Fuzzers for functions

[Janiczek]

The idea, as far as I understand it, is to generate a list of mappings from a to b, and convert that list to a function.

There are a bunch of functions to change these: map works as usual, to change the b into c, but we can also have coMap (profunctor?) that works on the input instead of on the output: given a z -> a function, it changes a -> b to z -> b.

The simplest generated functions map all values to some default value, and more complicated functions have exceptions from the default (ie. "map 9 to 1, map everything else to 0"). Such functions with exceptions do shrink towards the "no exception" case (a constant function).

Prior art:

• https://www.google.com/search?q=%22Shrinking+and+showing+functions%22+Koen+Claessen
• https://www.youtube.com/watch?v=CH8UQJiv9Q4
• https://hackage.haskell.org/package/QuickCheck-2.14.3/docs/Test-QuickCheck-Function.html
• https://hackage.haskell.org/package/QuickCheck-2.13.1/docs/Test-QuickCheck.html#t:Function
• https://hackage.haskell.org/package/QuickCheck-2.13.1/docs/Test-QuickCheck.html#v:Fun
• https://hackage.haskell.org/package/QuickCheck-2.13.1/docs/Test-QuickCheck-Arbitrary.html#t:CoArbitrary

A classic poster child example of "hey we can generate functions" in the PBT context is testing that map f (filter p xs) == filter p (map f xs). (This is not true.)