Topic
Generalized algebraic data type
About: Generalized algebraic data type is a research topic. Over the lifetime, 282 publications have been published within this topic receiving 10396 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1996
TL;DR: The language PCF as mentioned in this paper is a model-programming language for lambda xxx with type variables type inference with polymorphic declarations, and it can be seen as a generalization of the notion of simply typed lambda calculus.
Abstract: Part 1 Introduction: model programming languages lambda notation equations, reduction and semantics types and type systems notation and mathematical conventions set-theoretic background syntax and semantics induction. Part 2 The language PCF: syntax of PCF PCF programmes and their semantics PCF reduction and symbolic interpreters PCF programming examples, expressive power and limitations variations and extensions of PCF. Part 3 Universal algebra and algebraic data types: preview of algebraic specification algebras, signatures and terms equations, soundness and completeness homomorphisms and initiality algebraic data types rewrite systems. Part 4 Simply-typed lambda calculus: types terms proof systems Henkin models, soundness and completeness. Part 5 Models of typed lambda calculus: domain-theoretic models and fixed points fixed-point induction computational adequacy and full abstraction recursion-theoretic models partial equivalence relations and recursion. Part 6 Imperative programmes: while programmes operational semantics denotational semantics before-after assertions about while programmes semantics of additional programme constructs. Part 7 Categories and recursive types: Cartesian closed categories Kripke lambda models and functor categories domain models of recursive types. Part 8 Logical relations: introduction to logical relations logical relations over applicative structures proof-theoretic results partial surjections and specific models representation independence generalizations of logical relations. Part 9 Polymorphism and modularity: predicative polymorphic calculus impredicative polymorphism data abstraction and existential types general products, sums and programme modules. Part 10 subtyping and related concepts: simply typed lambda calculus with subtyping records, semantic models of subtyping recursive types and a record model of objects polymorphism with subtype constraints. Part 11 Type inference: introduction to type inference type inference for lambda xxx with type variables type inference with polymorphic declarations.
610 citations
16 Sep 2006
TL;DR: Wobbly types are presented, which express in a declarative way the uncertainty caused by the incremental nature of typical type-inference algorithms.
Abstract: Generalized algebraic data types (GADTs), sometimes known as "guarded recursive data types" or "first-class phantom types", are a simple but powerful generalization of the data types of Haskell and ML. Recent works have given compelling examples of the utility of GADTs, although type inference is known to be difficult. Our contribution is to show how to exploit programmer-supplied type annotations to make the type inference task almost embarrassingly easy. Our main technical innovation is wobbly types, which express in a declarative way the uncertainty caused by the incremental nature of typical type-inference algorithms.
365 citations
15 Jan 2003
TL;DR: The main contribution of the paper lies in the recognition and then the formalization of a programming notion that is of both theoretical interest and practical use.
Abstract: We introduce a notion of guarded recursive (g.r.) datatype constructors, generalizing the notion of recursive datatypes in functional programming languages such as ML and Haskell. We address both theoretical and practical issues resulted from this generalization. On one hand, we design a type system to formalize the notion of g.r. datatype constructors and then prove the soundness of the type system. On the other hand, we present some significant applications (e.g., implementing objects, implementing staged computation, etc.) of g.r. datatype constructors, arguing that g.r. datatype constructors can have far-reaching consequences in programming. The main contribution of the paper lies in the recognition and then the formalization of a programming notion that is of both theoretical interest and practical use.
340 citations
TL;DR: This family of tagless interpretations for a higher-order typed object language in a typed metalanguage (Haskell or ML) that require no dependent types, generalized algebraic data types, or postprocessing to eliminate tags demonstrates again that it is useful to abstract over higher-kinded types.
Abstract: We have built the first family of tagless interpretations for a higher-order typed object language in a typed metalanguage (Haskell or ML) that require no dependent types, generalized algebraic data types, or postprocessing to eliminate tags. The statically type-preserving interpretations include an evaluator, a compiler (or staged evaluator), a partial evaluator, and call-by-name and call-by-value continuation-passing style (CPS) transformers. Our principal technique is to encode de Bruijn or higher-order abstract syntax using combinator functions rather than data constructors. In other words, we represent object terms not in an initial algebra but using the coalgebraic structure of the λ-calculus. Our representation also simulates inductive maps from types to types, which are required for typed partial evaluation and CPS transformations. Our encoding of an object term abstracts uniformly over the family of ways to interpret it, yet statically assures that the interpreters never get stuck. This family of interpreters thus demonstrates again that it is useful to abstract over higher-kinded types.
241 citations
TL;DR: The imtlal algebra approach is adopted as providing an appropriate semantics for spec~ficauons, and the effects of the present concepts and results on the initial algebras are studied.
Abstract: In the framework of a category spec of equational speoficatlons of abstract data types, tmplementations are defined to be certain pairs of morphlsms with a common target Th~s concept covers, among others, arbitrary recurslon schemes for defining the derived operations It is shown that for given single steps of a multilevel tmplementatlon, there is always a multtlevel tmplementatlon composed of these steps, but there ts no effective construction of th~s overall implementauon Some suggestions are gtven for practtcal composition of tmplementat~ons Utdlzmg pushouts Parametric specifications and parameter assignments are defined to be spectal morphlsms in spec, and parameter substitution ~s made precise by means of pushouts Since actual parameters can agam be parametrtc, parameter subsututton can be tterated. Thts tterauon ts shown to be assoctatwe Whtle the subject is being treated on a syntactical level in terms of speclfieauons, the imtlal algebra approach ts adopted as providing an appropriate semantics for spec~ficauons, and the effects of the present concepts and results on the initial algebras are studied
151 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 2 |
| 2019 | 1 |
| 2018 | 2 |
| 2017 | 1 |
| 2016 | 7 |
| 2015 | 7 |