Variants

[arnaudgolfouse]

This allow variants in various places:

• simply recursive functions (logic and program)
• loops (this allows loops in ghost code!)

Together with a rework of the WellFounded trait, to allow variants on custom types.

Fixes #561, #754.

[jhjourdan]

Great job!

All in all, I think that most of this is OK, but the way variant assertion are inserted need to be improved:

• For loops, it should really rely on the WTO, and therefore I think that this should really be done by the backend. In particular, I'm not sure that we should store sets of variants to check at "continue" blocks. Instead, when entering a WTO component whose head has a variant, create a new handler for the head of the loop that will check the variant decrease, and make all the jumps from inside the component point to this new handler.

• For recursive calls in program code, I would really prefer not translating operands to terms. This would be yet another translation from places to XXX, and I'm afraid of subtle semantic differences betwen the versions. Instead, please use a method similar to the one for loop I propose above: create a new sub-handler for recursive calls, and make it check that the variant decreases before performing the actual recursive call.

[jhjourdan]

(I'm in the process of reviewing this.)

[jhjourdan]

This is great work. I have a few comments here and there, and two other concerns:

• the definition of well foundedness is broken (see my comment)

• it would be great to demonstrate this new features on some of the already existing examples : PA and union find, of course, and perhaps binary search or other examples. This should not be so difficult, all the needed ingredients are already there.

[jhjourdan]

If you feel this is ready to merge, then please press the button ;)