Pub Date : 1993-06-19DOI: 10.1109/LICS.1993.287571
G. Plotkin
Summary form only given. Type theory and recursion are analyzed in terms of intuitionistic linear type theory. This is compatible with a general recursion operator for the intuitionistic functions. The author considers second-order intuitionistic linear type theory whose primitive type constructions are linear and intuitionistic function types and second-order quantification.<>
{"title":"Type theory and recursion","authors":"G. Plotkin","doi":"10.1109/LICS.1993.287571","DOIUrl":"https://doi.org/10.1109/LICS.1993.287571","url":null,"abstract":"Summary form only given. Type theory and recursion are analyzed in terms of intuitionistic linear type theory. This is compatible with a general recursion operator for the intuitionistic functions. The author considers second-order intuitionistic linear type theory whose primitive type constructions are linear and intuitionistic function types and second-order quantification.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74725872","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 : 1993-06-19DOI: 10.1109/LICS.1993.287591
P. Abdulla, B. Jonsson
The verification of a particular class of infinite-state systems, namely, systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels, is considered. This class is able to model, e.g., link protocols such as the Alternating Bit Protocol and HDLC. For this class of systems, it is shown that several interesting verification problems are decidable by giving algorithms for verifying: the reachability problem (whether a finite set of global states is reachable from some other global state of the system); the safety property over traces, formulated as regular sets of allowed finite traces; and eventuality properties (whether all computations of a system eventually reach a given set of states). The algorithms are used to verify some idealized sliding-window protocols with reasonable time and space resources.<>
{"title":"Verifying programs with unreliable channels","authors":"P. Abdulla, B. Jonsson","doi":"10.1109/LICS.1993.287591","DOIUrl":"https://doi.org/10.1109/LICS.1993.287591","url":null,"abstract":"The verification of a particular class of infinite-state systems, namely, systems consisting of finite-state processes that communicate via unbounded lossy FIFO channels, is considered. This class is able to model, e.g., link protocols such as the Alternating Bit Protocol and HDLC. For this class of systems, it is shown that several interesting verification problems are decidable by giving algorithms for verifying: the reachability problem (whether a finite set of global states is reachable from some other global state of the system); the safety property over traces, formulated as regular sets of allowed finite traces; and eventuality properties (whether all computations of a system eventually reach a given set of states). The algorithms are used to verify some idealized sliding-window protocols with reasonable time and space resources.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"76828199","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 : 1993-06-19DOI: 10.1109/LICS.1993.287590
Damian Niwinski, Alexei P. Stolboushkin
It is shown that no formula of first-order logic using linear ordering and the logical relation y=2x can define the property that the size of a finite model is divisible by 3. This answers a long-standing question that may be of relevance to certain open problems in circuit complexity.<>
{"title":"y=2x vs. y=3x","authors":"Damian Niwinski, Alexei P. Stolboushkin","doi":"10.1109/LICS.1993.287590","DOIUrl":"https://doi.org/10.1109/LICS.1993.287590","url":null,"abstract":"It is shown that no formula of first-order logic using linear ordering and the logical relation y=2x can define the property that the size of a finite model is divisible by 3. This answers a long-standing question that may be of relevance to certain open problems in circuit complexity.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89837030","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 : 1993-06-19DOI: 10.1109/LICS.1993.287570
B. Pierce, D. Sangiorgi
The pi -calculus is a process algebra that supports process mobility by focusing on the communication of channels. R. Milner's (1991) presentation of the pi -calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. The authors extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed lambda -calculi. The greater precision of their type discipline yields stronger versions of some standard theorems about the pi -calculus. These can be used, for example, to obtain the validity of beta -reduction for the more efficient of Milner's encodings of the call-by-value lambda -calculus, for which beta -reduction does not hold in the ordinary pi -calculus. The authors define the syntax, typing, subtyping, and operational semantics of their calculus, prove that the typing rules are sound, apply the system to Milner's lambda -calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.<>
{"title":"Typing and subtyping for mobile processes","authors":"B. Pierce, D. Sangiorgi","doi":"10.1109/LICS.1993.287570","DOIUrl":"https://doi.org/10.1109/LICS.1993.287570","url":null,"abstract":"The pi -calculus is a process algebra that supports process mobility by focusing on the communication of channels. R. Milner's (1991) presentation of the pi -calculus includes a type system assigning arities to channels and enforcing a corresponding discipline in their use. The authors extend Milner's language of types by distinguishing between the ability to read from a channel, the ability to write to a channel, and the ability both to read and to write. This refinement gives rise to a natural subtype relation similar to those studied in typed lambda -calculi. The greater precision of their type discipline yields stronger versions of some standard theorems about the pi -calculus. These can be used, for example, to obtain the validity of beta -reduction for the more efficient of Milner's encodings of the call-by-value lambda -calculus, for which beta -reduction does not hold in the ordinary pi -calculus. The authors define the syntax, typing, subtyping, and operational semantics of their calculus, prove that the typing rules are sound, apply the system to Milner's lambda -calculus encodings, and sketch extensions to higher-order process calculi and polymorphic typing.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86366010","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 : 1993-06-19DOI: 10.1109/LICS.1993.287604
John C. Mitchell, R. Viswanathan
Standard ML of New Jersey (SML-NJ) uses weak-type variables to restrict the polymorphic use of functions that may allocate reference cells, manipulate continuations, or use exceptions. However, the type system used in the SML-NJ compiler has not been presented in a form other than source code and has not been proved correct. A type system, in the form of typing rules and an equivalent algorithm, that appears to subsume the implemented algorithm is presented. Both use type variables of only a slightly more general nature than the compiler. One insight in the analysis is that the indexed type of a free variable is used in two ways, once in describing the applicative behavior of the variable itself and once in describing the larger term containing the variable. Taking this into account, an application rule that is more general than SML-NJ is formulated for applications of polymorphic functions to imperative arguments. The soundness of the type system is proved for imperative code using operational semantics.<>
{"title":"Standard ML-NJ weak polymorphism and imperative constructs","authors":"John C. Mitchell, R. Viswanathan","doi":"10.1109/LICS.1993.287604","DOIUrl":"https://doi.org/10.1109/LICS.1993.287604","url":null,"abstract":"Standard ML of New Jersey (SML-NJ) uses weak-type variables to restrict the polymorphic use of functions that may allocate reference cells, manipulate continuations, or use exceptions. However, the type system used in the SML-NJ compiler has not been presented in a form other than source code and has not been proved correct. A type system, in the form of typing rules and an equivalent algorithm, that appears to subsume the implemented algorithm is presented. Both use type variables of only a slightly more general nature than the compiler. One insight in the analysis is that the indexed type of a free variable is used in two ways, once in describing the applicative behavior of the variable itself and once in describing the larger term containing the variable. Taking this into account, an application rule that is more general than SML-NJ is formulated for applications of polymorphic functions to imperative arguments. The soundness of the type system is proved for imperative code using operational semantics.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85427547","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 : 1993-06-19DOI: 10.1109/LICS.1993.287568
M. Hennessy
A higher-order process calculus is defined in which one can describe processes which transmit as messages other processes; it may be viewed as a generalization of the lazy lambda -calculus. The authors present a denotational model for the language, obtained by generalizing the domain equation for S. Abramsky's (1990) model of the lazy lambda -calculus. It is shown to be fully abstract with respect to three different behavioural preorders. The first is based on observing the ability of processes to perform an action in all contexts, the second on testing, and the final one on satisfying certain kinds of modal formulae.<>
{"title":"A fully abstract denotational model for higher-order processes","authors":"M. Hennessy","doi":"10.1109/LICS.1993.287568","DOIUrl":"https://doi.org/10.1109/LICS.1993.287568","url":null,"abstract":"A higher-order process calculus is defined in which one can describe processes which transmit as messages other processes; it may be viewed as a generalization of the lazy lambda -calculus. The authors present a denotational model for the language, obtained by generalizing the domain equation for S. Abramsky's (1990) model of the lazy lambda -calculus. It is shown to be fully abstract with respect to three different behavioural preorders. The first is based on observing the ability of processes to perform an action in all contexts, the second on testing, and the final one on satisfying certain kinds of modal formulae.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78655080","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 : 1993-06-19DOI: 10.1109/LICS.1993.287574
L. Lakshmanan, K. Ashraf, Jiawei Han
The problems of stage-preserving linearization and one-boundedness are studied for a class of nonlinear single rule recursive programs, and syntactic characterizations are developed for both. The characterizations lead to a polynomial-time algorithm for the former and a linear-time algorithm for the latter. Stage-preserving linearization results in a significant improvement in evaluation efficiency, compared to a linearization that does not preserve stages. The class of nonlinear strips that are stage-preserving linearizable includes several classes of programs that can be linearized only using a mix of left and right linear rules, as well as programs that cannot be linearized using previously known techniques. The study makes use of a technique based on the notion of homomorphic tree embeddings.<>
{"title":"Homomorphic tree embeddings and their applications to recursive program optimization","authors":"L. Lakshmanan, K. Ashraf, Jiawei Han","doi":"10.1109/LICS.1993.287574","DOIUrl":"https://doi.org/10.1109/LICS.1993.287574","url":null,"abstract":"The problems of stage-preserving linearization and one-boundedness are studied for a class of nonlinear single rule recursive programs, and syntactic characterizations are developed for both. The characterizations lead to a polynomial-time algorithm for the former and a linear-time algorithm for the latter. Stage-preserving linearization results in a significant improvement in evaluation efficiency, compared to a linearization that does not preserve stages. The class of nonlinear strips that are stage-preserving linearizable includes several classes of programs that can be linearized only using a mix of left and right linear rules, as well as programs that cannot be linearized using previously known techniques. The study makes use of a technique based on the notion of homomorphic tree embeddings.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89362237","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 : 1993-06-19DOI: 10.1109/LICS.1993.287565
M. Pentus
Basic categorial grammars are the context-free ones. Another kind of categorial grammars was introduced by J. Lambek (1958). These grammars are based on a syntactic calculus, known as the Lambek calculus. Chomsky (1963) conjectured that these grammars are also equivalent to context-free ones. Every basic categorial grammar (and thus every context-free grammar) is equivalent to a Lambek grammar. Conversely, some special kinds of Lambek grammars are context-free. These grammars use weakly unidirectional types, or types of order at most two. The main result of this paper says that Lambek grammars generate only context-free languages. Thus they are equivalent to context-free grammars and also to basic categorial grammars. The Chomsky conjecture, that all languages recognized by the Lambek calculus are context-free, is thus proved.<>
{"title":"Lambek grammars are context free","authors":"M. Pentus","doi":"10.1109/LICS.1993.287565","DOIUrl":"https://doi.org/10.1109/LICS.1993.287565","url":null,"abstract":"Basic categorial grammars are the context-free ones. Another kind of categorial grammars was introduced by J. Lambek (1958). These grammars are based on a syntactic calculus, known as the Lambek calculus. Chomsky (1963) conjectured that these grammars are also equivalent to context-free ones. Every basic categorial grammar (and thus every context-free grammar) is equivalent to a Lambek grammar. Conversely, some special kinds of Lambek grammars are context-free. These grammars use weakly unidirectional types, or types of order at most two. The main result of this paper says that Lambek grammars generate only context-free languages. Thus they are equivalent to context-free grammars and also to basic categorial grammars. The Chomsky conjecture, that all languages recognized by the Lambek calculus are context-free, is thus proved.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83552931","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 : 1993-06-19DOI: 10.1109/LICS.1993.287582
K. Barwise, J. Seligman
The view that computers are information processors is commonplace. They are used, for the most part successfully, throughout our society, as reliable links in the transmission of information and knowledge. Yet the formulation of a precise, qualitative conception of information and a theory of the transmission of information has proved elusive, despite the many other successes of computer science. The authors set out the motivation for and a skeleton of a new mathematical model of information flow, one that is compatible with less than perfect flow.<>
{"title":"Imperfect information flow","authors":"K. Barwise, J. Seligman","doi":"10.1109/LICS.1993.287582","DOIUrl":"https://doi.org/10.1109/LICS.1993.287582","url":null,"abstract":"The view that computers are information processors is commonplace. They are used, for the most part successfully, throughout our society, as reliable links in the transmission of information and knowledge. Yet the formulation of a precise, qualitative conception of information and a theory of the transmission of information has proved elusive, despite the many other successes of computer science. The authors set out the motivation for and a skeleton of a new mathematical model of information flow, one that is compatible with less than perfect flow.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84124109","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 : 1993-06-19DOI: 10.1109/LICS.1993.287601
S. Chou, Xiao Gao, Jing-Zhong Zhang
The authors present a method that can produce traditional proofs for a class of geometry statements whose hypotheses can be described constructively and whose conclusions can be represented by polynomial equations of three kinds of geometry quantities: ratios of lengths, areas of triangles, and Pythagoras differences of triangles. This class covers a large portion of the geometry theorems about straight lines and circles. The method involves the elimination of the constructed points from the conclusion using a few basic geometry propositions. The authors' program, Euclid, implements this method and can produce traditional proofs of many hard geometry theorems. Currently, it has produced proofs of 400 nontrivial theorems entirely automatically, and the proofs produced are generally short and readable. This method seems to be the first one to produce traditional proofs for hard geometry theorems efficiently.<>
{"title":"Automated production of traditional proofs for constructive geometry theorems","authors":"S. Chou, Xiao Gao, Jing-Zhong Zhang","doi":"10.1109/LICS.1993.287601","DOIUrl":"https://doi.org/10.1109/LICS.1993.287601","url":null,"abstract":"The authors present a method that can produce traditional proofs for a class of geometry statements whose hypotheses can be described constructively and whose conclusions can be represented by polynomial equations of three kinds of geometry quantities: ratios of lengths, areas of triangles, and Pythagoras differences of triangles. This class covers a large portion of the geometry theorems about straight lines and circles. The method involves the elimination of the constructed points from the conclusion using a few basic geometry propositions. The authors' program, Euclid, implements this method and can produce traditional proofs of many hard geometry theorems. Currently, it has produced proofs of 400 nontrivial theorems entirely automatically, and the proofs produced are generally short and readable. This method seems to be the first one to produce traditional proofs for hard geometry theorems efficiently.<<ETX>>","PeriodicalId":6322,"journal":{"name":"[1993] Proceedings Eighth Annual IEEE Symposium on Logic in Computer Science","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"1993-06-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83697201","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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