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The sentence:
A WSGI-compliant server or gateway should document what variables it provides, along with their definitions as appropriate.
How to understand with their definitions as appropriate?
either:
with their appropriate definitions
or:
with their definitions as it is appropriate
which one is correct?
It means something like your second option, but your wording is also unclear.
I would paraphrase it as insofar as (or "to the degree that") it is appropriate to do so.
Try re-reading it as "...when appropriate." and see if it makes more sense to you like that.
In many contexts such as this, the phrase "...for X do Y as appropriate..." indicates that doing Y may or may not be appropriate for every X, and so Y should only be done on a case-by-case basis.
Similar phrasings include "as needed" or "as necessary".
As an example, let's imagine an ice-cream shop!
As an ice-cream shop employee, you should take a new cone and fill it with the ice-cream of the customer's choice. Then you should add toppings as requested.
Why do the instructions say "as requested"? Because not all customers want toppings! If the instructions only said "... add toppings." then following the instructions (too literally) would mean adding toppings for every customer.
A better wording in this example might be "Then you should add any requested toppings." but sometimes the "... as required" construction is just more appropriate.
Back to your example:
[A WSGI-compliant server or gateway] should [document what variables it provides], [along with their definitions as appropriate].
Breaking the sentence into those main pieces, we can basically understand that last chunk to mean "... and document the definitions for those variables as appropriate".
I cannot think of any reason why documentation for the definition of a variable would be inappropriate... but perhaps this choice of phrasing is being used more in a business-sense than a technical-sense so as to allow more wiggle-room if they ever get sued and want to argue that something wasn't strictly required.
With X as adjective means:
You are looping through a number of things, doing something to each thing.
For each time you do something, you may encounter the condition adjective
If that condition is true for the particular thing you are doing, with X applies.
You won't know whether or not adjective is true until you start the loop (that's what the as communicates).
An X should document what variables it provides, along with their definitions as appropriate.
is the same as saying
An X should document what variables it provides. During any time where it does this, while it is looping through each variable, the variable's definition should be documented if X determines documentation is appropriate for that variable.
I can say this as I worked as a programmer for a number of years: too many people in information technology write poor English, and a few take pride in writing poor English. Your question involves just such a sentence.
Servers do not “document” anything. Nor do they “provide” variables. I think what is meant is
The documentation for a WSGI-compliant server or gateway should list and define all supported variables.
