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| -- Adapted encodings from https://dl.acm.org/doi/pdf/10.1145/3571255 | |
| structure EffectSet (AbstractState : Type) : Type 1 where | |
| Ops : (precondition : AbstractState → Prop) → Type | |
| Ret : (precondition : AbstractState → Prop) → Ops precondition → Type | |
| Transition : (precondition : AbstractState → Prop) → Ops precondition → (AbstractState → Prop) | |
| inductive HoareFreer (AbstractState : Type) (es : EffectSet AbstractState) : | |
| (precondition : AbstractState → Prop) → (postcondition : AbstractState → Prop) → (result : Type) → Type 1 where | |
| | End : {result : Type} → {condition : AbstractState → Prop} → | |
| (res : result) → HoareFreer AbstractState es condition condition result | |
| | RunAndThen : {pre post : AbstractState → Prop} → | |
| (instr : es.Ops pre) → | |
| (continuation : es.Ret pre instr → HoareFreer AbstractState es (es.Transition pre instr) post result) → | |
| HoareFreer AbstractState es pre post result | |
| inductive GetSetOps (S : Type) where | |
| | Get | |
| | Set : S → GetSetOps S | |
| def HoareGetSet (S : Type) : EffectSet S := | |
| { Ops := Function.const _ (GetSetOps S), | |
| Ret := fun pre => (fun | |
| | .Get => { s : S // pre s } | |
| | .Set _ => Unit | |
| ), | |
| Transition := fun pre => (fun | |
| | .Get => pre | |
| | .Set operand => fun s => s = operand | |
| ) | |
| } |
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