International Conference on Formal Structures for Computation and Deduction最新文献

Cyclic Proofs for Arithmetical Inductive Definitions 算术归纳定义的循环证明

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-06-14 DOI: 10.4230/LIPIcs.FSCD.2023.27

Anupam Das, Lukas Melgaard

引用次数: 0

The Logical Essence of Compiling With Continuations 续编的逻辑本质

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-04-28 DOI: 10.48550/arXiv.2304.14752

J. E. Santo, Filipa Mendes

{"title":"The Logical Essence of Compiling With Continuations","authors":"J. E. Santo, Filipa Mendes","doi":"10.48550/arXiv.2304.14752","DOIUrl":"https://doi.org/10.48550/arXiv.2304.14752","url":null,"abstract":"The essence of compiling with continuations is that conversion to continuation-passing style (CPS) is equivalent to a source language transformation converting to administrative normal form (ANF). Taking as source language Moggi's computational lambda-calculus (lbc), we define an alternative to the CPS-translation with target in the sequent calculus LJQ, named value-filling style (VFS) translation, and making use of the ability of the sequent calculus to represent contexts formally. The VFS-translation requires no type translation: indeed, double negations are introduced only when encoding the VFS target language in the CPS target language. This optional encoding, when composed with the VFS-translation reconstructs the original CPS-translation. Going back to direct style, the\"essence\"of the VFS-translation is that it reveals a new sublanguage of ANF, the value-enclosed style (VES), next to another one, the continuation-enclosing style (CES): such an alternative is due to a dilemma in the syntax of lbc, concerning how to expand the application constructor. In the typed scenario, VES and CES correspond to an alternative between two proof systems for call-by-value, LJQ and natural deduction with generalized applications, confirming proof theory as a foundation for intermediate representations.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"5 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117073881","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}

引用次数: 0

Compositional Confluence Criteria 合成合流标准

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-03-07 DOI: 10.4230/LIPIcs.FSCD.2022.28

Kiraku Shintani, Nao Hirokawa

引用次数: 1

An Analysis of Tennenbaum's Theorem in Constructive Type Theory 建构型理论中的Tennenbaum定理分析

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-02-28 DOI: 10.4230/LIPIcs.FSCD.2022.9

Marc Hermes, Dominik Kirst

{"title":"An Analysis of Tennenbaum's Theorem in Constructive Type Theory","authors":"Marc Hermes, Dominik Kirst","doi":"10.4230/LIPIcs.FSCD.2022.9","DOIUrl":"https://doi.org/10.4230/LIPIcs.FSCD.2022.9","url":null,"abstract":"Tennenbaum's theorem states that the only countable model of Peano arithmetic (PA) with computable arithmetical operations is the standard model of natural numbers. In this paper, we use constructive type theory as a framework to revisit, analyze and generalize this result. The chosen framework allows for a synthetic approach to computability theory, exploiting that, externally, all functions definable in constructive type theory can be shown computable. We then build on this viewpoint and furthermore internalize it by assuming a version of Church's thesis, which expresses that any function on natural numbers is representable by a formula in PA. This assumption provides for a conveniently abstract setup to carry out rigorous computability arguments, even in the theorem's mechanization. Concretely, we constructivize several classical proofs and present one inherently constructive rendering of Tennenbaum's theorem, all following arguments from the literature. Concerning the classical proofs in particular, the constructive setting allows us to highlight differences in their assumptions and conclusions which are not visible classically. All versions are accompanied by a unified mechanization in the Coq proof assistant.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"17 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114739925","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}

引用次数: 4

Rewriting modulo traced comonoid structure 改写模迹共子体结构

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-02-19 DOI: 10.48550/arXiv.2302.09631

D. Ghica, G. Kaye

{"title":"Rewriting modulo traced comonoid structure","authors":"D. Ghica, G. Kaye","doi":"10.48550/arXiv.2302.09631","DOIUrl":"https://doi.org/10.48550/arXiv.2302.09631","url":null,"abstract":"In this paper we adapt previous work on rewriting string diagrams using hypergraphs to the case where the underlying category has a traced comonoid structure, in which wires can be forked and the outputs of a morphism can be connected to its input. Such a structure is particularly interesting because any traced Cartesian (dataflow) category has an underlying traced comonoid structure. We show that certain subclasses of hypergraphs are fully complete for traced comonoid categories: that is to say, every term in such a category has a unique corresponding hypergraph up to isomorphism, and from every hypergraph with the desired properties, a unique term in the category can be retrieved up to the axioms of traced comonoid categories. We also show how the framework of double pushout rewriting (DPO) can be adapted for traced comonoid categories by characterising the valid pushout complements for rewriting in our setting. We conclude by presenting a case study in the form of recent work on an equational theory for sequential circuits: circuits built from primitive logic gates with delay and feedback. The graph rewriting framework allows for the definition of an operational semantics for sequential circuits.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"94 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131395704","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}

引用次数: 2

E-unification for Second-Order Abstract Syntax 二阶抽象句法的e统一

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-02-11 DOI: 10.48550/arXiv.2302.05815

Nikolai Kudasov

引用次数: 0

On the Lattice of Program Metrics 关于程序度量的格

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-02-10 DOI: 10.48550/arXiv.2302.05022

Ugo Dal Lago, Naohiko Hoshino, Paolo Pistone

{"title":"On the Lattice of Program Metrics","authors":"Ugo Dal Lago, Naohiko Hoshino, Paolo Pistone","doi":"10.48550/arXiv.2302.05022","DOIUrl":"https://doi.org/10.48550/arXiv.2302.05022","url":null,"abstract":"In this paper we are concerned with understanding the nature of program metrics for calculi with higher-order types, seen as natural generalizations of program equivalences. Some of the metrics we are interested in are well-known, such as those based on the interpretation of terms in metric spaces and those obtained by generalizing observational equivalence. We also introduce a new one, called the interactive metric, built by applying the well-known Int-Construction to the category of metric complete partial orders. Our aim is then to understand how these metrics relate to each other, i.e., whether and in which cases one such metric refines another, in analogy with corresponding well-studied problems about program equivalences. The results we obtain are twofold. We first show that the metrics of semantic origin, i.e., the denotational and interactive ones, lie emph{in between} the observational and equational metrics and that in some cases, these inclusions are strict. Then, we give a result about the relationship between the denotational and interactive metrics, revealing that the former is less discriminating than the latter. All our results are given for a linear lambda-calculus, and some of them can be generalized to calculi with graded comonads, in the style of Fuzz.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"12 6","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"120911172","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}

引用次数: 1

For the Metatheory of Type Theory, Internal Sconing Is Enough 对于类型理论的元理论来说，内部搜索就足够了

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-02-10 DOI: 10.48550/arXiv.2302.05190

Rafael Bocquet, A. Kaposi, Christian Sattler

引用次数: 3

Strategies as Resource Terms, and their Categorical Semantics 策略作为资源术语及其范畴语义

International Conference on Formal Structures for Computation and Deduction Pub Date : 2023-02-09 DOI: 10.48550/arXiv.2302.04685

Lison Blondeau-Patissier, P. Clairambault, Lionel Vaux Auclair

{"title":"Strategies as Resource Terms, and their Categorical Semantics","authors":"Lison Blondeau-Patissier, P. Clairambault, Lionel Vaux Auclair","doi":"10.48550/arXiv.2302.04685","DOIUrl":"https://doi.org/10.48550/arXiv.2302.04685","url":null,"abstract":"As shown by Tsukada and Ong, normal (extensional) simply-typed resource terms correspond to plays in Hyland-Ong games, quotiented by Melli`es' homotopy equivalence. Though inspiring, their proof is indirect, relying on the injectivity of the relational model w.r.t. both sides of the correspondence - in particular, the dynamics of the resource calculus is taken into account only via the compatibility of the relational model with the composition of normal terms defined by normalization. In the present paper, we revisit and extend these results. Our first contribution is to restate the correspondence by considering causal structures we call augmentations, which are canonical representatives of Hyland-Ong plays up to homotopy. This allows us to give a direct and explicit account of the connection with normal resource terms. As a second contribution, we extend this account to the reduction of resource terms: building on a notion of strategies as weighted sums of augmentations, we provide a denotational model of the resource calculus, invariant under reduction. A key step - and our third contribution - is a categorical model we call a resource category, which is to the resource calculus what differential categories are to the differential {lambda}-calculus.","PeriodicalId":284975,"journal":{"name":"International Conference on Formal Structures for Computation and Deduction","volume":"88 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-02-09","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133249348","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}

引用次数: 0

The Formal Theory of Monads, Univalently 一元的形式理论

International Conference on Formal Structures for Computation and Deduction Pub Date : 2022-12-16 DOI: 10.48550/arXiv.2212.08515

N. V. D. Weide

引用次数: 0