Logical Relations and Inductive/Coinductive Types
نویسنده
چکیده
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 deenitions can be reduced to positive in some cases.
منابع مشابه
Inductive and Coinductive Session Types in Higher-Order Concurrent Programs
We develop a theory of inductive and coinductive session types in a computational interpretation of linear logic, enabling the representation of potentially infinite interactions in a compositionally sound way that preserves logical soundness, a major stepping stone towards a full dependent type theory for expressing and reasoning about session-based concurrent higher order distributed programs...
متن کاملCall-by-Value and Call-by-Name Dual Calculi with Inductive and Coinductive Types
This paper extends the dual calculus with inductive types and coinductive types. The paper first introduces a non-deterministic dual calculus with inductive and coinductive types. Besides the same duality of the original dual calculus, it has the duality of inductive and coinductive types, that is, the duality of terms and coterms for inductive and coinductive types, and the duality of their re...
متن کاملGlobal semantic typing for inductive and coinductive computing
Inductive and coinductive types are commonly construed as ontological (Church-style) types, denoting canonical data-sets such as natural numbers, lists, and streams. For various purposes, notably the study of programs in the context of global (“uninterpreted”) semantics, it is preferable to think of types as semantical properties (Curry-style). Intrinsic theories were introduced in the late 199...
متن کاملGeneral recursion via coinductive types
A fertile field of research in theoretical computer science investigates the representation of general recursive functions in intensional type theories. Among the most successful approaches are: the use of wellfounded relations, implementation of operational semantics, formalization of domain theory, and inductive definition of domain predicates. Here, a different solution is proposed: exploiti...
متن کاملLinear Abadi and Plotkin Logic
We present a formalization of a version of Abadi and Plotkin’s logic for parametricity for a polymorphic dual intuitionistic/linear type theory with fixed points, and show, following Plotkin’s suggestions, that it can be used to define a wide collection of types, including existential types, inductive types, coinductive types and general recursive types. We show that the recursive types satisfy...
متن کامل