Peter Freyd wrote on 11/21/2005:
... NOTATION: Every group-valued functor from a category of R-modules, commutative R, can be canonically lifted to a module-valued functor. Given two such functors, S and T, we follow the CS tradition of denoting their composition, "first apply S then T" as S;T (hence (S;T)(A) = T(S(A)).
Actually it is an RA (Relation Algebra) tradition dating back to the 19th century. In my LICS'92 evening history talk, "Origins of the Calculus of Binary Relations", http://boole.stanford.edu/pub/ocbr.pdf, I attributed it as follows.
But this view of composition/concatenation as a form of conjunction predates even Peirce and would appear to be due to De Morgan in 1860 [DeM]. The following footnote appears exactly one-third of the way through De Morgan's ``On the Syllogism IV'' (p.221 in Heath's anthology ``On the Syllogism'' [DeM66]). Here De Morgan argues that, allowing for the obvious differences, composition L;M of relations L and M resembles conjunction XY of ``terms'' (predicates) X and Y. Indeed he notates composition LM the better to suggest conjunction---the L;M notation which is now in almost universal use, and is in (fortuitous?) agreement with Algol 60 and dynamic logic [Pr76], was introduced later by Peirce.
I still don't know whether RA played any role in the adoption of ; by Algol 60. However Algol 60 used ; not as a statement terminator (as in C or Java) but as an associative infix operator between statements, suggestive of RA influence. (Perhaps so as not to overly inconvenience those who tended to think of semicolon as a terminator anyway, the empty string was permitted as a statement, inadvertently complicating the task of generating the language Algol 60 with an unambiguous context-free grammar.) Vaughan Pratt