Metavariable
In logic, a metavariable (also metalinguistic variable[1] or syntactical variable)[2] is a symbol or symbol string which belongs to a metalanguage and stands for elements of some object language. For instance, in the sentence
- Let A and B be two sentences of a language ℒ
the symbols A and B are part of the metalanguage in which the statement about the object language ℒ is formulated.
schemata and because such "variables" do not actually range over a domain.[3]
: 220
The convention is that a metavariable is to be uniformly substituted with the same instance in all its appearances in a given schema. This is in contrast with
formal grammars where the nonterminals on the right of a production can be substituted by different instances.[4]
Attempts to formalize the notion of metavariable result in some kind of type theory.[5]
See also
Notes
- ^ Hunter 1973, p. 13.
- ^ Shoenfield 2001, p. 7.
- ^ Corcoran 2006, p. 220.
- ^ Tennent 2002, pp. 36–37, 210.
- ISBN 3-540-40801-0. pp. 484–497
References
- Corcoran, J. (2006). "Schemata: the Concept of Schema in the History of Logic" (PDF). Bulletin of Symbolic Logic. 12 (2): 219–240. S2CID 6909703.
- ISBN 9780520023567.
- ISBN 978-1-56881-135-2.
- Tennent, R. D. (2002). Specifying Software: A Hands-On Introduction. Cambridge University Press. ISBN 978-0-521-00401-5.
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