I started tidying things a little bit and it snowballed into quite a few changes, hopefully for the best. Main changes are:
Change in the way we import files. The main constructions are imported at once with From CTree Require Import CTree. The main equational theory for equ and sbisim is obtained at once with From CTree Require Import Eq. For weak bisimulation, you should import manually From CTree Require Import Eq.WBisim.
Relations (equ, sbisim, wbisim) are now definitions and not notations so that in particular we can search for lemmas about them. Be careful to follow the import discipline described above to make sure you get in scope the tactics taking care of the necessary unfolding and folding.
Following @nchappe 's suggestion, I added a up-to Vis context and proved it sound for sbisim --- the tactic upto_vis is the simplest way to use it.
Provided a few other tactics:
upto_bind: application of an upto bind principle for equ or sbisim, in front of a gfp, t _ or bt _ goal. In the case of equ, introduce an evar for the intermediate relation.
upto_bind_eq: the same, but specifically for a goal where both prefixes are the same --- discharge them automatically with reflexivity
upto_bind with SS: for equ, provides the desired intermediate relation.
play/playL/playR/eplayL/eplayR to exploit sbisim hypotheses
etrans: automatic solving for trans --- Quite stupid, just a bunch of hint resolve.
Tried to make the naming conventions more consistent, so a fair bit of changes
trans does not reduce with cbn and simpl, making it necessary to unfold it manually sometimes. It's annoying, but very convenient for the automation, I'm not quite decided yet about this.
I started tidying things a little bit and it snowballed into quite a few changes, hopefully for the best. Main changes are:
From CTree Require Import CTree. The main equational theory forequandsbisimis obtained at once withFrom CTree Require Import Eq. For weak bisimulation, you should import manuallyFrom CTree Require Import Eq.WBisim.equ,sbisim,wbisim) are now definitions and not notations so that in particular we can search for lemmas about them. Be careful to follow the import discipline described above to make sure you get in scope the tactics taking care of the necessary unfolding and folding.Viscontext and proved it sound forsbisim--- the tacticupto_visis the simplest way to use it.upto_bind: application of an upto bind principle forequorsbisim, in front of agfp,t _orbt _goal. In the case ofequ, introduce an evar for the intermediate relation.upto_bind_eq: the same, but specifically for a goal where both prefixes are the same --- discharge them automatically withreflexivityupto_bind with SS: forequ, provides the desired intermediate relation.play/playL/playR/eplayL/eplayRto exploitsbisimhypothesesetrans: automatic solving fortrans--- Quite stupid, just a bunch of hint resolve.transdoes not reduce withcbnandsimpl, making it necessary to unfold it manually sometimes. It's annoying, but very convenient for the automation, I'm not quite decided yet about this.