[TUHS] Array index history

Doug McIlroy doug at cs.dartmouth.edu
Thu Jun 8 12:27:05 AEST 2017

>  Who started this? Why was the change made?

Arrays in Fortran and Algol were indexed from 1 by default, but
Algol (IIRC) generalized that to allow first:last declarations. 
NPL used first,last for the SUBSTR operation. But first,last 
begets off-by-one errors. The successor slice begins at last+1.
The formula for the position of 1-indexed a[i,j] is a mess.
First,length is much cleaner: the successor begins at
first+length. I convinced the committee of that, so when
NPL became PL/I, first,length was the convention. Zero-
indexing is also a clean first,length notation. BCPL,
where a[i] was synonymous with rv(a+i), had it. Dennis, who
knew a good thing when he saw it, took it over. Dijkstra,
too, often inveighed against 1-indexing, and opined that
zero was the true computer-science way. 

1-indexing certainly came into programming languages from
the math tradition for matrix notation. Of course in
math series are often indexed from zero, so one may
pick and choose. Off hand I can only think of one CS
context where 1 comes in handy: heapsort.


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