DanilaFe/agda-spa
1
0
Fork 0
Code Issues Pull Requests Packages Projects Releases Wiki Activity

Make FiniteHeightLattice extend Lattice and derive Top/Bot

Browse Source 
Co-Authored-By: Claude Opus 4.8 <noreply@anthropic.com>
This commit is contained in:
Danila Fedorin
2026-06-25 18:42:28 -05:00
parent acef0f202b
commit cbad43efdc
11 changed files with 61 additions and 102 deletions
Download Patch File Download Diff File Expand all files Collapse all files

10
lean/Spa/Analysis/Forward.lean
View File

@@ -7,7 +7,7 @@ namespace Spa
namespace Forward
variable {L : Type} [Lattice L] {prog : Program} [E : StmtEvaluator L prog]
variable {L : Type} [FiniteHeightLattice L] {prog : Program} [E : StmtEvaluator L prog]
def updateVariablesForState (s : prog.State) (sv : StateVariables L prog) :
VariableValues L prog :=
@@ -33,8 +33,6 @@ lemma variablesAt_updateAll (s : prog.State) (sv : StateVariables L prog) :
variablesAt s (updateAll sv) = updateVariablesForState s sv :=
updateAll_mem_eq (variablesAt_mem s (updateAll sv))
variable [FiniteHeightLattice L]
def analyze (sv : StateVariables L prog) : StateVariables L prog :=
updateAll (joinAll sv)
@@ -58,7 +56,7 @@ lemma joinForKey_initialState :
variable [I : LatticeInterpretation L] [V : ValidStmtEvaluator L prog]
omit [FiniteHeightLattice L] [DecidableEq L] in
omit [DecidableEq L] in
lemma eval_fold_valid {s : prog.State} {bss : List BasicStmt}
{vs : VariableValues L prog} {ρ₁ ρ₂ : Env}
(hbss : EvalBasicStmts ρ₁ bss ρ₂) (hvs : ⟦ vs ⟧ ρ₁) :
@@ -67,7 +65,7 @@ lemma eval_fold_valid {s : prog.State} {bss : List BasicStmt}
| nil => exact hvs
| cons hbs _ ih => exact ih (ValidStmtEvaluator.valid hbs hvs)
omit [FiniteHeightLattice L] [DecidableEq L] in
omit [DecidableEq L] in
lemma updateVariablesForState_matches {s : prog.State}
{sv : StateVariables L prog} {ρ₁ ρ₂ : Env}
(hbss : EvalBasicStmts ρ₁ (prog.code s) ρ₂)
@@ -75,7 +73,7 @@ lemma updateVariablesForState_matches {s : prog.State}
⟦ updateVariablesForState s sv ⟧ ρ₂ :=
eval_fold_valid hbss hvs
omit [FiniteHeightLattice L] [DecidableEq L] in
omit [DecidableEq L] in
lemma updateAll_matches {s : prog.State} {sv : StateVariables L prog}
{ρ₁ ρ₂ : Env} (hbss : EvalBasicStmts ρ₁ (prog.code s) ρ₂)
(hvs : ⟦ variablesAt s sv ⟧ ρ₁) :