Inductive, coinductive, and pointed types
نویسندگان
چکیده
منابع مشابه
Bootstrapping Inductive and Coinductive Types in HasCASL
We discuss the treatment of initial datatypes and final process types in the wide-spectrum language HasCASL. In particular, we present specifications that illustrate how datatypes and process types arise as bootstrapped concepts using HasCASL’s type class mechanism, and we describe constructions of types of finite and infinite trees that establish the conservativity of datatype and process type...
متن کاملLogical Relations and Inductive/Coinductive Types
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 کاملMixed Inductive/Coinductive Types and Strong Normalization
We introduce the concept of guarded saturated sets, saturated sets of strongly normalizing terms closed under folding of corecursive functions. Using this tool, we can model equi-inductive and equicoinductive types with terminating recursion and corecursion principles. Two type systems are presented: Mendler (co)iteration and sized types. As an application we show that we can directly represent...
متن کاملMonad Translating Inductive and Coinductive Types
We show that the call-by-name monad translation of simply typed lambda calculus extended with sum and product types extends to special and general inductive and coinductive types so that its crucial property of preserving typings and βand commuting reductions is maintained. Specific similar-purpose translations such as CPS translations follow from the general monad translations by specializatio...
متن کاملCPS Translating Inductive and Coinductive Types [Extended Abstract]
We investigate CPS translatability of typed al uli with indu tive and oindu tive types. We show that tenable Plotkin-style all-by-name CPS translations exist for simply typed al uli with a natural number type and stream types and, more generally, with arbitrary positive indu tive and oindu tive types. These translations also work in the presen e of ontrol operators and generalize for dependentl...
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ژورنال
عنوان ژورنال: ACM SIGPLAN Notices
سال: 1996
ISSN: 0362-1340,1558-1160
DOI: 10.1145/232629.232640