30 lines
1.4 KiB
Coq
30 lines
1.4 KiB
Coq
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Require Import base.
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Require Import Policy.
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Require Import Mealy.
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(** Formally, a view partition is an assignment of an equivalence
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relation [≈{u}] for every domain [u] *)
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Class ViewPartition `(M : Mealy state action out) (domain : Type) := {
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view_partition :> domain -> relation state;
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view_partition_is_equiv :> forall v, Equivalence (view_partition v)
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}.
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Notation "S ≈{ U } T" := (view_partition U S T)
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(at level 70, format "S ≈{ U } T").
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Class OutputConsistent {domain : Type} `{M : Mealy state action out}
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(P : Policy action domain) (VP: ViewPartition M domain) :=
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output_consistent : (forall a s t, s ≈{dom a} t -> output s a = output t a).
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Class LocallyRespectsPolicy {domain : Type} `{M : Mealy state action out}
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(P : Policy action domain) (VP: ViewPartition M domain) :=
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locally_respects_policy : (forall a u s, ¬(policy (dom a) u) -> s ≈{u} (step s a)).
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Class WeakStepConsistent {domain : Type} `{M : Mealy state action out}
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(P : Policy action domain) (VP: ViewPartition M domain) :=
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weak_step_consistent : (forall a s t u, s ≈{dom a} t -> s ≈{u} t -> (step s a) ≈{u} (step t a)).
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Class StepConsistent {domain : Type} `{M : Mealy state action out}
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(P : Policy action domain) (VP: ViewPartition M domain) :=
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step_consistent : (forall a s t u, s ≈{u} t -> (step s a) ≈{u} (step t a)).
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