"prefix point" vs. "postfix point"

[jaakov]

Hallo zusammen,

Let (X,<=) be a poset and f: X -> X.

An x from X is now called
- a "prefix point" if f(x) <= x, and
- a "postfix point" if x <= f(x).
(Of course, there are variants "prefixed point", "prefixpoint",
"pre-fixpoint", "prefix-point", similar for "post...".).

However, in old literature (and seldom now) the names have been swapped:
In such papers and books, an x from X has been called
- a "postfix point" if f(x) <= x, and
- a "prefix point" if x <= f(x).
(With similar combinations of white spaces, hyphens, and "ed".)

Who was the first to create this confusion and why he or she did that?

Thanks in advance,

Jaakov.

[Paul Levy]

Dear Jaakov,
The first usage you mention appeared in Smyth and Plotkin 1982
https://homepages.inf.ed.ac.uk/gdp/publications/Category_Theoretic_Solution.pdf
The second appeared in Cousot and Cousot 1979
http://www.di.ens.fr/~cousot/COUSOTpapers/publications.www/CousotCousot-PacJMath-82-1-1979.pdf
Best regards,
Paul