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Switch FiniteMap Fin n -> L representation

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This helps automatically derive lattice laws for it

Signed-off-by: Danila Fedorin <danila.fedorin@gmail.com>
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-25 13:28:30 -05:00
parent c4e5747b6d
commit 5ac881559d
6 changed files with 163 additions and 450 deletions
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8
lean/Spa/Analysis/Constant.lean
View File

@@ -77,12 +77,12 @@ theorem eval_mono (e : Expr) : Monotone (eval prog e) := by
intro vs₁ vs₂ h
simp only [eval]
by_cases hk : k ∈ prog.vars
· rw [dif_pos (FiniteMap.memKey_iff.mpr hk),
dif_pos (FiniteMap.memKey_iff.mpr hk)]
· rw [dif_pos (FiniteMap.MemKey_iff.mpr hk),
dif_pos (FiniteMap.MemKey_iff.mpr hk)]
exact FiniteMap.le_of_mem_mem prog.vars_nodup h
(FiniteMap.locate _).2 (FiniteMap.locate _).2
· rw [dif_neg (fun hm => hk (FiniteMap.memKey_iff.mp hm)),
dif_neg (fun hm => hk (FiniteMap.memKey_iff.mp hm))]
· rw [dif_neg (fun hm => hk (FiniteMap.MemKey_iff.mp hm)),
dif_neg (fun hm => hk (FiniteMap.MemKey_iff.mp hm))]
| num n =>
intro vs₁ vs₂ _
exact le_refl _

2
lean/Spa/Analysis/Forward/Lattices.lean
View File

@@ -20,7 +20,7 @@ variable {L prog}
omit [Lattice L] in
theorem states_memKey (s : prog.State) (sv : StateVariables L prog) :
FiniteMap.MemKey s sv :=
FiniteMap.memKey_iff.mpr (prog.states_complete s)
FiniteMap.MemKey_iff.mpr (prog.states_complete s)
def variablesAt (s : prog.State) (sv : StateVariables L prog) :
VariableValues L prog :=

8
lean/Spa/Analysis/Sign.lean
View File

@@ -137,12 +137,12 @@ theorem eval_mono (e : Expr) : Monotone (eval prog e) := by
intro vs₁ vs₂ h
simp only [eval]
by_cases hk : k ∈ prog.vars
· rw [dif_pos (FiniteMap.memKey_iff.mpr hk),
dif_pos (FiniteMap.memKey_iff.mpr hk)]
· rw [dif_pos (FiniteMap.MemKey_iff.mpr hk),
dif_pos (FiniteMap.MemKey_iff.mpr hk)]
exact FiniteMap.le_of_mem_mem prog.vars_nodup h
(FiniteMap.locate _).2 (FiniteMap.locate _).2
· rw [dif_neg (fun hm => hk (FiniteMap.memKey_iff.mp hm)),
dif_neg (fun hm => hk (FiniteMap.memKey_iff.mp hm))]
· rw [dif_neg (fun hm => hk (FiniteMap.MemKey_iff.mp hm)),
dif_neg (fun hm => hk (FiniteMap.MemKey_iff.mp hm))]
| num n =>
intro vs₁ vs₂ _
cases n <;> exact le_refl _