[isabelle] Lifting package and state transformers
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
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?
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