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Representing Nested Inductive Types Using Wtypes
"... We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive ..."
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Cited by 8 (4 self)
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We show that strictly positive inductive types, constructed from polynomial functors, constant exponentiation and arbitrarily nested inductive
ControlFlow Analysis of HigherOrder Languages
, 1991
"... representing the official policies, either expressed or implied, of ONR or the U.S. Government. Keywords: dataflow analysis, Scheme, LISP, ML, CPS, type recovery, higherorder functions, functional programming, optimising compilers, denotational semantics, nonstandard Programs written in powerful, ..."
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Cited by 365 (10 self)
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at compile time. I give examples of how this information can be used to perform several dataflow analysis optimisations, including copy propagation, inductionvariable elimination, uselessvariable elimination, and type recovery. The analysis is defined in terms of a nonstandard semantic interpretation
The type theoretic interpretation of Constructive Set Theory: inductive definitions
 Logic, Methodology and Philosophy of Science VII
, 1986
"... Abstract. We present a generalisation of the typetheoretic interpretation of constructive set theory into MartinLöf type theory. The original interpretation treated logic in MartinLöf type theory via the propositionsastypes interpretation. The generalisation involves replacing MartinLöf type ..."
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Cited by 148 (9 self)
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as types, and restricted formulas as small types. By a small type we mean here a type represented by an element of the type universe that is part of the type theory in which CZF is interpreted. The propositionsastypes representation of logic is used in proving the validity of three schemes of CZF, namely
Inductive Definitions in the System Coq Rules and Properties
, 1992
"... In the pure Calculus of Constructions, it is possible to represent data structures and predicates using higherorder quantification. However, this representation is not satisfactory, from the point of view of both the efficiency of the underlying programs and the power of the logical system. For ..."
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Cited by 191 (2 self)
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In the pure Calculus of Constructions, it is possible to represent data structures and predicates using higherorder quantification. However, this representation is not satisfactory, from the point of view of both the efficiency of the underlying programs and the power of the logical system
Containers  Constructing Strictly Positive Types
, 2004
"... ... with disjoint coproducts and initial algebras of container functors (the categorical analogue of Wtypes) — and then establish that nested strictly positive inductive and coinductive types, which we call strictly positive types, exist in any MartinLöf category. Central to our development are t ..."
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Cited by 83 (28 self)
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... with disjoint coproducts and initial algebras of container functors (the categorical analogue of Wtypes) — and then establish that nested strictly positive inductive and coinductive types, which we call strictly positive types, exist in any MartinLöf category. Central to our development
Inductive Types and Exact Completion
 Ann. Pure Appl. Logic
, 2002
"... Using the theory of exact completions, we show that a specific class of pretopoi, consisting of what we might call "realizability pretopoi", can act as categorical models of certain predicative type theories, including MartinLof type theory. Our main theoretical instrument for doing so is ..."
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Cited by 9 (8 self)
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is a categorical notion, the notion of weak Wtypes, an "intensional" analogue of the "extensional " notion of Wtypes introduced in an article by Moerdijk and Palmgren ([6]). 1
NESL: A nested dataparallel language (version 2.6
, 1993
"... The views and conclusions contained in this document are those of the authors and should not be interpreted as necessarily representing the official policies or endorsements, either expressed or implied, of Wright Laboratory or the U. S. Government. Keywords: Dataparallel, parallel algorithms, supe ..."
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Cited by 112 (8 self)
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, supercomputers, nested parallelism, This report describes Nesl, a stronglytyped, applicative, dataparallel language. Nesl is intended to be used as a portable interface for programming a variety of parallel and vector computers, and as a basis for teaching parallel algorithms. Parallelism is supplied through a
Visibility Culling Using Hierarchical Occlusion Maps
 In Proc. of ACM SIGGRAPH
, 1997
"... : We present hierarchical occlusion maps (HOM) for visibility culling on complex models with high depth complexity. The culling algorithm uses an object space bounding volume hierarchy and a hierarchy of image space occlusion maps. Occlusion maps represent the aggregate of projections of the occlude ..."
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Cited by 124 (8 self)
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: We present hierarchical occlusion maps (HOM) for visibility culling on complex models with high depth complexity. The culling algorithm uses an object space bounding volume hierarchy and a hierarchy of image space occlusion maps. Occlusion maps represent the aggregate of projections
Representing Inductively Defined Sets by Wellorderings in MartinLöf's Type Theory
, 1996
"... We prove that every strictly positive endofunctor on the category of sets generated by MartinLof's extensional type theory has an initial algebra. This representation of inductively defined sets uses essentially the wellorderings introduced by MartinLof in "Constructive Mathematics and C ..."
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Cited by 16 (0 self)
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We prove that every strictly positive endofunctor on the category of sets generated by MartinLof's extensional type theory has an initial algebra. This representation of inductively defined sets uses essentially the wellorderings introduced by MartinLof in "Constructive Mathematics
Inductive and Coinductive types with Iteration and Recursion
 Proceedings of the 1992 Workshop on Types for Proofs and Programs, Bastad
, 1992
"... We study (extensions of) simply and polymorphically typed lambda calculus from a point of view of how iterative and recursive functions on inductive types are represented. The inductive types can usually be understood as initial algebras in a certain category and then recursion can be defined in ter ..."
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Cited by 59 (1 self)
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We study (extensions of) simply and polymorphically typed lambda calculus from a point of view of how iterative and recursive functions on inductive types are represented. The inductive types can usually be understood as initial algebras in a certain category and then recursion can be defined
Results 1  10
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