical results provide an algorithmic way to safely explore regular approximations with completion. This has been implemented in Timbuk and used to verify safety properties, automatically and efficiently, on first-order and higher-order functional programs.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123634865","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 : 2018-07-09DOI: 10.4230/LIPIcs.FSCD.2018.25
L. T. D. Nguyên
This paper establishes a bridge between linear logic and mainstream graph theory, building previous work by Retore (2003). We show that the problem of correctness for MLL+Mix proof nets is equivalent to the problem of uniqueness of a perfect matching. By applying matching theory, we obtain new results for MLL+Mix proof nets: a linear-time correctness criterion, a quasi-linear sequentialization algorithm, and a characterization of the sub-polynomial complexity of the correctness problem. We also use graph algorithms to compute the dependency relation of Bagnol et al. (2015) and the kingdom ordering of Bellin (1997), and relate them to the notion of blossom which is central to combinatorial maximum matching algorithms.
{"title":"Unique perfect matchings and proof nets","authors":"L. T. D. Nguyên","doi":"10.4230/LIPIcs.FSCD.2018.25","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.25","url":null,"abstract":"This paper establishes a bridge between linear logic and mainstream graph theory, building previous work by Retore (2003). We show that the problem of correctness for MLL+Mix proof nets is equivalent to the problem of uniqueness of a perfect matching. By applying matching theory, we obtain new results for MLL+Mix proof nets: a linear-time correctness criterion, a quasi-linear sequentialization algorithm, and a characterization of the sub-polynomial complexity of the correctness problem. We also use graph algorithms to compute the dependency relation of Bagnol et al. (2015) and the kingdom ordering of Bellin (1997), and relate them to the notion of blossom which is central to combinatorial maximum matching algorithms.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"151 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124216455","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 : 2018-07-09DOI: 10.4230/LIPIcs.FSCD.2018.9
Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret
We study anti-unification for possibly cyclic, unranked term-graphs and develop an algorithm, which computes a minimal complete set of generalizations for them. For bisimilar graphs the algorithm computes the join in the lattice generated by a functional bisimulation. These results generalize anti-unification for ranked and unranked terms to the corresponding term-graphs, and solve also anti-unification problems for rational terms and dags. Our results open a way to widen anti-unification based code clone detection techniques from a tree representation to a graph representation of the code.
{"title":"Term-Graph Anti-Unification","authors":"Alexander Baumgartner, Temur Kutsia, Jordi Levy, Mateu Villaret","doi":"10.4230/LIPIcs.FSCD.2018.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.9","url":null,"abstract":"We study anti-unification for possibly cyclic, unranked term-graphs and develop an algorithm, which computes a minimal complete set of generalizations for them. For bisimilar graphs the algorithm computes the join in the lattice generated by a functional bisimulation. These results generalize anti-unification for ranked and unranked terms to the corresponding term-graphs, and solve also anti-unification problems for rational terms and dags. Our results open a way to widen anti-unification based code clone detection techniques from a tree representation to a graph representation of the code.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129540226","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 : 2018-07-09DOI: 10.4230/LIPIcs.FSCD.2018.6
Nirina Andrianarivelo, P. Réty
Prefix-constrained rewriting is a strict extension of context-sensitive rewriting. We study the confluence of prefix-constrained rewrite systems, which are composed of rules of the form L : l→ r where L is a regular string language that defines the allowed rewritable positions. The usual notion of Knuth-Bendix’s critical pair needs to be extended using regular string languages, and the convergence of all critical pairs is not enough to ensure local confluence. Thanks to an additional restriction we get local confluence, and then confluence for terminating systems, which makes the word problem decidable. Moreover we present an extended Knuth-Bendix completion procedure, to transform a non-confluent prefix-constrained rewrite system into a confluent one. 2012 ACM Subject Classification Theory of computation → Rewrite systems
{"title":"Confluence of Prefix-Constrained Rewrite Systems","authors":"Nirina Andrianarivelo, P. Réty","doi":"10.4230/LIPIcs.FSCD.2018.6","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.6","url":null,"abstract":"Prefix-constrained rewriting is a strict extension of context-sensitive rewriting. We study the confluence of prefix-constrained rewrite systems, which are composed of rules of the form L : l→ r where L is a regular string language that defines the allowed rewritable positions. The usual notion of Knuth-Bendix’s critical pair needs to be extended using regular string languages, and the convergence of all critical pairs is not enough to ensure local confluence. Thanks to an additional restriction we get local confluence, and then confluence for terminating systems, which makes the word problem decidable. Moreover we present an extended Knuth-Bendix completion procedure, to transform a non-confluent prefix-constrained rewrite system into a confluent one. 2012 ACM Subject Classification Theory of computation → Rewrite systems","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"183 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124284937","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 : 2018-07-09DOI: 10.4230/LIPIcs.FSCD.2018.29
Amin Timany, Matthieu Sozeau
In order to avoid well-known paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : *s. Such type systems are called cumulative if for any type A we have that A : Type_i implies A : Type_{i+1}. The Predicative Calculus of Inductive Constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present the Predicative Calculus of Cumulative Inductive Constructions (pCuIC) which extends the cumulativity relation to inductive types. We discuss cumulative inductive types as present in Coq 8.7 and their application to formalization and definitional translations.
{"title":"Cumulative Inductive Types In Coq","authors":"Amin Timany, Matthieu Sozeau","doi":"10.4230/LIPIcs.FSCD.2018.29","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.29","url":null,"abstract":"In order to avoid well-known paradoxes associated with self-referential definitions, higher-order dependent type theories stratify the theory using a countably infinite hierarchy of universes (also known as sorts), Type_0 : Type_1 : *s. Such type systems are called cumulative if for any type A we have that A : Type_i implies A : Type_{i+1}. The Predicative Calculus of Inductive Constructions (pCIC) which forms the basis of the Coq proof assistant, is one such system. In this paper we present the Predicative Calculus of Cumulative Inductive Constructions (pCuIC) which extends the cumulativity relation to inductive types. We discuss cumulative inductive types as present in Coq 8.7 and their application to formalization and definitional translations.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-07-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133454656","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.2018.10
G. Bellin, W. Heijltjes
Bi-Intuitionistic Linear Logic (BILL) is an extension of Intuitionistic Linear Logic with a par, dual to the tensor, and subtraction, dual to linear implication. It is the logic of categories with a monoidal closed and a monoidal co-closed structure that are related by linear distributivity, a strength of the tensor over the par. It conservatively extends Full Intuitionistic Linear Logic (FILL), which includes only the par. We give proof nets for the multiplicative, unit-free fragment MBILL-. Correctness is by local rewriting in the style of Danos contractibility, which yields sequentialization into a relational sequent calculus extending the existing one for FILL. We give a second, geometric correctness condition combining Danos-Regnier switching and Lamarche's Essential Net criterion, and demonstrate composition both inductively and as a one-off global operation.
{"title":"Proof Nets for Bi-Intuitionistic Linear Logic","authors":"G. Bellin, W. Heijltjes","doi":"10.4230/LIPIcs.FSCD.2018.10","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2018.10","url":null,"abstract":"Bi-Intuitionistic Linear Logic (BILL) is an extension of Intuitionistic Linear Logic with a par, dual to the tensor, and subtraction, dual to linear implication. It is the logic of categories with a monoidal closed and a monoidal co-closed structure that are related by linear distributivity, a strength of the tensor over the par. It conservatively extends Full Intuitionistic Linear Logic (FILL), which includes only the par.\u0000We give proof nets for the multiplicative, unit-free fragment MBILL-. Correctness is by local rewriting in the style of Danos contractibility, which yields sequentialization into a relational sequent calculus extending the existing one for FILL. We give a second, geometric correctness condition combining Danos-Regnier switching and Lamarche's Essential Net criterion, and demonstrate composition both inductively and as a one-off global operation.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"129 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":"124236061","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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