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21
Using dependent types to express modular structure
 In Thirteenth ACM Symposium on Principles of Programming Languages
, 1986
"... Several related typed languages for modular programming and data abstraction have been proposed recently, including Pebble, SOL, and ML modules. We review and compare the basic typetheoretic ideas behind these languages and evaluate how they ..."
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Cited by 125 (5 self)
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Several related typed languages for modular programming and data abstraction have been proposed recently, including Pebble, SOL, and ML modules. We review and compare the basic typetheoretic ideas behind these languages and evaluate how they
Polytypic Values Possess Polykinded Types
, 2000
"... A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the socalled kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to ..."
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Cited by 107 (20 self)
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A polytypic value is one that is defined by induction on the structure of types. In Haskell the type structure is described by the socalled kind system, which distinguishes between manifest types like the type of integers and functions on types like the list type constructor. Previous approaches to polytypic programming were restricted in that they only allowed to parameterize values by types of one fixed kind. In this paper we show how to define values that are indexed by types of arbitrary kinds. It appears that these polytypic values possess types that are indexed by kinds. We present several examples that demonstrate that the additional exibility is useful in practice. One paradigmatic example is the mapping function, which describes the functorial action on arrows. A single polytypic definition yields mapping functions for datatypes of arbitrary kinds including first and higherorder functors. Polytypic values enjoy polytypic properties. Using kindindexed logical relations we prove...
TypeIndexed Data Types
 SCIENCE OF COMPUTER PROGRAMMING
, 2004
"... A polytypic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of polytypic functions are the functions that can be derived in Haskell, such as show , read , and ` '. More advanced examples are functions for digital searching, patt ..."
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Cited by 59 (21 self)
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A polytypic function is a function that can be instantiated on many data types to obtain data type specific functionality. Examples of polytypic functions are the functions that can be derived in Haskell, such as show , read , and ` '. More advanced examples are functions for digital searching, pattern matching, unification, rewriting, and structure editing. For each of these problems, we not only have to define polytypic functionality, but also a typeindexed data type: a data type that is constructed in a generic way from an argument data type. For example, in the case of digital searching we have to define a search tree type by induction on the structure of the type of search keys. This paper shows how to define typeindexed data types, discusses several examples of typeindexed data types, and shows how to specialize typeindexed data types. The approach has been implemented in Generic Haskell, a generic programming extension of the functional language Haskell.
Types, Abstraction, and Parametric Polymorphism, Part 2
, 1991
"... The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logicalrelations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesianclosedcategory models of the simply typed lambda calculus and P ..."
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Cited by 53 (1 self)
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The concept of relations over sets is generalized to relations over an arbitrary category, and used to investigate the abstraction (or logicalrelations) theorem, the identity extension lemma, and parametric polymorphism, for Cartesianclosedcategory models of the simply typed lambda calculus and PLcategory models of the polymorphic typed lambda calculus. Treatments of Kripke relations and of complete relations on domains are included.
Domain Theoretic Models Of Polymorphism
, 1989
"... We give an illustration of a construction useful in producing and describing models of Girard and Reynolds' polymorphic calculus. The key unifying ideas are that of a Grothendieck fibration and the category of continuous sections associated with it, constructions used in indexed category theory; th ..."
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Cited by 34 (2 self)
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We give an illustration of a construction useful in producing and describing models of Girard and Reynolds' polymorphic calculus. The key unifying ideas are that of a Grothendieck fibration and the category of continuous sections associated with it, constructions used in indexed category theory; the universal types of the calculus are interpreted as the category of continuous sections of the fibration. As a major example a new model for the polymorphic calculus is presented. In it a type is interpreted as a Scott domain. In fact, understanding universal types of the polymorphic calculus as categories of continuous sections appears to be useful generally. For example, the technique also applies to the finitary projection model of Bruce and Longo, and a recent model of Girard. (Indeed the work here was inspired by Girard's and arose through trying to extend the construction of his model to Scott domains.) It is hoped that by pinpointing a key construction this paper will help towards...
SecondOrder Signature: A Tool for Specifying Data Models
 Query Processing, and Optimization. Proc. ACM SIGMOD Conf
, 1993
"... We propose a framework for the specification of extensible database systems. A particular goal is to implement a software component for parsing and rulebased optimization that can be used with widely varying data models and query languages as well as representation and query processing systems. T ..."
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Cited by 29 (19 self)
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We propose a framework for the specification of extensible database systems. A particular goal is to implement a software component for parsing and rulebased optimization that can be used with widely varying data models and query languages as well as representation and query processing systems. The key idea is to use secondorder signature (and algebra), a system of two coupled manysorted signatures, where the toplevel signature offers kinds and type constructors and the bottomlevel signature provides polymorphic operations over the types defined as terms of the top level. Hence the top level can be used to define a data or representation model and the bottom level to describe a query algebra or a query processing algebra. We show the applicability of this framework by examples drawn from relational modeling and query processing.
Reasoning about Continuations with Control Effects
, 1989
"... We present a new static analysis method for firstclass continuations that uses an effect system to classify the control domain behavior of expressions in a typed polymorphic language. We introduce two new control effects, goto and comefrom, that describe the control flow properties of expressions. ..."
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Cited by 25 (4 self)
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We present a new static analysis method for firstclass continuations that uses an effect system to classify the control domain behavior of expressions in a typed polymorphic language. We introduce two new control effects, goto and comefrom, that describe the control flow properties of expressions. An expression that does not haveagoto effect is said to be continuation following because it will always call its passed return continuation. An expression that does not haveacomefrom effect is said to be continuation discarding because it will never preserve its return continuation for later use. Unobservable control effects can be masked by the effect system. Control effect soundness theorems guarantee that the effects computed statically by the effect system are a conservative approximation of the dynamic behavior of an expression. The effect