Simple precedence grammar
A simple precedence grammar is a context-free formal grammar that can be parsed with a simple precedence parser.[1] The concept was first created in 1964 by Claude Pair[2], and was later rediscovered, from ideas due to Robert Floyd, by Niklaus Wirth and Helmut Weber who published a paper, entitled EULER: a generalization of ALGOL, and its formal definition, published in 1966 in the Communications of the ACM.[3]
Formal definition
G = (N, Σ, P, S) is a simple precedence grammar if all the production rules in P comply with the following constraints:
- There are no erasing rules (ε-productions)
- There are no useless rules (unreachable symbols or unproductive rules)
- For each pair of symbols X, Y (X, Y (N ∪ Σ)) there is only one Wirth–Weber precedence relation.
- G is uniquely inversible
Examples
- precedence table
Notes
- The Theory of Parsing, Translation, and Compiling: Compiling, Alfred V. Aho, Jeffrey D. Ullman, Prentice–Hall, 1972.
- Claude Pair (1964). "Arbres, piles et compilation". Revue française de traitement de l'information., in English Trees, stacks and compiling
- Machines, Languages, and Computation, Prentice–Hall, 1978, ISBN 9780135422588,
Wirth and Weber [1966] generalized Floyd's precedence grammars, obtaining the simple precedence grammars.
gollark: I would start by establishing a numbering/encoding system by sending Fibonacci or whatever, then defining (through examples, probably) arithmetic operations, and then... it might be hard to relate physical information actually, hm.
gollark: It's pictographic, except bad.
gollark: I would probably *not* do it this way, but it's a start.
gollark: Presumably, an entire civilization working on it might come up with some sensible interpretations.
gollark: https://en.wikipedia.org/wiki/Arecibo_message
References
- Alfred V. Aho, Jeffrey D. Ullman (1977). Principles of Compiler Design. 1st Edition. Addison–Wesley.
- William A. Barrett, John D. Couch (1979). Compiler construction: Theory and Practice. Science Research Associate.
- Jean-Paul Tremblay, P. G. Sorenson (1985). The Theory and Practice of Compiler Writing. McGraw–Hill.
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