memoize and options

[mahrud]

Should memoize be sensitive to options?

I can see arguments both ways:

1. sometimes the options contain important parameters, like coefficient ring or variable name (e.g. see https://github.com/Macaulay2/M2/pull/3481#discussion_r1768381949);
2. on the other hand, sometimes options are just verbosity level or strategy, and if the code has already run maybe we don't care about that.

I don't think using memoize (as opposed to other means of caching) should be recommended anyway, so maybe this is a moot point.

[pzinn]

Note that it's not so easy to use memoize with say a method with options, as I think I pointed out in some other thread. e.g., givin

f= method(Options=>new OptionTable from{a=>1})

neither

f ZZ := o -> memoize(x -> (print (x,o#a); x+o#a))

nor

f ZZ := memoize(o -> x -> (print (x,o#a); x+o#a))

will work, as can be checked by applying repeatedly. this does work:

f ZZ := memoize(o -> memoize(x -> (print (x,o#a); x+o#a)))

but seems heavy. If one wants to ignore the option for memoize purposes, I don't even know any simple option.

[mahrud]

Related problem for memoizing methods:

i1 : f = method();

i2 : f ZZ := x -> 2*x;

i3 : f = memoize f;

i4 : f QQ := x -> 3*x;

i5 : f(1_ZZ)

o5 = 2

i6 : f(1_QQ)
stdio:6:1:(3): error: no method found for applying MethodFunction[] to:
     argument   :  1 (of class QQ)