support strongest-postcondition reasoning
lsf37 opened this issue · comments
We currently have _sp
rules for a number of the basic monad constructs, and we're using them manually in some situations, e.g. to avoid case blow-up in wp reasoning or when chaining trivial steps in corres proofs.
We should:
- consistently support at least all of the basic nondet monad constructs with
_sp
rules -- I think they do have to be manually stated, but their proofs should all follow automatically from the correspondingwp
rule - have a basic
sp
tactic, analogous towp
, but not as sophisticated. For a first version, I would propose a simple Eisbach method that repeatedly applies ansp
set, and potentially automatically does ansp_pre
(analogously towp_pre
). - find (most of) the existing manual
_sp
proofs and replace these to make sure the automation works and is convenient enough to use
I don't think we need a full-blown wp
equivalent for sp
, because we do not want to switch over to general sp
reasoning or use more of it than necessary (to avoid duplicating rules for kernel functions). This issue only proposes to make those instances where it would be beneficial to use more ergonomic to use and easier to read/review.
MCS seems to have a higher use count of sp
rules, so we should make sure to test the method there.
There is also a question about which other monads to support (e.g. error and/or reader monad), but so far most of the instances I've seen are on the plain nondet monad, so I'd vote for starting small and doing that one properly first.