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1,395
Second-Order Matching via Explicit Substitutions ⋆
"... Abstract. Matching is a basic operation extensively used in computation. Second-order matching, in particular, provides an adequate environment for expressing program transformations and pattern recognition for automated deduction. The past few years have established the benefit of using explicit su ..."
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substitutions for theorem proving and higher-order unification. In this paper, we will make use of explicit substitutions to facilitate matching: we develop a second-order matching algorithm via the λσ-style of explicit substitutions. We introduce a convenient notation for matching in the λσ
Third-Order Matching via Explicit Substitutions
"... Abstract. We show how Dowek’s third-order matching decision proce-dure can be adapted to the simply typed λσ-calculus of explicit substitu-tions. The advantages of this approach include being closer to low-level implementations based on the λ-calculus, where substitution has to be made explicit. The ..."
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Abstract. We show how Dowek’s third-order matching decision proce-dure can be adapted to the simply typed λσ-calculus of explicit substitu-tions. The advantages of this approach include being closer to low-level implementations based on the λ-calculus, where substitution has to be made explicit
Topological Simultaneous Localization and Mapping (SLAM): Toward Exact Localization Without Explicit Localization
- IEEE Transactions on Robotics and Automation
, 2001
"... One of the critical components of mapping an unknown environment is the robot's ability to locate itself on a partially explored map. This becomes challenging when the robot experiences positioning error, does not have an external positioning device, nor the luxury of engineered landmarks place ..."
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Cited by 224 (10 self)
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, however, is using the graph structure of the GVG, via a graph matching process, to localize the robot. Experimental results verify the described work. Index Terms---Exploration, localization, mapping, mobile robots, motion planning, tologoical maps, Voronoi diagrams. I.
Higher-order Unification via Explicit Substitutions (Extended Abstract)
- Proceedings of LICS'95
, 1995
"... Higher-order unification is equational unification for βη-conversion. But it is not first-order equational unification, as substitution has to avoid capture. In this paper higher-order unification is reduced to first-order equational unification in a suitable theory: the &lambda ..."
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Cited by 104 (11 self)
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Higher-order unification is equational unification for βη-conversion. But it is not first-order equational unification, as substitution has to avoid capture. In this paper higher-order unification is reduced to first-order equational unification in a suitable theory: the &
Nominal Logic: A First Order Theory of Names and Binding
- Information and Computation
, 2001
"... This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal L ..."
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Cited by 219 (15 self)
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This paper formalises within first-order logic some common practices in computer science to do with representing and reasoning about syntactical structures involving named bound variables (as opposed to nameless terms, explicit substitutions, or higher order abstract syntax). It introduces Nominal
Meshless deformations based on shape matching
- ACM TRANS. GRAPH
, 2005
"... We present a new approach for simulating deformable objects. The underlying model is geometrically motivated. It handles pointbased objects and does not need connectivity information. The approach does not require any pre-processing, is simple to compute, and provides unconditionally stable dynamic ..."
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Cited by 169 (12 self)
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simulations. The main idea of our deformable model is to replace energies by geometric constraints and forces by distances of current positions to goal positions. These goal positions are determined via a generalized shape matching of an undeformed rest state with the current deformed state of the point cloud
Tractable and Intractable Second-Order Matching Problems
- In Proc. 5th Ann. Int. Computing and Combinatorics Conference (COCOON'99), LNCS 1627
, 1999
"... . The second-order matching problem is the problem of determining, for a finite set {#t i , s i # | i # I} of pairs of a second-order term t i and a first-order closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I ..."
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Cited by 11 (2 self)
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. The second-order matching problem is the problem of determining, for a finite set {#t i , s i # | i # I} of pairs of a second-order term t i and a first-order closed term s i , called a matching expression, whether or not there exists a substitution # such that t i # = s i for each i # I
Krylov Projection Methods For Model Reduction
, 1997
"... This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov p ..."
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Cited by 213 (3 self)
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This dissertation focuses on efficiently forming reduced-order models for large, linear dynamic systems. Projections onto unions of Krylov subspaces lead to a class of reducedorder models known as rational interpolants. The cornerstone of this dissertation is a collection of theory relating Krylov
A Markovian Canonical Form of Second-Order Matrix-Exponential Processes
- European Journal of Operations Research
"... Besides the fact that – by definition – matrix-exponential processes (MEPs) are more general than Markovian arrival processes (MAPs), only very little is known about the pre-cise relationship of these processes in matrix notation. For the first time, this paper proves the persistent conjecture that ..."
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Cited by 13 (2 self)
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that – in two dimensions – the respective sets, MAP(2) and MEP(2), are indeed identical with respect to the stationary behavior. Furthermore, this equivalence extends to acyclic MAPs, i.e., AMAP(2), so that AMAP (2) ≡ MAP (2) ≡ MEP (2). For higher orders, these equivalences do not hold. The second-order
A weak calculus with explicit operators for pattern matching and substitution
- In Tison [Tis02
, 2002
"... Abstract. In this paper we propose a Weak Lambda Calculus called λPw having explicit operators for Pattern Matching and Substitution. This formalism is able to specify functions defined by cases via pattern matching constructors as done by most modern functional programming languages such as OCAML. ..."
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Cited by 6 (0 self)
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Abstract. In this paper we propose a Weak Lambda Calculus called λPw having explicit operators for Pattern Matching and Substitution. This formalism is able to specify functions defined by cases via pattern matching constructors as done by most modern functional programming languages such as OCAML
Results 1 - 10
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