TITLE: Is functional programming a branch of mathematics?
QUESTION [13 upvotes]: In Theory mainly concerned with lambda-calculus?, F. G. Dorais wrote, of the idea that the lambda-calulus defines a domain of mathematics:

That would never stick unless there's another good reason. Besides, the schism between cs and math is very recent, I would contend that "functional programming" is actually a math term, historically speaking. More importantly, it would be wrong to use a term different than those who use it most, namely theoretical computer scientists, who are very competent mathematicians by the way. 

The idea, I think, is that the overlap between the kind of constructive mathematics that follows the formulae-as-types correspondence, and pure functional programming is so substantial that the core of the two topics is essentially the same subject.
Is this true?

REPLY [3 votes]: I think most people here would agree that Category Theory is part of mathematics.
The study of strongly-typed functional programming languages is really just the study of cartesian closed categories, so I think that this particular part of functional programming is legitimate mathematics.  And Domain Theory is the study of the category of complete partial orders with bottom, so I would include that too.
I don't think I would extend that to untyped or dynamically-typed languages (LISP).  Also, I'd probably pick a term other than "functional programming" since subfields of math are rarely named with gerunds ("strongly typed functional languages" is probably the most accurate, but a bit verbose).