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Inductive-Data-Type Systems
, 2002
"... In a previous work ("Abstract Data Type Systems", TCS 173(2), 1997), the leI two authors presented a combined lmbined made of a (strongl normal3zG9 alrmal rewrite system and a typed #-calA#Ik enriched by pattern-matching definitions folnitio a certain format,calat the "General Schem ..."
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Cited by 821 (23 self)
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;General Schema", whichgeneral39I theusual recursor definitions fornatural numbers and simil9 "basic inductive types". This combined lmbined was shown to bestrongl normalIk39f The purpose of this paper is toreformul33 and extend theGeneral Schema in order to make it easil extensibl3 to capture a
The ordinal numbers
- Journal of Formalized Mathematics
, 1989
"... Summary. We present the choice function rule in the beginning of the article. In the main part of the article we formalize the base of cardinal theory. In the first section we introduce the concept of cardinal numbers and order relations between them. We present here Cantor-Bernstein theorem and oth ..."
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Cited by 731 (68 self)
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and other properties of order relation of cardinals. In the second section we show that every set has cardinal number equipotence to it. We introduce notion of alephs and we deal with the concept of finite set. At the end of the article we show two schemes of cardinal induction. Some definitions are based
Learning Stochastic Logic Programs
, 2000
"... Stochastic Logic Programs (SLPs) have been shown to be a generalisation of Hidden Markov Models (HMMs), stochastic context-free grammars, and directed Bayes' nets. A stochastic logic program consists of a set of labelled clauses p:C where p is in the interval [0,1] and C is a first-order r ..."
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Cited by 1194 (81 self)
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-order range-restricted definite clause. This paper summarises the syntax, distributional semantics and proof techniques for SLPs and then discusses how a standard Inductive Logic Programming (ILP) system, Progol, has been modied to support learning of SLPs. The resulting system 1) nds an SLP with uniform
PolySet Theory
- http://www.rbjones.com/rbjpub/pp/doc/t020.pdf. p011.tex; 25/01/2010; 13:13; p.12 13
"... This document is concerned with the specification of an interpretation of the first order language of set theory. The purpose of this is to provide an ontological basis for foundation systems suitable for the formal derivation of mathematics. The ontology is to include the pure well-founded sets of ..."
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Cited by 259 (2 self)
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of rank up to some arbitrary large cardinal together with the graphs of the polymorphic functions definable mathematical concepts. The interpretation is constructed by defining “names ” or “representatives ” for the sets in the domain of discourse by transfinite inductive definition in the context of a
PolyP - a polytypic programming language extension
- POPL '97: The 24th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
, 1997
"... Many functions have to be written over and over again for different datatypes, either because datatypes change during the development of programs, or because functions with similar functionality are needed on different datatypes. Examples of such functions are pretty printers, debuggers, equality fu ..."
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Cited by 188 (32 self)
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functions, unifiers, pattern matchers, rewriting functions, etc. Such functions are called polytypic functions. A polytypic function is a function that is defined by induction on the structure of user-defined datatypes. This paper extends a functional language (a subset of Haskell) with a construct
Functional interpretation and inductive definitions
- Journal of Symbolic Logic
"... Abstract. Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees. 1. ..."
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Cited by 7 (3 self)
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Abstract. Extending Gödel’s Dialectica interpretation, we provide a functional interpretation of classical theories of positive arithmetic inductive definitions, reducing them to theories of finite-type functionals defined using transfinite recursion on well-founded trees. 1.
Inductive Families
- Formal Aspects of Computing
, 1997
"... A general formulation of inductive and recursive definitions in Martin-Lof's type theory is presented. It extends Backhouse's `Do-It-Yourself Type Theory' to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets ar ..."
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Cited by 77 (13 self)
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A general formulation of inductive and recursive definitions in Martin-Lof's type theory is presented. It extends Backhouse's `Do-It-Yourself Type Theory' to include inductive definitions of families of sets and definitions of functions by recursion on the way elements of such sets
Sparse Permutation Invariant Covariance Estimation
- Electronic Journal of Statistics
, 2008
"... The paper proposes a method for constructing a sparse estimator for the inverse covariance (concentration) matrix in high-dimensional settings. The estimator uses a penalized normal likelihood approach and forces sparsity by using a lasso-type penalty. We establish a rate of con-vergence in the Fro ..."
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Cited by 164 (8 self)
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to be positive definite, but we avoid having to use semi-definite programming by re-parameterizing the objective function
Multifractional Brownian motion: definition and preliminary results
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, 1995
"... We generalize the definition of the fractional Brownian motion of exponent H to the case where H is no longer a constant, but a function of the time index of the process. This allows us to model non stationary continuous processes, and we show that H(t) and 2 \Gamma H(t) are indeed respectively t ..."
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Cited by 102 (4 self)
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We generalize the definition of the fractional Brownian motion of exponent H to the case where H is no longer a constant, but a function of the time index of the process. This allows us to model non stationary continuous processes, and we show that H(t) and 2 \Gamma H(t) are indeed respectively
A General Formulation of Simultaneous Inductive-Recursive Definitions in Type Theory
- Journal of Symbolic Logic
, 1998
"... The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löf's universe à la Tarski. A set U0 of codes for small sets is generated inductively at the same time as a function T0 , which maps a code to the corresponding small set, is defined by re ..."
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Cited by 77 (9 self)
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The first example of a simultaneous inductive-recursive definition in intuitionistic type theory is Martin-Löf's universe à la Tarski. A set U0 of codes for small sets is generated inductively at the same time as a function T0 , which maps a code to the corresponding small set, is defined
Results 1 - 10
of
1,939