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In computer science and programming, one frequently wishes to create a process that takes a certain type of input and spits something (immaterial to this discussion) out. However, in many cases we also want to create an extremely similar process that takes in a different type of input (this difference is usually just a technicality in comparison to what the last process ate up) and spits out the same thing that the last process did.

We frequently name processes. In the case we're considering, we want to name the two processes above. Of course, different processes get different names; however, the two different process above don't really seem sufficiently different to warrant different names. It's just by the hair of a technicality that the two (or more) processes are different.

Some programming languages allow you to use the same name for these technically different processes. Some languages don't. However in languages that do, the practice of recycling the same name for slightly different purposes is called "overloading".

Is there a precise common language term for this idea of "overloading" that would carry the same idea without possibly implying other notions?

"Overload" is commonly interpreted to put too much weight on something instead of just adding more weight that the thing can still manage.

I can think of the terms "stretch" and "recycle," but the former loads too much metaphor and the latter carries an overtone that the previous purpose an object had is no longer going to be pursued. With an overloaded name, one can anticipate that the several different processes that it is used on will EACH be used forever and periodically.

I want to port this usage to mathematics. An example sentence that I want to alter is:

"We say that f is continuous at x (a point) if ... . To overload the term, we say that f is continuous on X (a set) if ... ."

Not all mathematics people are computer science people.

  • Did you look in a thesaurus for recycle? Things like 'reuse'? – Mitch Apr 24 '18 at 19:47
  • Yes. Reuse, recycle, repurpose each imply, at least to me, that the previous purpose is being tossed aside. – user70564 Apr 24 '18 at 19:50
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    In the context of computer science, "overloading" is exactly the single word you want and is what others familiar with the domain would expect. Are you trying to apply this to an adjacent domain (i.e. an industrial engineering process design, for example, where overload could mean too much weight)? Or in what example sentence would you want the word you're looking for? – user662852 Apr 24 '18 at 19:53
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    Concerning reuse, recycle, and repurpose implying discarding of the previous purpose: I think you just have to get over it, honestly. It's not like a plastic food container that you "reuse" by turning it into a pot for plants. We're talking about words being reused. But all kinds of words have multiple meanings determined by context. It's not like the word can't be used for the "old" meaning once we've used it for the "new" one. I actually don't even understand why you need a term for this phenomenon. Just use the word again in the new way. Done! – John Y Apr 24 '18 at 22:03
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Would "extends" or "redefines" work for your purposes?

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  • Extends seems the most appropriate: the definition is extended from points (local) to sets of points (global). Redefine, to me at least, seems to imply the set definition replaces the point definition, which isn't what the asker wants. – JJJ Apr 25 '18 at 3:57
  • "Extends" is the best option here. – user70564 Apr 25 '18 at 19:15
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What I'm understanding from your question is that you would like to find a synonym for overload (in the CS sense you explained) that mathematicians would have an easier time understanding.

I would suggest

repurpose

adapt to or use for a new purpose (Collins)

Example:

There's a trick we can use here, we can repurpose this function and use it is this slightly different way. In the language we're working with, we don't actually have to change the way the function is defined. The usage is close enough that it works as a variant.

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