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Typedirected partial evaluation
 Proceedings of the TwentyThird Annual ACM Symposium on Principles of Programming Languages
, 1996
"... Abstract. Typedirected partial evaluation stems from the residualization of arbitrary static values in dynamic contexts, given their type. Its algorithm coincides with the one for coercing asubtype value into a supertype value, which itself coincides with the one of normalization in thecalculus. T ..."
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Cited by 219 (38 self)
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Abstract. Typedirected partial evaluation stems from the residualization of arbitrary static values in dynamic contexts, given their type. Its algorithm coincides with the one for coercing asubtype value into a supertype value, which itself coincides with the one of normalization in thecalculus. Typedirected partial evaluation is thus used to specialize compiled, closed programs, given their type. Since Similix, letinsertion is a cornerstone of partial evaluators for callbyvalue procedural programs with computational e ects. It prevents the duplication of residual computations, and more generally maintains the order of dynamic side e ects in residual programs. This article describes the extension of typedirected partial evaluation to insert residual let expressions. This extension requires the userto annotate arrowtypes with e ect information. It is achieved by delimiting and abstracting control, comparably to continuationbased specialization in direct style. It enables typedirected partial evaluation of e ectful programs (e.g.,ade nitional lambdainterpreter for an imperative language) that are in direct style. The residual programs are in Anormal form. 1
Firstclass phantom types
, 2003
"... Classical phantom types are datatypes in which type constraints are expressed using type variables that do not appear in the datatype cases themselves. They can be used to embed typed languages into Haskell or ML. However, while such encodings guarantee that only wellformed data can be constructed, ..."
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Cited by 112 (2 self)
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Classical phantom types are datatypes in which type constraints are expressed using type variables that do not appear in the datatype cases themselves. They can be used to embed typed languages into Haskell or ML. However, while such encodings guarantee that only wellformed data can be constructed, they do not permit typesafe deconstruction without additional tagging and runtime checks. We introduce firstclass phantom types, which make such constraints explicit via type equations. Examples of firstclass phantom types include typed type representations and typed higherorder abstract syntax trees. These types can be used to support typed generic functions, dynamic typing, and staged compilation in higherorder, statically typed languages such as Haskell or Standard ML. In our system, type constraints can be equations between type constructors as well as type functions of higherorder kinds. We prove type soundness and decidability for a Haskelllike language extended by firstclass phantom types. 1
A theory of overloading
 ACM Transactions on Programming Languages and Systems (TOPLAS
, 2002
"... Abstract We introduce a novel approach for debugging illtyped programs in the Hindley/Milner system. We map the typing problem for a program to a system of constraints each attached to program code that generates the constraints. We use reasoning about constraint satisfiability and implication to f ..."
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Cited by 64 (21 self)
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Abstract We introduce a novel approach for debugging illtyped programs in the Hindley/Milner system. We map the typing problem for a program to a system of constraints each attached to program code that generates the constraints. We use reasoning about constraint satisfiability and implication to find minimal justifications of type errors, and to explain unexpected types that arise. Through an interactive process akin to declarative debugging, a user can track down exactly where a type error occurs. We are able to capture various extensions of the Hindley/Milner system such as type annotations and Haskellstyle type class overloading. The approach has been implemented as part of the Chameleon system.
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, ..."
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Cited by 62 (23 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.
Typing dynamic typing
 ICFP ’02: Proceedings of the 7th ACM SIGPLAN International Conference on Functional Programming
, 2002
"... Even when programming in a statically typed language we every now and then encounter statically untypable values; such values result from interpreting values or from communicating with the outside world. To cope with this problem most languages include some form of dynamic types. It may be that the ..."
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Cited by 58 (2 self)
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Even when programming in a statically typed language we every now and then encounter statically untypable values; such values result from interpreting values or from communicating with the outside world. To cope with this problem most languages include some form of dynamic types. It may be that the core language has been explicitly extended with such a type, or that one is allowed to live dangerously by using functions like unsafeCoerce. We show how, by a careful use of existentially and universally quantified types, one may achieve the same effect, without extending the language with new or unsafe features. The techniques explained are universally applicable, provided the core language is expressive enough; this is the case for the common implementations of Haskell. The techniques are used in the description of a type checking compiler that, starting from an expression term, constructs a typed function representing the semantics of that expression. In this function the overhead associated with the type checking is only once being paid for; in this sense we have thus achieved static type checking.
Finally Tagless, Partially Evaluated  Tagless Staged Interpreters for Simpler Typed Languages
 UNDER CONSIDERATION FOR PUBLICATION IN J. FUNCTIONAL PROGRAMMING
"... We have built the first family of tagless interpretations for a higherorder 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 typepreserving interpretations include an ..."
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We have built the first family of tagless interpretations for a higherorder 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 typepreserving interpretations include an evaluator, a compiler (or staged evaluator), a partial evaluator, and callbyname and callbyvalue CPS transformers. Our principal technique is to encode de Bruijn or higherorder 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 λcalculus. 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 higherkinded types.
Fully Reflexive Intensional Type Analysis
 In Fifth ACM SIGPLAN International Conference on Functional Programming
, 2000
"... Compilers for polymorphic languages can use runtime type inspection to support advanced implementation techniques such as tagless garbage collection, polymorphic marshalling, and flattened data structures. Intensional type analysis is a typetheoretic framework for expressing and certifying such typ ..."
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Cited by 39 (5 self)
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Compilers for polymorphic languages can use runtime type inspection to support advanced implementation techniques such as tagless garbage collection, polymorphic marshalling, and flattened data structures. Intensional type analysis is a typetheoretic framework for expressing and certifying such typeanalyzing computations. Unfortunately, existing approaches to intensional analysis do not work well on types with universal, existential, or fixpoint quantifiers. This makes it impossible to code applications such as garbage collection, persistence, or marshalling which must be able to examine the type of any runtime value. We present a typed intermediate language that supports fully reflexive intensional type analysis. By fully reflexive, we mean that typeanalyzing operations are applicable to the type of any runtime value in the language. In particular, we provide both typelevel and termlevel constructs for analyzing quantified types. Our system supports structural induction on quant...
An Implementation of Session Types
 In PADL, volume 3057 of LNCS
, 2004
"... A session type is an abstraction of a set of sequences of heterogeneous values sent and received over a communication channel. Session types can be used for specifying streambased Internet protocols. ..."
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Cited by 34 (0 self)
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A session type is an abstraction of a set of sequences of heterogeneous values sent and received over a communication channel. Session types can be used for specifying streambased Internet protocols.
A Semantic Account of TypeDirected Partial Evaluation
 In Gopalan Nadathur, editor, International Conference on Principles and Practice of Declarative Programming, number 1702 in Lecture
, 1999
"... We formally characterize partial evaluation of functional programs as a normalization problem in an equational theory, and derive a typebased normalizationbyevaluation algorithm for computing normal forms in this setting. We then establish the correctness of this algorithm using a semantic ar ..."
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Cited by 27 (2 self)
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We formally characterize partial evaluation of functional programs as a normalization problem in an equational theory, and derive a typebased normalizationbyevaluation algorithm for computing normal forms in this setting. We then establish the correctness of this algorithm using a semantic argument based on Kripke logical relations. For simplicity, the results are stated for a nonstrict, purely functional language; but the methods are directly applicable to stating and proving correctness of typedirected partial evaluation in MLlike languages as well.
TypeCase: A Design Pattern for TypeIndexed Functions
, 2005
"... A typeindexed function is a function that is defined for each member of some family of types. Haskell's type class mechanism provides collections of open typeindexed functions, in which the indexing family can be extended by defining a new type class instance but the collection of functions i ..."
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Cited by 26 (12 self)
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A typeindexed function is a function that is defined for each member of some family of types. Haskell's type class mechanism provides collections of open typeindexed functions, in which the indexing family can be extended by defining a new type class instance but the collection of functions is fixed. The purpose of this paper is to present TypeCase: a design pattern that allows the definition of closed typeindexed functions, in which the index family is fixed but the collection of functions is extensible. It is inspired by Cheney and Hinze's work on lightweight approaches to generic programming. We generalise their techniques as a design pattern. Furthermore, we show that typeindexed functions with typeindexed types, and consequently generic functions with generic types, can also be encoded in a lightweight manner, thereby overcoming one of the main limitations of the lightweight approaches.