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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(5) initial (x~T(d)) = x<br />
(6) x (y z) =(x y) z<br />
(7) T(d). first = d<br />
NOTES ON DATA STRUCTURING<br />
(8) x -~ T( ) = (ff-'T(d)).first = x.first<br />
(9) final (T(d)) = T( )<br />
(10) x ¢ T( ) = final (ff-'T(d))= final (x)-'T(d)<br />
Note:<br />
(11)<br />
(12)<br />
(13)<br />
(14)<br />
(~5)<br />
(I6)<br />
last, initial, first, and final are not defined for T( )<br />
T( ) ends y<br />
x T(d) ends y ~_ y -¢ T( ) & y. last = d & x ends initial (y)<br />
xbeginsT( ) ~x= T( )<br />
x begins y T(d) ~_ x = f--'T(d) v x begins y<br />
length (T()) = 0<br />
length (x-'T(d)) = succ(length (x))<br />
For an ordered sequence type we have'<br />
(17) T( ) ~< y<br />
(18) x< 7"( )=x= r( )<br />
(19) x, y -~ T( ) = (x ~< y _= x. first < y. first v (x. first = y. first<br />
& final (x) ~< final (y)))<br />
Abbreviati<strong>on</strong>s:<br />
(20) x" T(d) means x" = x T(d)<br />
(21) d from x means d: = x.first; x: = final (x)<br />
(22) d back from x means d: = x.last; x: = initial (x)<br />
(23) from x means x: = final (x)<br />
(24) back from x means x:= initial (x)<br />
(25) T(dl, dE .... , d,) stands for<br />
(r( ,r(d.))<br />
(26) [dl, dE, ..., dn] stands for T(dl, d2, ..., dn)<br />
(27) If x = [d~, d2 .... , d~] then<br />
for d in x do S stands for<br />
s~; sL ; . . ; s~.<br />
for d in x take E stands for<br />
[E~, E~,..., e~,]<br />
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