Pub Date : 1992-06-22DOI: 10.1109/LICS.1992.185534
S. Abramsky, R. Jagadeesan
A new formal embodiment of J.-Y. Girard's (1989) geometry of interaction program is given. The geometry of interaction interpretation considered is defined, and the computational interpretation is sketched in terms of dataflow nets. Some examples that illustrate the key ideas underlying the interpretation are given. The results, which include the semantic analogue of cut-elimination, stated in terms of a finite convergence property, are outlined.<>
{"title":"New foundations for the geometry of interaction","authors":"S. Abramsky, R. Jagadeesan","doi":"10.1109/LICS.1992.185534","DOIUrl":"https://doi.org/10.1109/LICS.1992.185534","url":null,"abstract":"A new formal embodiment of J.-Y. Girard's (1989) geometry of interaction program is given. The geometry of interaction interpretation considered is defined, and the computational interpretation is sketched in terms of dataflow nets. Some examples that illustrate the key ideas underlying the interpretation are given. The results, which include the semantic analogue of cut-elimination, stated in terms of a finite convergence property, are outlined.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"26 1","pages":"211-222"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87660218","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.1992.185545
A. Aiken, E. Wimmers
It is shown that systems of set constraints that use all the standard set operations, especially unrestricted union and complement, can be solved. The centerpiece of the development is an algorithm that incrementally transforms a system of constraints while preserving the set of solutions. Eventually, either the system is shown to be inconsistent or all solutions can be exhibited. Most of the work is in proving that if this algorithm does not discover an inconsistency, then the system has a solution. This is done by showing that the system of constraints generated by the algorithm can be transformed into an equivalent set of equations that are guaranteed to have a solution. These equations are essentially tree automata.<>
{"title":"Solving systems of set constraints","authors":"A. Aiken, E. Wimmers","doi":"10.1109/LICS.1992.185545","DOIUrl":"https://doi.org/10.1109/LICS.1992.185545","url":null,"abstract":"It is shown that systems of set constraints that use all the standard set operations, especially unrestricted union and complement, can be solved. The centerpiece of the development is an algorithm that incrementally transforms a system of constraints while preserving the set of solutions. Eventually, either the system is shown to be inconsistent or all solutions can be exhibited. Most of the work is in proving that if this algorithm does not discover an inconsistency, then the system has a solution. This is done by showing that the system of constraints generated by the algorithm can be transformed into an equivalent set of equations that are guaranteed to have a solution. These equations are essentially tree automata.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"111 1","pages":"329-340"},"PeriodicalIF":0.0,"publicationDate":"1992-06-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"82886619","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 : 1992-01-01DOI: 10.1109/LICS.1992.185543
J. Tiuryn
The satisfiability problem for subtype inequalities in simple types is studied. The naive algorithm that solves this problem runs in nondeterministic exponential time for every predefined poset of atomic subtypings the satisfiability problem for subtype inequalities is PSPACE-hard. On the other hand, it is proved that if the poset of atomic subtypings is a disjoint union of lattices, then the satisfiability problem for subtype inequalities is solvable in PTIME. This result covers the important special case of the unification problem that can be obtained when the atomic subtype relation is equality.<>
{"title":"Subtype inequalities","authors":"J. Tiuryn","doi":"10.1109/LICS.1992.185543","DOIUrl":"https://doi.org/10.1109/LICS.1992.185543","url":null,"abstract":"The satisfiability problem for subtype inequalities in simple types is studied. The naive algorithm that solves this problem runs in nondeterministic exponential time for every predefined poset of atomic subtypings the satisfiability problem for subtype inequalities is PSPACE-hard. On the other hand, it is proved that if the poset of atomic subtypings is a disjoint union of lattices, then the satisfiability problem for subtype inequalities is solvable in PTIME. This result covers the important special case of the unification problem that can be obtained when the atomic subtype relation is equality.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"8 1","pages":"308-315"},"PeriodicalIF":0.0,"publicationDate":"1992-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"84384654","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 : 1992-01-01DOI: 10.1109/LICS.1992.185555
P. Freyd, E. Robinson, G. Rosolini
The authors consider the idea of treating a parametrized type as an arbitrary functor from some parametrizing category to a category of types, and giving elements semantics as natural transformations. They show that under reasonable hypotheses this is only possible when the parametrizing category is a groupoid. This suggests a semantics for a semiparametric form of polymorphism. They discuss the interpretation of this form of parametricity in a PER model, and show that it coincides with the ostensibly stronger form derived from dinaturality.<>
{"title":"Functional parametricity","authors":"P. Freyd, E. Robinson, G. Rosolini","doi":"10.1109/LICS.1992.185555","DOIUrl":"https://doi.org/10.1109/LICS.1992.185555","url":null,"abstract":"The authors consider the idea of treating a parametrized type as an arbitrary functor from some parametrizing category to a category of types, and giving elements semantics as natural transformations. They show that under reasonable hypotheses this is only possible when the parametrizing category is a groupoid. This suggests a semantics for a semiparametric form of polymorphism. They discuss the interpretation of this form of parametricity in a PER model, and show that it coincides with the ostensibly stronger form derived from dinaturality.<<ETX>>","PeriodicalId":6412,"journal":{"name":"[1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science","volume":"29 1","pages":"444-452"},"PeriodicalIF":0.0,"publicationDate":"1992-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"88484601","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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