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Polytypic programming
, 2000
"... ... PolyP extends a functional language (a subset of Haskell) with a construct for defining polytypic functions by induction on the structure of userdefined datatypes. Programs in the extended language are translated to Haskell. PolyLib contains powerful structured recursion operators like catamorp ..."
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Cited by 93 (12 self)
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... PolyP extends a functional language (a subset of Haskell) with a construct for defining polytypic functions by induction on the structure of userdefined datatypes. Programs in the extended language are translated to Haskell. PolyLib contains powerful structured recursion operators like catamorphisms, maps and traversals, as well as polytypic versions of a number of standard functions from functional programming: sum, length, zip, (==), (6), etc. Both the specification of the library and a PolyP implementation are presented.
Indexed InductionRecursion
, 2001
"... We give two nite axiomatizations of indexed inductiverecursive de nitions in intuitionistic type theory. They extend our previous nite axiomatizations of inductiverecursive de nitions of sets to indexed families of sets and encompass virtually all de nitions of sets which have been used in ..."
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Cited by 44 (16 self)
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We give two nite axiomatizations of indexed inductiverecursive de nitions in intuitionistic type theory. They extend our previous nite axiomatizations of inductiverecursive de nitions of sets to indexed families of sets and encompass virtually all de nitions of sets which have been used in intuitionistic type theory. The more restricted of the two axiomatization arises naturally by considering indexed inductiverecursive de nitions as initial algebras in slice categories, whereas the other admits a more general and convenient form of an introduction rule.
Universes for Generic Programs and Proofs in Dependent Type Theory
 Nordic Journal of Computing
, 2003
"... We show how to write generic programs and proofs in MartinL of type theory. To this end we consider several extensions of MartinL of's logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introduction, el ..."
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Cited by 42 (2 self)
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We show how to write generic programs and proofs in MartinL of type theory. To this end we consider several extensions of MartinL of's logical framework for dependent types. Each extension has a universes of codes (signatures) for inductively defined sets with generic formation, introduction, elimination, and equality rules. These extensions are modeled on Dybjer and Setzer's finitely axiomatized theories of inductiverecursive definitions, which also have a universe of codes for sets, and generic formation, introduction, elimination, and equality rules.
Comparing Libraries for Generic Programming in Haskell
, 2008
"... Datatypegeneric programming is defining functions that depend on the structure, or “shape”, of datatypes. It has been around for more than 10 years, and a lot of progress has been made, in particular in the lazy functional programming language Haskell. There are more than 10 proposals for generic p ..."
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Cited by 20 (10 self)
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Datatypegeneric programming is defining functions that depend on the structure, or “shape”, of datatypes. It has been around for more than 10 years, and a lot of progress has been made, in particular in the lazy functional programming language Haskell. There are more than 10 proposals for generic programming libraries or language extensions for Haskell. To compare and characterize the many generic programming libraries in a typed functional language, we introduce a set of criteria and develop a generic programming benchmark: a set of characteristic examples testing various facets of datatypegeneric programming. We have implemented the benchmark for nine existing Haskell generic programming libraries and present the evaluation of the libraries. The comparison is useful for reaching a common standard for generic programming, but also for a programmer who has to choose a particular approach for datatypegeneric programming.
Functional Generic Programming and Type Theory
, 2002
"... Functional generic programming is an area of research concerning programs parameterized by types. Such parameterization is a powerful method of abstraction that allows the programmer to dene and reuse common patterns of computation that work over many dierent datatypes. ..."
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Cited by 7 (3 self)
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Functional generic programming is an area of research concerning programs parameterized by types. Such parameterization is a powerful method of abstraction that allows the programmer to dene and reuse common patterns of computation that work over many dierent datatypes.
Recursive Families of Inductive Types
, 2000
"... Families of inductive types defined by recursion arise in the formalization of mathematical theories. An example is the family of term algebras on the type of signatures. Type theory does not allow the direct definition of such families. We state the problem abstractly by defining a notion, strong p ..."
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Cited by 1 (1 self)
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Families of inductive types defined by recursion arise in the formalization of mathematical theories. An example is the family of term algebras on the type of signatures. Type theory does not allow the direct definition of such families. We state the problem abstractly by defining a notion, strong positivity, that characterizes these families. Then we investigate its solutions. First, we construct a model using wellorderings. Second, we use an extension...