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  1. Frontiers of Computer Science in China
  2. Frontiers of Computer Science in China : Volume 2
  3. Frontiers of Computer Science in China : Volume 2, Issue 1, March 2008
  4. Calculi of meta-variables
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Frontiers of Computer Science in China : Volume 11
Frontiers of Computer Science in China : Volume 10
Frontiers of Computer Science in China : Volume 9
Frontiers of Computer Science in China : Volume 8
Frontiers of Computer Science in China : Volume 7
Frontiers of Computer Science in China : Volume 6
Frontiers of Computer Science in China : Volume 5
Frontiers of Computer Science in China : Volume 4
Frontiers of Computer Science in China : Volume 3
Frontiers of Computer Science in China : Volume 2
Frontiers of Computer Science in China : Volume 2, Issue 4, December 2008
Frontiers of Computer Science in China : Volume 2, Issue 3, September 2008
Frontiers of Computer Science in China : Volume 2, Issue 2, June 2008
Frontiers of Computer Science in China : Volume 2, Issue 1, March 2008
Basic research in computer science and software engineering at SKLCS
Calculi of meta-variables
Human factors in continuous time-concerned cooperative systems represented by NΣ-labeled calculus
Semantics of sub-probabilistic programs
Computational origami environment on the web
On the verification of polynomial system solvers
Fraction-free matrix factors: new forms for LU and QR factors
An extended EM algorithm for subspace clustering
Gibbs artifact reduction for POCS super-resolution image reconstruction
Arnetminer: expertise oriented search using social networks
ID-based deniable ring authentication with constant-size signature
Frontiers of Computer Science in China : Volume 1

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Calculi of meta-variables

Content Provider Springer Nature Link
Author SATO, Masahiko Sakurai, Takafumi Kameyama, Yukiyoshi Igarashi, Atsushi
Copyright Year 2008
Abstract The notion of meta-variable plays a fundamental role when we define formal systems such as logical and computational calculi. Yet it has been usually understood only informally as is seen in most textbooks of logic. Based on our observations of the usages of metavariables in textbooks, we propose two formal systems that have the notion of meta-variable.In both calculi, each variable is given a level (non-negative integer), which classifies variables into object variables (level 0), meta-variables (level 1), metameta-variables (level 2) and so on. Then, simple arity systems are used to exclude meaningless terms like a meta-level function operating on the metameta-level. A main difference of the two calculi lies in the definitions of substitution. The first calculus uses textual substitution, which can often be found in definitions of quantified formulae: when a term is substituted for a meta-variable, free object-level variables in the term may be captured. The second calculus is based on the observation that predicates can be regarded as meta-level functions on object-level terms, hence uses capture-avoiding substitution.We show that both calculi enjoy a number of properties including Church-Rosser and Strong Normalization, which are indispensable when we use them as frameworks to define logical systems.
Starting Page 12
Ending Page 21
Page Count 10
File Format PDF
ISSN 16737350
Journal Frontiers of Computer Science in China
Volume Number 2
Issue Number 1
e-ISSN 16737466
Language English
Publisher SP Higher Education Press
Publisher Date 2008-03-28
Publisher Institution Chinese Universities
Publisher Place Heidelberg
Access Restriction Subscribed
Subject Keyword meta-variable logical framework context λ-calculus Computer Science
Content Type Text
Resource Type Article
Subject Theoretical Computer Science Computer Science
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