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It is somewhat common to write $f(x_0,x_1;\ z_0,z_1)$ to indicate that $f$ is a function of $x_0,\ x_1,\ z_0,\&\ z_0$, but that the $z$ arguments should be thought of as fixed by the context, while variation with respect to the $x$ arguments are core to the discussion.

For example when discussion the partial derivatives of $f$ with respect to the $x$'s for fixed $z$'s or the probability as a function of the $x$'s given the $z$'s.

In theorem proving this often feels like "a distinction without a difference", but in programing it may indicate the expectation of some sort of parameter specific optimization. The derived function $f_{z_0,z_1}(x_0,x_1)$ may be more efficiently implemented than the general function $f(x_0,x_1,z_0,z_1)$. Some systems have tried to automate the generation of an optimized derived function given parameter values, but they never really caught on.

I am writing and it would be extremely convenient to have a name for this. The passage is starting to feel repetitive and hard to read.

I don't want to create my own name, because I distinctly remember reading some reasonably authoritative source that referred to this as the "such-and-such" convention. So creating my own term would likely be a faux pas.

But I can't remember the name or re-find the passage.

GPU Programmer
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  • Using a semicolon to separate variables from parameters is quite common. Why exactly is it more efficient to write $f_{z_0, z_1}(x_0, x_1)$ than $f(x_0, x_1;z_0, z_1)$? – David Scholz Feb 15 '21 at 16:26
  • There is no extra efficiency in the writing, but there might be extra efficiency in the computing. Because in many cases you can do parameter specific optimizations. – GPU Programmer Feb 15 '21 at 16:32
  • Oh I see, but when describing an algorithm for fixed $z_0, z_1$ and this algorithm is different from the general version (otherwise how could it be more efficient?), then why not just introduce a new function name saying that it is equal to $f$ but with fixed parameters? I feel like this is the usual way to proceed, at least that‘s what I‘ve seen most of the time. – David Scholz Feb 15 '21 at 16:41
  • Actually, we have a set of all such functions and any element of that set is a function $f$ with some fixed pair of parameters. – David Scholz Feb 15 '21 at 16:47
  • Parameter specific optimization need not be sweeping enough to count as a new algorithm. It could be as humble as constant folding. More typically it would be something in between, like loop optimization or CAS (Computer Algebra System) simplification. – GPU Programmer Feb 16 '21 at 17:35

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