II. Notes on Data Structuring * - Cornell University
II. Notes on Data Structuring * - Cornell University
II. Notes on Data Structuring * - Cornell University
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Abbreviati<strong>on</strong>s'<br />
NOTES ON DATA STRUCTURING 169<br />
(4) x.sl" = xl stands for x'= T(xl, x.s2 ..... x.s,)<br />
x.s~" = x~ ,, ,, x" = r(x.s,, x~, . . ., x.s,)<br />
. . . ° .<br />
X.S n" = x n . . . . X" = T(x.sl, x.s2 .... , xn).<br />
(5) If x is a T then<br />
with x do S or with x take S stands for<br />
S1,$2, ...,Sn<br />
S X. S1,X. S 2 , . . . , X . Sn<br />
which means that each of the subscripts of S replaces all free occurrences<br />
of the corresp<strong>on</strong>ding superscript in S.<br />
(6) (xl, x z, ..., x,) stands for T(xl, x2 ..... x,) in those c<strong>on</strong>texts where<br />
an expressi<strong>on</strong> of type T is expected.<br />
The following axiom applies if the Cartesian product type is to be regarded<br />
as ordered"<br />
(7) x
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