On Sun, Apr 25, 2021, at 2:04 AM, Olle Härstedt wrote:
> > A total function is a function that is defined over the entire domain of its
> > inputs.  For example, addition is a total function over integers, because
> > for every possible pair of integers you pass to it there is a logical return
> > value.  However, square root is not a total function over integers because
> > there are some integers you pass it for which there is not representable
> > return value.  (Negative numbers, unless you get into imaginary numbers
> > which PHP doesn't support.)  In those cases, you have to throw an exception
> > or return an error code or similar.
> 
> Maybe nitpicking, but PHP-land shouldn't make up their own
> definitions: "A total function is a function that is defined for all
> possible values of its input. That is, it terminates and returns a
> value." 
> https://softwareengineering.stackexchange.com/questions/334874/in-the-context-of-functional-programming-what-are-total-functions-and-partia
> 
> Which means a total function is guaranteed to not have any errors,
> like exceptions or division by zero. Compare with languages F* or Koka
> which support this notation.

That... is literally what I said.  There was no making up definitions.  I was 
using the actual mathematical definition.  PHP is quite capable of having total 
functions, they're a good thing, and we should try to encourage them where 
feasible.

--Larry Garfield

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