By M. Laudet (auth.), M. Laudet, D. Lacombe, L. Nolin, M. Schützenberger (eds.)
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Extra resources for Symposium on Automatic Demonstration: Held at Versailles/France, December 1968
T n PAL this can be writ- as follows: (in~ cator) (definition) (identifier) (category) 0 nat := PN type 1 0 real := PN tyDe 2 0 := -- real 5 a := -- real 4 b := PN real == -- nat 5 6 := -- real 7 0 n n x power := PN real 8 n Y := -- real 9 Y d := power(n,y) real 10 Y e := prod(d,y) real 11 Y f := prod(d, d) real 12 g ,= e(d) real 15 Y - 38 - This happens to be a nested book in the sense of 3. S0,but that does not have any consequence for the present discussion. It is also a very simple case in the sense that the categories are all very simple.
1 A line consists of 4 parts: -33 (i) an indicator, (ii) an identifier, (iii) a definition, (iv) a category. 2 In every line the identifier part (ii) is a symbol that has not been used in previous lines. (This stipulation is unusual in every-day mathematics: a symbol like x is used repeatedly in different senses. ) An identifier used as identifier part of a line will be called a pro~er identifier. There is a second kind of identifiers: those that play the rSle of bound variables. Again, in contrast with existing habits we shall use each bound variable only once, and a bound variable has to be different from previously introduced proper identifiers.
By adding new grammar rules without cancelling the old ones. It is hardly necessary to consider such extensions for the present purpose, since it can be expected that the same goal can be reached by means of superimposed languages. W e might think about facilities for easy identification of two things of different categories (see sec. 2), embedding of one category into another, etc. If such matters can be handled satisfactorily, they can be handled by a superimposed language. The only reasons for doing it without such a language ~ay be computer time and memory space.
Symposium on Automatic Demonstration: Held at Versailles/France, December 1968 by M. Laudet (auth.), M. Laudet, D. Lacombe, L. Nolin, M. Schützenberger (eds.)