| import Mathlib |
| import OAI.Combinatorics.IndependentSets.Encoding.GeometryExpr |
|
|
| namespace OAI |
|
|
| namespace LargeIndependentSets.GeometryNames |
| open IndependentSetsCut.CounterMachine UniformLC |
| open scoped Classical |
| noncomputable section |
| variable (L R : Type) [Fintype L] [Fintype R] (n D : ℕ) [NeZero D] |
|
|
| def pointEquiv : StaticPoint L R n D ≃ Fin (staticCount L R n D) := |
| Fintype.equivFin (StaticPoint L R n D) |
|
|
| lemma nodeEquiv_val {nu nv : ℕ} (x : Node L R n D nu nv) : |
| (nodeEquiv L R n D nu nv x).val= |
| (pointEquiv L R n D x.2).val+staticCount L R n D* |
| ((finFunctionFinEquiv x.1.2).val+nv^n*(finFunctionFinEquiv x.1.1).val) := rfl |
|
|
| def pointLookup (f : StaticPoint L R n D → ℕ) (x : Expr) : Expr := |
| Expr.finLookup (fun i => f ((pointEquiv L R n D).symm i)) x |
|
|
| lemma pointLookup_eval (f : StaticPoint L R n D → ℕ) (x : Expr) (s : List Bool) (a : ℕ → ℕ) |
| (v : StaticPoint L R n D) (hv : x.eval s a=(pointEquiv L R n D v).val) : |
| (pointLookup L R n D f x).eval s a=f v := by |
| rw [pointLookup,Expr.finLookup_eval _ _ _ _ (pointEquiv L R n D v) hv,Equiv.symm_apply_apply] |
|
|
| lemma pointExpr_code (t : Table L R) (x : Expr) (a : ℕ → ℕ) (i : Fin (size L R n D t)) |
| (hi : x.eval t.bits a=i.val) : |
| (pointExpr L R n D x).eval t.bits a= |
| (pointEquiv L R n D ((nodeEquiv L R n D t.nu t.nv).symm i).2).val := |
| pointExpr_eval L R n D t x a i hi |
|
|
| end |
| end LargeIndependentSets.GeometryNames |
|
|
| end OAI |
|
|
