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Use 'interp' to add [[ bla ]] notation for analysis

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Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
This commit is contained in:
Danila Fedorin
2026-06-23 13:29:54 -05:00
parent 8ce6e5e4e4
commit ed88f4ce94
5 changed files with 34 additions and 32 deletions
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24
lean/Spa/Analysis/Forward/Lattices.lean
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@@ -1,5 +1,6 @@
import Spa.Language
import Spa.Lattice.FiniteMap
import Spa.Interp
namespace Spa
@@ -66,32 +67,33 @@ theorem variablesAt_joinAll (s : prog.State) (sv : StateVariables L prog) :
variable [I : LatticeInterpretation L]
omit [FiniteHeightLattice L] in
def interpV (vs : VariableValues L prog) (ρ : Env) : Prop :=
∀ (k : String) (l : L), (k, l) ∈ vs →
∀ (v : Value), Env.Mem (k, v) ρ → I.interp l v
instance : Interp (VariableValues L prog) (Env → Prop) where
interp (vs : VariableValues L prog) (ρ : Env) : Prop :=
∀ (k : String) (l : L), (k, l) ∈ vs →
∀ (v : Value), Env.Mem (k, v) ρ → I.interp l v
theorem interpV_botV_nil : interpV (botV L prog) [] := by
theorem interp_botV_nil : ⟦ botV L prog ⟧ [] := by
intro k l _ v hmem
cases hmem
omit [FiniteHeightLattice L] in
theorem interpV_sup {vs₁ vs₂ : VariableValues L prog} {ρ : Env}
(h : interpV vs₁ ρ ∨ interpV vs₂ ρ) : interpV (vs₁ ⊔ vs₂) ρ := by
theorem interp_sup {vs₁ vs₂ : VariableValues L prog} {ρ : Env}
(h : ⟦ vs₁⟧ ρ ∨ ⟦ vs₂ ⟧ ρ) : ⟦ vs₁ ⊔ vs₂ ⟧ ρ := by
intro k l hmem v hv
obtain ⟨l₁, l₂, rfl, h₁, h₂⟩ := FiniteMap.mem_sup hmem
rcases h with h | h
· exact I.interp_sup v (Or.inl (h _ _ h₁ _ hv))
· exact I.interp_sup v (Or.inr (h _ _ h₂ _ hv))
theorem interpV_foldr {vs : VariableValues L prog}
theorem interp_foldr {vs : VariableValues L prog}
{vss : List (VariableValues L prog)} {ρ : Env}
(hvs : interpV vs ρ) (hmem : vs ∈ vss) :
interpV (vss.foldr (· ⊔ ·) (botV L prog)) ρ := by
(hvs : ⟦ vs ⟧ ρ) (hmem : vs ∈ vss) :
⟦ vss.foldr (· ⊔ ·) (botV L prog) ⟧ ρ := by
induction vss with
| nil => cases hmem
| cons vs' vss' ih =>
rcases List.mem_cons.mp hmem with rfl | hmem'
· exact interpV_sup (Or.inl hvs)
· exact interpV_sup (Or.inr (ih hmem'))
· exact interp_sup (Or.inl hvs)
· exact interp_sup (Or.inr (ih hmem'))
end Spa