Re: [isabelle] Lifting package and state transformers
> On 17 May 2016, at 06:52, Andreas Lochbihler <andreas.lochbihler at inf.ethz.ch> wrote:
> Dear experts of the lifting package,
> I wonder whether I can automate certain liftings with the Lifting package. Concretely, suppose I have a function foo and I want to lift it to a type of state transformers:
> datatype ('s, 'm) stateT = StateT (run_state: "'s => 'm")
> context fixes foo :: "('a => 'm) => 'm" begin
> definition foo_state :: "('a => ('s, 'm) stateT) => ('s, 'm) stateT"
> where "foo_state f = StateT (%s. foo (%a. run_state (f a) s))"
> Can I (somehow) use lift_definition to define foo_state? I am thinking of something like the following:
> setup_lifting ...
> lift_definition foo_state :: "('a => ('s, 'm) stateT) => ('s, 'm) stateT" is foo
> Unfortunately, I have no idea what theorem provide to setup_lifting to make this work. I tried with the obvious one
> type_definition run_state StateT UNIV
> but that did not work. Any ideas?
This obviously does not work, since with the above type_definition lift_definition expects you to tell what to do with the state âs. The following works.
datatype ('s, 'm) stateT = StateT (run_state: "'s => 'm")
context fixes foo :: "('a => 'm) => 'm" begin
lemma typedef_stateT: "type_definition run_state StateT UNIV"
by unfold_locales auto
lift_definition foo_state :: "('a => ('s, 'm) stateT) => ('s, 'm) stateT" is
"Îf s. foo (Îa. f a s)" .
So you can automatically insert the morphisms StateT and run_state, but I donât think you can come up with a type_definition that hides the threading through of the state âs from the user.
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