Pub Date : 1992-06-22DOI: 10.1109/LICS.1992.185519
E. Grädel, G. McColm
It is shown that transitive closure logic (FO+TC) is strictly more powerful than deterministic transitive closure logic (FO+DTC) on unordered structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every query in (FO+DTC) is first-order expressible. On the other hand, there are simple (FO+pos TC) queries on these classes that cannot be defined by first-order formulas.<>
{"title":"Deterministic vs. nondeterministic transitive closure logic","authors":"E. Grädel, G. McColm","doi":"10.1109/LICS.1992.185519","DOIUrl":"https://doi.org/10.1109/LICS.1992.185519","url":null,"abstract":"It is shown that transitive closure logic (FO+TC) is strictly more powerful than deterministic transitive closure logic (FO+DTC) on unordered structures. In fact, on certain classes of graphs, such as hypercubes or regular graphs of large degree and girth, every query in (FO+DTC) is first-order expressible. On the other hand, there are simple (FO+pos TC) queries on these classes that cannot be defined by first-order formulas.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"151 1","pages":"58-63"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86163716","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 : 1992-06-22DOI: 10.1109/LICS.1992.185522
Hiroshi Nakano
The catch/throw mechanism, a programming construct for nonlocal exit, plays an important role when programmers handle exceptional situations. A constructive formalization that captures the mechanism in the proofs-as-programs notion is given. A modified version of LJ equipped with inference rules corresponding to the operations of catch and throw is introduced. Then it is shown that one can actually extract programs that made use of the catch/throw mechanism from proofs under a certain realizability interpretation. Although the catch/throw mechanism provides only a restricted access to the current continuation, the formulation remains constructive.<>
{"title":"A constructive formalization of the catch and throw mechanism","authors":"Hiroshi Nakano","doi":"10.1109/LICS.1992.185522","DOIUrl":"https://doi.org/10.1109/LICS.1992.185522","url":null,"abstract":"The catch/throw mechanism, a programming construct for nonlocal exit, plays an important role when programmers handle exceptional situations. A constructive formalization that captures the mechanism in the proofs-as-programs notion is given. A modified version of LJ equipped with inference rules corresponding to the operations of catch and throw is introduced. Then it is shown that one can actually extract programs that made use of the catch/throw mechanism from proofs under a certain realizability interpretation. Although the catch/throw mechanism provides only a restricted access to the current continuation, the formulation remains constructive.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"16 1","pages":"82-89"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83441729","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 : 1992-06-22DOI: 10.1109/LICS.1992.185536
P. Lincoln, John C. Mitchell
It is proved that the standard sequent calculus proof system of linear logic is equivalent to a natural deduction style proof system. The natural deduction system is used to investigate the pragmatic problems of type inference and type safety for a linear lambda calculus. Although terms do not have a single most-general type (for either the standard sequent presentation or the natural deduction formulation), there is a set of most-general types that may be computed using unification. The natural deduction system also facilitates the proof that the type of an expression is preserved by any evaluation step. An execution model and implementation is described, using a variant of the three-instruction machine. A novel feature of the implementation is that garbage-collected nonlinear memory is distinguished from linear memory, which does not require garbage collection and for which it is possible to do secure update in place.<>
{"title":"Operational aspects of linear lambda calculus","authors":"P. Lincoln, John C. Mitchell","doi":"10.1109/LICS.1992.185536","DOIUrl":"https://doi.org/10.1109/LICS.1992.185536","url":null,"abstract":"It is proved that the standard sequent calculus proof system of linear logic is equivalent to a natural deduction style proof system. The natural deduction system is used to investigate the pragmatic problems of type inference and type safety for a linear lambda calculus. Although terms do not have a single most-general type (for either the standard sequent presentation or the natural deduction formulation), there is a set of most-general types that may be computed using unification. The natural deduction system also facilitates the proof that the type of an expression is preserved by any evaluation step. An execution model and implementation is described, using a variant of the three-instruction machine. A novel feature of the implementation is that garbage-collected nonlinear memory is distinguished from linear memory, which does not require garbage collection and for which it is possible to do secure update in place.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"148 1","pages":"235-246"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83807397","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 : 1992-06-22DOI: 10.1109/LICS.1992.185539
D. Caucal
The monadic second-order theory of term rewritings is considered. It is shown that the monadic theory of the rewriting (or the suffix rewriting) of a ground rewrite system is undecidable. Furthermore, the first-order theory is undecidable for the prefix derivation according to a linear context-free grammar on linear terms. Nevertheless, a new notion on terms with variables is introduced: a term is entire if each of its subterms either is a variable, or is without variable or has the same variables as the term. It is shown that the monadic theory is decidable (respectively undecidable) for the prefix rewriting according to a rewrite system on entire terms, with an axiom (respectively without axiom).<>
{"title":"Monadic theory of term rewritings","authors":"D. Caucal","doi":"10.1109/LICS.1992.185539","DOIUrl":"https://doi.org/10.1109/LICS.1992.185539","url":null,"abstract":"The monadic second-order theory of term rewritings is considered. It is shown that the monadic theory of the rewriting (or the suffix rewriting) of a ground rewrite system is undecidable. Furthermore, the first-order theory is undecidable for the prefix derivation according to a linear context-free grammar on linear terms. Nevertheless, a new notion on terms with variables is introduced: a term is entire if each of its subterms either is a variable, or is without variable or has the same variables as the term. It is shown that the monadic theory is decidable (respectively undecidable) for the prefix rewriting according to a rewrite system on entire terms, with an axiom (respectively without axiom).<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"11 1","pages":"266-273"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84220363","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 : 1992-06-22DOI: 10.1109/LICS.1992.185541
Anil Seth
The author shows a class of type-two feasible functionals, C/sub 2/, that satisfies Cook's conditions, (1990) and cannot be expressed as the lambda closure of type-one poly-time functions and any recursively enumerable set of type-two feasible functionals. Further, no class of total type-two functionals containing this class is representable as the lambda closure of a recursively enumerable set of type-two total computable functionals and type-one poly-time functions. The definition of C/sub 2/ provides a clear computational procedure for functionals of C/sub 2/. Using functionals of class C/sub 2/ a more general notion of polynomial-time reducibility between two arbitrary type-one functions can be introduced.<>
{"title":"There is no recursive axiomatization for feasible functionals of type 2","authors":"Anil Seth","doi":"10.1109/LICS.1992.185541","DOIUrl":"https://doi.org/10.1109/LICS.1992.185541","url":null,"abstract":"The author shows a class of type-two feasible functionals, C/sub 2/, that satisfies Cook's conditions, (1990) and cannot be expressed as the lambda closure of type-one poly-time functions and any recursively enumerable set of type-two feasible functionals. Further, no class of total type-two functionals containing this class is representable as the lambda closure of a recursively enumerable set of type-two total computable functionals and type-one poly-time functions. The definition of C/sub 2/ provides a clear computational procedure for functionals of C/sub 2/. Using functionals of class C/sub 2/ a more general notion of polynomial-time reducibility between two arbitrary type-one functions can be introduced.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"76 1","pages":"286-295"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"79964918","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 : 1992-06-22DOI: 10.1109/LICS.1992.185532
Ian A. Mason, C. Talcott
A.R. Meyer and K. Sieber (Proc. 15th ACM. Symp. on Principles of Programming Languages, 1988, p.191-208) gave a series of examples of programs that are operationally equivalent (according to the intended semantics of block-structured Algol-like programs) but are not given equivalent denotations in traditional denotational semantics. They propose various modifications to the denotational semantics that solve some of these discrepancies, but not all. The present authors approach the same problem, but from an operational rather than a denotational perspective. They present the first-order part of a new logic for reasoning about programs, and they use this logic to prove the equivalence of the Meyer-Sieber examples.<>
A.R. Meyer和K. Sieber(第15期ACM)。计算机协会。on Principles of Programming Languages, 1988, p.191-208)给出了一系列程序的例子，这些程序在操作上是等价的(根据块结构类algol程序的预期语义)，但在传统的指称语义中没有给出等价的表意。他们提出了对指称语义的各种修改，以解决其中的一些差异，但不是全部。目前的作者接近同样的问题，但从操作而不是外延的角度来看。他们提出了一种新的程序推理逻辑的一阶部分，并用这种逻辑证明了Meyer-Sieber例子的等价性。
{"title":"References, local variables and operational reasoning","authors":"Ian A. Mason, C. Talcott","doi":"10.1109/LICS.1992.185532","DOIUrl":"https://doi.org/10.1109/LICS.1992.185532","url":null,"abstract":"A.R. Meyer and K. Sieber (Proc. 15th ACM. Symp. on Principles of Programming Languages, 1988, p.191-208) gave a series of examples of programs that are operationally equivalent (according to the intended semantics of block-structured Algol-like programs) but are not given equivalent denotations in traditional denotational semantics. They propose various modifications to the denotational semantics that solve some of these discrepancies, but not all. The present authors approach the same problem, but from an operational rather than a denotational perspective. They present the first-order part of a new logic for reasoning about programs, and they use this logic to prove the equivalence of the Meyer-Sieber examples.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"23 1","pages":"186-197"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78545614","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 : 1992-06-22DOI: 10.1109/LICS.1992.185515
D. Kapur, P. Narendran
An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, and its termination can be easily established. Its complexity is easily analyzed and shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense.<>
{"title":"Double-exponential complexity of computing a complete set of AC-unifiers","authors":"D. Kapur, P. Narendran","doi":"10.1109/LICS.1992.185515","DOIUrl":"https://doi.org/10.1109/LICS.1992.185515","url":null,"abstract":"An algorithm for computing a complete set of unifiers for two terms involving associative-commutative function symbols is presented. It is based on a nondeterministic algorithm given by the authors in 1986 to show the NP-completeness of associative-commutative unifiability. The algorithm is easy to understand, and its termination can be easily established. Its complexity is easily analyzed and shown to be doubly exponential in the size of the input terms. The analysis also shows that there is a double-exponential upper bound on the size of a complete set of unifiers of two input terms. Since there is a family of simple associative-commutative unification problems which have complete sets of unifiers whose size is doubly exponential, the algorithm is optimal in its order of complexity in this sense.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"49 1","pages":"11-21"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74314547","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 : 1992-06-22DOI: 10.1109/LICS.1992.185530
J. Talpin, P. Jouvelot
The type and effect discipline, a framework for reconstructing the principal type and the minimal effect of expressions in implicitly typed polymorphic functional languages that support imperative constructs, is introduced. The type and effect discipline outperforms other polymorphic type systems. Just as types abstract collections of concrete values, effects denote imperative operations on regions. Regions abstract sets of possibly aliased memory locations. Effects are used to control type generalization in the presence of imperative constructs while regions delimit observable side effects. The observable effects of an expression range over the regions that are free in its type environment and its type; effects related to local data structures can be discarded during type reconstruction. The type of an expression can be generalized with respect to the variables that are not free in the type environment or in the observable effect.<>
{"title":"The type and effect discipline","authors":"J. Talpin, P. Jouvelot","doi":"10.1109/LICS.1992.185530","DOIUrl":"https://doi.org/10.1109/LICS.1992.185530","url":null,"abstract":"The type and effect discipline, a framework for reconstructing the principal type and the minimal effect of expressions in implicitly typed polymorphic functional languages that support imperative constructs, is introduced. The type and effect discipline outperforms other polymorphic type systems. Just as types abstract collections of concrete values, effects denote imperative operations on regions. Regions abstract sets of possibly aliased memory locations. Effects are used to control type generalization in the presence of imperative constructs while regions delimit observable side effects. The observable effects of an expression range over the regions that are free in its type environment and its type; effects related to local data structures can be discarded during type reconstruction. The type of an expression can be generalized with respect to the variables that are not free in the type environment or in the observable effect.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"18 1","pages":"162-173"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74934165","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 : 1992-06-22DOI: 10.1109/LICS.1992.185557
Ugo de'Liguoro, A. Piperno, R. Statman
Retractions existing in all models of simply typed lambda -calculus are studied and related to other relations among types, such as isomorphisms, surjections, and injections. A formal system to deduce the existence of such retractions is shown to be sound and complete with respect to retractions definable by linear lambda -terms. Results aiming at a system complete with respect to the provable retractions tout court are established.<>
{"title":"Retracts in simply type lambda beta eta -calculus","authors":"Ugo de'Liguoro, A. Piperno, R. Statman","doi":"10.1109/LICS.1992.185557","DOIUrl":"https://doi.org/10.1109/LICS.1992.185557","url":null,"abstract":"Retractions existing in all models of simply typed lambda -calculus are studied and related to other relations among types, such as isomorphisms, surjections, and injections. A formal system to deduce the existence of such retractions is shown to be sound and complete with respect to retractions definable by linear lambda -terms. Results aiming at a system complete with respect to the provable retractions tout court are established.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"59 1","pages":"461-469"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90628188","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 : 1992-06-22DOI: 10.1109/LICS.1992.185533
M. Kanovich
The question of developing a computational interpretation of J.-Y. Girard's (1987) linear logic and obtaining efficient decision algorithms for this logic, based on the bottom-up approach, is addressed. The approach taken is to start with the simplest natural fragment of linear logic and then expand it step-by-step. The smallest natural Horn fragment of Girard's linear logic is considered, and it is proved that this fragment is NP-complete. As a corollary, an affirmative solution for the problem of whether the multiplicative fragment of Girard's linear logic is NP-complete is obtained. Then a complete computational interpretation for Horn fragments enriched by two additive connectives and by the storage operator is given. Within the framework of this interpretation, it becomes possible to explicitly formalize and clarify the computational aspects of the fragments of linear logic in question and establish exactly the complexity level of these fragments.<>
{"title":"Horn programming in linear logic is NP-complete","authors":"M. Kanovich","doi":"10.1109/LICS.1992.185533","DOIUrl":"https://doi.org/10.1109/LICS.1992.185533","url":null,"abstract":"The question of developing a computational interpretation of J.-Y. Girard's (1987) linear logic and obtaining efficient decision algorithms for this logic, based on the bottom-up approach, is addressed. The approach taken is to start with the simplest natural fragment of linear logic and then expand it step-by-step. The smallest natural Horn fragment of Girard's linear logic is considered, and it is proved that this fragment is NP-complete. As a corollary, an affirmative solution for the problem of whether the multiplicative fragment of Girard's linear logic is NP-complete is obtained. Then a complete computational interpretation for Horn fragments enriched by two additive connectives and by the storage operator is given. Within the framework of this interpretation, it becomes possible to explicitly formalize and clarify the computational aspects of the fragments of linear logic in question and establish exactly the complexity level of these fragments.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"1 1","pages":"200-210"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83545240","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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