We present a system of linear session types that integrates several features aimed at verification of different properties of concurrent programs, specifically types indexed with arithmetic expressions, linear constraints and quantification. We prove the standard type safety properties of session fidelity and deadlock freedom. In order to control the verbosity of programs we introduce implicit syntax and an algorithm for reconstruction, which is complete under some mild assumptions on the structure of types. We then illustrate the expressive power of our language (called Rast) with a variety of examples, including normalization for the linear λ-calculus, balanced ternary arithmetic, binary counters and tries.
{"title":"Verified Linear Session-Typed Concurrent Programming","authors":"Ankush Das, F. Pfenning","doi":"10.1145/3414080.3414087","DOIUrl":"https://doi.org/10.1145/3414080.3414087","url":null,"abstract":"We present a system of linear session types that integrates several features aimed at verification of different properties of concurrent programs, specifically types indexed with arithmetic expressions, linear constraints and quantification. We prove the standard type safety properties of session fidelity and deadlock freedom. In order to control the verbosity of programs we introduce implicit syntax and an algorithm for reconstruction, which is complete under some mild assumptions on the structure of types. We then illustrate the expressive power of our language (called Rast) with a variety of examples, including normalization for the linear λ-calculus, balanced ternary arithmetic, binary counters and tries.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"1193 ","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132948922","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}
This paper revisits the Interaction Abstract Machine (IAM), a machine based on Girard’s Geometry of Interaction, introduced by Mackie and Danos & Regnier. It is an unusual machine, not relying on environments, presented on linear logic proof nets, and whose soundness proof is convoluted and passes through various other formalisms. Here we provide a new direct proof of its correctness, based on a variant of Sands’s improvements, a natural notion of bisimulation. Moreover, our proof is carried out on a new presentation of the IAM, defined as a machine acting directly on λ-terms, rather than on linear logic proof nets.
{"title":"The Machinery of Interaction","authors":"Beniamino Accattoli, Ugo Dal Lago, G. Vanoni","doi":"10.1145/3414080.3414108","DOIUrl":"https://doi.org/10.1145/3414080.3414108","url":null,"abstract":"This paper revisits the Interaction Abstract Machine (IAM), a machine based on Girard’s Geometry of Interaction, introduced by Mackie and Danos & Regnier. It is an unusual machine, not relying on environments, presented on linear logic proof nets, and whose soundness proof is convoluted and passes through various other formalisms. Here we provide a new direct proof of its correctness, based on a variant of Sands’s improvements, a natural notion of bisimulation. Moreover, our proof is carried out on a new presentation of the IAM, defined as a machine acting directly on λ-terms, rather than on linear logic proof nets.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121955916","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}
Justification Logic is a refinement of modal logic where the modality is annotated with a reason s for “knowing” A and written . The expression s is a proof of A that may be encoded as a lambda calculus term of type A, according to the propositions-as-types interpretation. Our starting point is the observation that terms of type are reductions between lambda calculus terms. Reductions are usually encoded as rewrites essential tools in analyzing the reduction behavior of lambda calculus and term rewriting systems, such as when studying standardization, needed strategies, Lévy permutation equivalence, etc. We explore a new propositions-as-types interpretation for Justification Logic, based on the principle that terms of type are proof terms encoding reductions (with source s). Note that this provides a logical language to reason about rewrites.
{"title":"Rewrites as Terms through Justification Logic","authors":"Pablo Barenbaum, E. Bonelli","doi":"10.1145/3414080.3414091","DOIUrl":"https://doi.org/10.1145/3414080.3414091","url":null,"abstract":"Justification Logic is a refinement of modal logic where the modality is annotated with a reason s for “knowing” A and written . The expression s is a proof of A that may be encoded as a lambda calculus term of type A, according to the propositions-as-types interpretation. Our starting point is the observation that terms of type are reductions between lambda calculus terms. Reductions are usually encoded as rewrites essential tools in analyzing the reduction behavior of lambda calculus and term rewriting systems, such as when studying standardization, needed strategies, Lévy permutation equivalence, etc. We explore a new propositions-as-types interpretation for Justification Logic, based on the principle that terms of type are proof terms encoding reductions (with source s). Note that this provides a logical language to reason about rewrites.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"31 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130689569","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}
We present new algorithms to compute candidate keys and third normal form design of a relational database schema, using strategic port graph rewriting. More precisely, we define port graph rewriting rules and strategies that implement a candidate key definition and Ullman’s algorithm to decompose a relation schema into lossless 3NF schemata. We show the correctness of the resulting database schema by proving soundness, completeness and termination of our strategic graph programs. These rules and strategies provide a declarative and visual description of the algorithms, and permit a fine-grained analysis of the computation steps involved in the normalisation process. The algorithms have been implemented in Porgy, a visual, interactive modelling tool.
{"title":"Finding Candidate Keys and 3NF via Strategic Port Graph Rewriting","authors":"M. Fernández, János Varga","doi":"10.1145/3414080.3414090","DOIUrl":"https://doi.org/10.1145/3414080.3414090","url":null,"abstract":"We present new algorithms to compute candidate keys and third normal form design of a relational database schema, using strategic port graph rewriting. More precisely, we define port graph rewriting rules and strategies that implement a candidate key definition and Ullman’s algorithm to decompose a relation schema into lossless 3NF schemata. We show the correctness of the resulting database schema by proving soundness, completeness and termination of our strategic graph programs. These rules and strategies provide a declarative and visual description of the algorithms, and permit a fine-grained analysis of the computation steps involved in the normalisation process. The algorithms have been implemented in Porgy, a visual, interactive modelling tool.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114892154","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}
We introduce a language-independent framework for reasoning about program inverters by conditional term rewriting systems. These systems can model the three fundamental forms of inversion, i.e., full, partial and semi-inversion, in declarative languages. The correctness of the generic inversion algorithm introduced in this contribution is proven for all well-behaved rule inverters, and we demonstrate that this class of inverters encompasses several of the inversion algorithms published throughout the past years. This new generic approach enables us to establish fundamental properties, e.g., orthogonality, for entire classes of well-behaved full inverters, partial inverters and semi-inverters regardless of their particular local rule inverters. We study known inverters as well as classes of inverters that yield left-to-right deterministic systems; left-to-right determinism is a desirable property, e.g., for functional programs; however, at the same time it is not generally a property of inverted systems. This generic approach enables a more systematic design of program inverters and fills a gap in our knowledge of program inversion.
{"title":"Inversion Framework: Reasoning about Inversion by Conditional Term Rewriting Systems","authors":"M. H. Kirkeby, R. Glück","doi":"10.1145/3414080.3414089","DOIUrl":"https://doi.org/10.1145/3414080.3414089","url":null,"abstract":"We introduce a language-independent framework for reasoning about program inverters by conditional term rewriting systems. These systems can model the three fundamental forms of inversion, i.e., full, partial and semi-inversion, in declarative languages. The correctness of the generic inversion algorithm introduced in this contribution is proven for all well-behaved rule inverters, and we demonstrate that this class of inverters encompasses several of the inversion algorithms published throughout the past years. This new generic approach enables us to establish fundamental properties, e.g., orthogonality, for entire classes of well-behaved full inverters, partial inverters and semi-inverters regardless of their particular local rule inverters. We study known inverters as well as classes of inverters that yield left-to-right deterministic systems; left-to-right determinism is a desirable property, e.g., for functional programs; however, at the same time it is not generally a property of inverted systems. This generic approach enables a more systematic design of program inverters and fills a gap in our knowledge of program inversion.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"21 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115567858","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}
Session types have consolidated as a formalism for the specification and static enforcement of communication protocols. Many different theories of dependent session types have been proposed, some enabling refined specifications on the content of messages, others allowing the structure of the protocols to depend on data exchanged in the protocol itself. In this work we continue a line of research studying the foundations of binary session types. In particular, we propose a variant of the linear π-calculus whose type structure encompasses virtually all dependent session types using just two type constructors: linear channel types and linear dependent pairs. We use Agda not only to formalize the metatheory of the calculus and obtain machine-checked proofs of type soundness, but also as host language in which we implement data-dependent protocols.
{"title":"A Dependently Typed Linear π-Calculus in Agda","authors":"L. Ciccone, L. Padovani","doi":"10.1145/3414080.3414109","DOIUrl":"https://doi.org/10.1145/3414080.3414109","url":null,"abstract":"Session types have consolidated as a formalism for the specification and static enforcement of communication protocols. Many different theories of dependent session types have been proposed, some enabling refined specifications on the content of messages, others allowing the structure of the protocols to depend on data exchanged in the protocol itself. In this work we continue a line of research studying the foundations of binary session types. In particular, we propose a variant of the linear π-calculus whose type structure encompasses virtually all dependent session types using just two type constructors: linear channel types and linear dependent pairs. We use Agda not only to formalize the metatheory of the calculus and obtain machine-checked proofs of type soundness, but also as host language in which we implement data-dependent protocols.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114783688","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}
We discuss the relationship between monads and their known generalisation, graded monads, which are especially useful for modelling computational effects equipped with a form of sequential composition. Specifically, we ask if a graded monad can be extended to a monad, and when such a degrading is in some sense canonical. Our particular examples are the graded monads of lists and non-empty lists indexed by their lengths, which gives us a pretext to study the space of all (non-graded) monad structures on the list and non-empty list endofunctors. We show that, in both cases, there exist infinitely many monad structures. However, while there are at least two ways to complete the graded monad structure on length-indexed lists to a monad structure on the list endofunctor, such a completion for non-empty lists is unique.
{"title":"Degrading Lists","authors":"Dylan McDermott, Maciej Piróg, Tarmo Uustalu","doi":"10.1145/3414080.3414084","DOIUrl":"https://doi.org/10.1145/3414080.3414084","url":null,"abstract":"We discuss the relationship between monads and their known generalisation, graded monads, which are especially useful for modelling computational effects equipped with a form of sequential composition. Specifically, we ask if a graded monad can be extended to a monad, and when such a degrading is in some sense canonical. Our particular examples are the graded monads of lists and non-empty lists indexed by their lengths, which gives us a pretext to study the space of all (non-graded) monad structures on the list and non-empty list endofunctors. We show that, in both cases, there exist infinitely many monad structures. However, while there are at least two ways to complete the graded monad structure on length-indexed lists to a monad structure on the list endofunctor, such a completion for non-empty lists is unique.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123179095","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}
Recursion and induction are mature, well-understood topics in programming. Yet their duals, corecursion and coinduction, are still exotic and underdeveloped programming features. We aim to put them on equal footing by giving a foundation for corecursion based on computation, analogous to the original computational foundation of recursion. At the lower level, we show how the connection between the two can be strengthened through their implementation details in an abstract machine. At the higher level, we develop a syntactic equational theory for inductive and coinductive reasoning based on control flow. We also observe the impact of evaluation strategy: call-by-name has efficient recursion and strong coinductive reasoning, but call-by-value has efficient corecursion and strong inductive reasoning.
{"title":"A Computational Understanding of Classical (Co)Recursion","authors":"P. Downen, Z. M. Ariola","doi":"10.1145/3414080.3414086","DOIUrl":"https://doi.org/10.1145/3414080.3414086","url":null,"abstract":"Recursion and induction are mature, well-understood topics in programming. Yet their duals, corecursion and coinduction, are still exotic and underdeveloped programming features. We aim to put them on equal footing by giving a foundation for corecursion based on computation, analogous to the original computational foundation of recursion. At the lower level, we show how the connection between the two can be strengthened through their implementation details in an abstract machine. At the higher level, we develop a syntactic equational theory for inductive and coinductive reasoning based on control flow. We also observe the impact of evaluation strategy: call-by-name has efficient recursion and strong coinductive reasoning, but call-by-value has efficient corecursion and strong inductive reasoning.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129001586","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}
Ekaterina Komendantskaya, W. Kokke, Daniel Kienitz
In this invited talk, we discuss state of the art in neural network verification. We propose the term continuous verification to characterise the family of methods that explore continuous nature of machine learning algorithms. We argue that methods of continuous verification must rely on robust programming language infrastructure (refinement types, automated proving, type-driven program synthesis), which provides a major opportunity for the declarative programming language community. Keywords: Neural Networks, Verification, AI.
{"title":"Continuous Verification of Machine Learning: a Declarative Programming Approach","authors":"Ekaterina Komendantskaya, W. Kokke, Daniel Kienitz","doi":"10.1145/3414080.3414081","DOIUrl":"https://doi.org/10.1145/3414080.3414081","url":null,"abstract":"In this invited talk, we discuss state of the art in neural network verification. We propose the term continuous verification to characterise the family of methods that explore continuous nature of machine learning algorithms. We argue that methods of continuous verification must rely on robust programming language infrastructure (refinement types, automated proving, type-driven program synthesis), which provides a major opportunity for the declarative programming language community. Keywords: Neural Networks, Verification, AI.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123291453","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}
We present a new approach based on spatial reasoning in Answer Set Programming (ASP), and a prototype software tool, for automatically evaluating construction safety compliance of real-world Building Information Models (BIM) that have both a geometric component and temporal component in the form of a construction plan and schedule (4D BIM). In the 4D BIM domain, geometries of building objects are large and complex making it highly impractical to represent geometries as ASP facts, unoptimised spatial reasoning can be prohibitively slow, and rounding errors in floating point arithmetic often result in logical contradictions. Our novel framework addresses these challenges by integrating a specialised geometry database, built-in spatial optimisations, and support for real arithmetic solving. We empirically evaluate our prototype software tool on two large 4D BIM models from real buildings to demonstrate the practicality and scalability of our new framework to real-world workplace hazard prevention tasks in construction safety-in-design analysis.
{"title":"Non-monotonic Spatial Reasoning for Safety Analysis in Construction","authors":"Beidi Li, J. Teizer, C. Schultz","doi":"10.1145/3414080.3414096","DOIUrl":"https://doi.org/10.1145/3414080.3414096","url":null,"abstract":"We present a new approach based on spatial reasoning in Answer Set Programming (ASP), and a prototype software tool, for automatically evaluating construction safety compliance of real-world Building Information Models (BIM) that have both a geometric component and temporal component in the form of a construction plan and schedule (4D BIM). In the 4D BIM domain, geometries of building objects are large and complex making it highly impractical to represent geometries as ASP facts, unoptimised spatial reasoning can be prohibitively slow, and rounding errors in floating point arithmetic often result in logical contradictions. Our novel framework addresses these challenges by integrating a specialised geometry database, built-in spatial optimisations, and support for real arithmetic solving. We empirically evaluate our prototype software tool on two large 4D BIM models from real buildings to demonstrate the practicality and scalability of our new framework to real-world workplace hazard prevention tasks in construction safety-in-design analysis.","PeriodicalId":328721,"journal":{"name":"Proceedings of the 22nd International Symposium on Principles and Practice of Declarative Programming","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2020-09-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126206946","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}
京公网安备 11010802042870号
京ICP备2023020795号-1
扫码关注我们
求助内容：
应助结果提醒方式：