2,223 research outputs found
Homeomorphic Embedding for Online Termination of Symbolic Methods
Well-quasi orders in general, and homeomorphic embedding in particular, have gained popularity to ensure the termination of techniques for program analysis, specialisation, transformation, and verification. In this paper we survey and discuss this use of homeomorphic embedding and clarify the advantages of such an approach over one using well-founded orders. We also discuss various extensions of the homeomorphic embedding relation. We conclude with a study of homeomorphic embedding in the context of metaprogramming, presenting some new (positive and negative) results and open problems
A Theory of Explicit Substitutions with Safe and Full Composition
Many different systems with explicit substitutions have been proposed to
implement a large class of higher-order languages. Motivations and challenges
that guided the development of such calculi in functional frameworks are
surveyed in the first part of this paper. Then, very simple technology in named
variable-style notation is used to establish a theory of explicit substitutions
for the lambda-calculus which enjoys a whole set of useful properties such as
full composition, simulation of one-step beta-reduction, preservation of
beta-strong normalisation, strong normalisation of typed terms and confluence
on metaterms. Normalisation of related calculi is also discussed.Comment: 29 pages Special Issue: Selected Papers of the Conference
"International Colloquium on Automata, Languages and Programming 2008" edited
by Giuseppe Castagna and Igor Walukiewic
Perspectives on neural proof nets
In this paper I will present a novel way of combining proof net proof search
with neural networks. It contrasts with the 'standard' approach which has been
applied to proof search in type-logical grammars in various different forms. In
the standard approach, we first transform words to formulas (supertagging) then
match atomic formulas to obtain a proof. I will introduce an alternative way to
split the task into two: first, we generate the graph structure in a way which
guarantees it corresponds to a lambda-term, then we obtain the detailed
structure using vertex labelling. Vertex labelling is a well-studied task in
graph neural networks, and different ways of implementing graph generation
using neural networks will be explored.Comment: This is an extended version of an invited talk for the workshop
End-to-End Compositional Models of Vector-Based Semantic
Introduction to linear logic and ludics, part II
This paper is the second part of an introduction to linear logic and ludics,
both due to Girard. It is devoted to proof nets, in the limited, yet central,
framework of multiplicative linear logic and to ludics, which has been recently
developped in an aim of further unveiling the fundamental interactive nature of
computation and logic. We hope to offer a few computer science insights into
this new theory
Sequentiality vs. Concurrency in Games and Logic
Connections between the sequentiality/concurrency distinction and the
semantics of proofs are investigated, with particular reference to games and
Linear Logic.Comment: 35 pages, appeared in Mathematical Structures in Computer Scienc
A formal representation of the method of learning
We show how the method of learning in science, education, and mathematics can be represented by a knowledge hypernet and its concept-relationship knowledge structure interpretations. We conclude that the method of learning is invariant over the three fields. The paper is particularly suited for teachers of science, particularly physics, and of mathematics, and in the philosophy of science, but is also relevant for educators at every level of instruction. Those working in the fields of cognitive science and knowledge representation can also benefit from this paper and its main references
Abstract State Machines 1988-1998: Commented ASM Bibliography
An annotated bibliography of papers which deal with or use Abstract State
Machines (ASMs), as of January 1998.Comment: Also maintained as a BibTeX file at http://www.eecs.umich.edu/gasm
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