Types for Proofs and Programs最新文献_第2页

A Formal Study of Boolean Games with Random Formulas as Payoff Functions 以随机公式作为支付函数的布尔博弈的形式化研究

Types for Proofs and Programs Pub Date : 2018-10-24 DOI: 10.4230/LIPIcs.TYPES.2016.14

Érik Martin-Dorel, S. Soloviev

引用次数: 5

Realizability at Work: Separating Two Constructive Notions of Finiteness 工作中的可实现性:分离两个建设性的有限性概念

Types for Proofs and Programs Pub Date : 2018-10-24 DOI: 10.4230/LIPIcs.TYPES.2016.6

M. Bezem, T. Coquand, Keiko Nakata, Erik Parmann

引用次数: 0

Semantic subtyping for non-strict languages 非严格语言的语义子类型

Types for Proofs and Programs Pub Date : 2018-10-12 DOI: 10.4230/LIPIcs.TYPES.2018.4

T. Petrucciani, Giuseppe Castagna, D. Ancona, E. Zucca

引用次数: 3

Cubical Assemblies, a Univalent and Impredicative Universe and a Failure of Propositional Resizing 立方体集合，一个单值和意指的全域以及命题大小调整的失败

Types for Proofs and Programs Pub Date : 2018-03-18 DOI: 10.4230/LIPIcs.TYPES.2018.7

Taichi Uemura

引用次数: 11

Design and Implementation of the Andromeda Proof Assistant 仙女座病毒验证助手的设计与实现

Types for Proofs and Programs Pub Date : 2018-02-17 DOI: 10.4230/LIPIcs.TYPES.2016.5

Andrej Bauer, Gaëtan Gilbert, Philipp G. Haselwarter, Matija Pretnar, Christopher A. Stone

{"title":"Design and Implementation of the Andromeda Proof Assistant","authors":"Andrej Bauer, Gaëtan Gilbert, Philipp G. Haselwarter, Matija Pretnar, Christopher A. Stone","doi":"10.4230/LIPIcs.TYPES.2016.5","DOIUrl":"https://doi.org/10.4230/LIPIcs.TYPES.2016.5","url":null,"abstract":"Andromeda is an LCF-style proof assistant where the user builds derivable judgments by writing code in a meta-level programming language AML. The only trusted component of Andromeda is a minimalist nucleus (an implementation of the inference rules of an object-level type theory), which controls construction and decomposition of type-theoretic judgments. \u0000Since the nucleus does not perform complex tasks like equality checking beyond syntactic equality, this responsibility is delegated to the user, who implements one or more equality checking procedures in the meta-language. The AML interpreter requests witnesses of equality from user code using the mechanism of algebraic operations and handlers. Dynamic checks in the nucleus guarantee that no invalid object-level derivations can be constructed. %even if the AML code (or interpreter) is untrusted. \u0000To demonstrate the flexibility of this system structure, we implemented a nucleus consisting of dependent type theory with equality reflection. Equality reflection provides a very high level of expressiveness, as it allows the user to add new judgmental equalities, but it also destroys desirable meta-theoretic properties of type theory (such as decidability and strong normalization). \u0000The power of effects and handlers in AML is demonstrated by a standard library that provides default algorithms for equality checking, computation of normal forms, and implicit argument filling. Users can extend these new algorithms by providing local \"hints\" or by completely replacing these algorithms for particular developments. We demonstrate the resulting system by showing how to axiomatize and compute with natural numbers, by axiomatizing the untyped $lambda$-calculus, and by implementing a simple automated system for managing a universe of types.","PeriodicalId":131421,"journal":{"name":"Types for Proofs and Programs","volume":"8 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2018-02-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128187158","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: 13

On Equality of Objects in Categories in Constructive Type Theory 论建构型理论中范畴对象的相等性

Types for Proofs and Programs Pub Date : 2017-08-06 DOI: 10.4230/LIPIcs.TYPES.2017.7

Erik Palmgren

引用次数: 8

Efficient Type Checking for Path Polymorphism 路径多态性的有效类型检查

Types for Proofs and Programs Pub Date : 2017-04-28 DOI: 10.4230/LIPIcs.TYPES.2015.6

Juan Edi, Andrés Viso, E. Bonelli

引用次数: 2

A Normalizing Computation Rule for Propositional Extensionality in Higher-Order Minimal Logic 高阶极小逻辑中命题可拓性的一种归一化计算规则

Types for Proofs and Programs Pub Date : 2016-09-30 DOI: 10.4230/LIPIcs.TYPES.2016.3

Robin Adams, M. Bezem, T. Coquand

{"title":"A Normalizing Computation Rule for Propositional Extensionality in Higher-Order Minimal Logic","authors":"Robin Adams, M. Bezem, T. Coquand","doi":"10.4230/LIPIcs.TYPES.2016.3","DOIUrl":"https://doi.org/10.4230/LIPIcs.TYPES.2016.3","url":null,"abstract":"The univalence axiom expresses the principle of extensionality for dependent type theory. However, if we simply add the univalence axiom to type theory, then we lose the property of canonicity - that every closed term computes to a canonical form. A computation becomes `stuck' when it reaches the point that it needs to evaluate a proof term that is an application of the univalence axiom. So we wish to find a way to compute with the univalence axiom. While this problem has been solved with the formulation of cubical type theory, where the computations are expressed using a nominal extension of lambda-calculus, it may be interesting to explore alternative solutions, which do not require such an extension. \u0000As a first step, we present here a system of propositional higher-order minimal logic (PHOML). There are three kinds of typing judgement in PHOML. There are terms which inhabit types, which are the simple types over $Omega$. There are proofs which inhabit propositions, which are the terms of type $Omega$. The canonical propositions are those constructed from $bot$ by implication $supset$. Thirdly, there are paths which inhabit equations $M =_A N$, where $M$ and $N$ are terms of type $A$. There are two ways to prove an equality: reflexivity, and propositional extensionality - logically equivalent propositions are equal. This system allows for some definitional equalities that are not present in cubical type theory, namely that transport along the trivial path is identity. \u0000We present a call-by-name reduction relation for this system, and prove that the system satisfies canonicity: every closed typable term head-reduces to a canonical form. This work has been formalised in Agda.","PeriodicalId":131421,"journal":{"name":"Types for Proofs and Programs","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2016-09-30","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131385768","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

Heterogeneous substitution systems revisited 异相替代系统的重新审视

Types for Proofs and Programs Pub Date : 2016-01-17 DOI: 10.4230/LIPIcs.TYPES.2015.2

Benedikt Ahrens, Ralph Matthes

引用次数: 148

A Type Theory for Probabilistic and Bayesian Reasoning 概率与贝叶斯推理的类型论

Types for Proofs and Programs Pub Date : 2015-11-30 DOI: 10.4230/LIPIcs.TYPES.2015.1

Robin Adams, B. Jacobs

引用次数: 17