منابع مشابه
Logical Relations for Monadic Types
ion of the morphism 〈u, v〉 in the subscone from 〈S,m,A〉⊗̃〈S1,m1, A1〉 to 〈S2,m2, A2〉 is then the pair 〈ẽ2 ◦ ũ,Λ(v)〉 given by the diagram: S m // ũ ## Λ(u◦e.1) 4 4 4 4 4 4 4 4 4 4 4 4 4 4 4 |A|
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Software security can be ensured by specifying and verifying security properties of software using formal methods with strong theoretical bases. In particular, programs can be modeled in the framework of lambda-calculi, and interesting properties can be expressed formally by contextual equivalence (a.k.a. observational equivalence). Furthermore, imperative features, which exist in most real-lif...
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datatype, in terms of the existence of a `simulation' relation between the implementations (Mitchell 1991). This principle was extended to encompass all the (possibly impredicative) existential types of the Girard-Reynolds polymorphic lambda calculus by Plotkin and Abadi (1993). Their Theorem 7 shows that the principle gives a necessary and su cient condition for equality at existential type in...
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We investigate a calculus with positive inductive and coin-ductive types , which we call ;; , using logical relations. We show that parametric theories have the strong categorical properties, that the rep-resentable functors and natural transformations have the expected properties. Finally we apply the theory to show that terms of functorial type are almost canonical and that monotone inductive...
متن کاملStep-Indexed Syntactic Logical Relations for Recursive and Quantified Types
We present a proof technique, based on syntactic logical relations, for showing contextual equivalence of expressions in a λ-calculus with recursive types and impredicative universal and existential types. We show that for recursive and polymorphic types, the method is both sound and complete with respect to contextual equivalence, while for existential types, it is sound but incomplete. Our de...
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ژورنال
عنوان ژورنال: Mathematical Structures in Computer Science
سال: 2008
ISSN: 0960-1295,1469-8072
DOI: 10.1017/s0960129508007172