{"title":"Compositional higher-order model checking via ω-regular games over Böhm trees","authors":"Takeshi Tsukada, C. Ong","doi":"10.1145/2603088.2603133","DOIUrl":null,"url":null,"abstract":"We introduce type-checking games, which are ω-regular games over Böhm trees, determined by a type of the Kobayashi-Ong intersection type system. These games are a higher-type extension of parity games over trees, determined by an alternating parity tree automaton. However, in contrast to these games over trees, the \"game boards\" of our type-checking games are composable, using the composition of Böhm trees. Moreover the winner (and winning strategies) of a composite game is completely determined by the respective winners (and winning strategies) of the component games. To our knowledge, type-checking games give the first compositional analysis of higher-order model checking, or the model checking of trees generated by recursion schemes. We study a higher-type analogue of higher-order model checking, namely, the problem to decide the winner of a type-checking game over the Böhm tree generated by an arbitrary λY-term. We introduce a new type-assignment system and use it to prove that the problem is decidable. On the semantic side, we develop a novel (two-level) arena game model for type-checking games, which is a cartesian closed category equipped with parametric monad and comonad that themselves form a parametrised adjunction.","PeriodicalId":20649,"journal":{"name":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2014-07-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"29","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Proceedings of the Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1145/2603088.2603133","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 29

Abstract

We introduce type-checking games, which are ω-regular games over Böhm trees, determined by a type of the Kobayashi-Ong intersection type system. These games are a higher-type extension of parity games over trees, determined by an alternating parity tree automaton. However, in contrast to these games over trees, the "game boards" of our type-checking games are composable, using the composition of Böhm trees. Moreover the winner (and winning strategies) of a composite game is completely determined by the respective winners (and winning strategies) of the component games. To our knowledge, type-checking games give the first compositional analysis of higher-order model checking, or the model checking of trees generated by recursion schemes. We study a higher-type analogue of higher-order model checking, namely, the problem to decide the winner of a type-checking game over the Böhm tree generated by an arbitrary λY-term. We introduce a new type-assignment system and use it to prove that the problem is decidable. On the semantic side, we develop a novel (two-level) arena game model for type-checking games, which is a cartesian closed category equipped with parametric monad and comonad that themselves form a parametrised adjunction.
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通过Böhm树上的ω-正则博弈来检查合成高阶模型
我们引入了类型检查博弈,它是Böhm树上的ω-规则博弈,由Kobayashi-Ong交集类型系统的一种类型确定。这些游戏是基于树的奇偶性游戏的高级扩展,由交替奇偶性树自动机决定。然而,与这些基于树的游戏不同,我们的类型检查游戏的“游戏板”是可组合的,使用Böhm树的组合。此外,复合游戏的赢家(和获胜策略)完全由组件游戏的各自赢家(和获胜策略)决定。据我们所知,类型检查游戏给出了高阶模型检查的第一个组成分析,或者递归方案生成的树的模型检查。我们研究了一个高阶模型检验的高类型类比,即在由任意λ y项生成的Böhm树上确定类型检验博弈赢家的问题。我们引入了一个新的类型分配系统,并用它来证明问题是可决定的。在语义方面,我们为类型检查游戏开发了一个新的(两级)竞技场游戏模型,这是一个笛卡儿封闭类别,配备了参数单子和common,它们本身形成了参数化的附加。
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