| import Mathlib |
|
|
| namespace OAI |
|
|
| section |
| open scoped BigOperators |
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|
|
| namespace ExactQuantumFactoring.AIGCompiler |
| open Std.Sat |
|
|
| /-- One real AIG atom per input bit. The initial graph has one false node. -/ |
| def inputsPrefix (n : ℕ) : (k : ℕ) → k ≤ n → |
| (g : AIG (Fin n)) × (Fin k → AIG.Ref g) |
| | 0, _ => ⟨AIG.empty, Fin.elim0⟩ |
| | k+1, h => |
| let old := inputsPrefix n k (by omega) |
| let res := old.1.mkAtom ⟨k, by omega⟩ |
| ⟨res.aig, Fin.snoc (fun i => (old.2 i).cast (AIG.LawfulOperator.le_size (f := AIG.mkAtom) old.1 (⟨k, by omega⟩ : Fin n))) res.ref⟩ |
|
|
| lemma inputsPrefix_size (n k : ℕ) (h : k ≤ n) : (inputsPrefix n k h).1.decls.size = k+1 := by |
| induction k with |
| | zero => simp [inputsPrefix, AIG.empty] |
| | succ k ih => simp [inputsPrefix, AIG.mkAtom, ih] |
|
|
| lemma inputsPrefix_correct (n k : ℕ) (h : k ≤ n) (x : Fin n → Bool) (i : Fin k) : |
| AIG.denote x ⟨(inputsPrefix n k h).1, (inputsPrefix n k h).2 i⟩ = x (i.castLE h) := by |
| induction k with |
| | zero => exact Fin.elim0 i |
| | succ k ih => |
| refine Fin.lastCases ?_ (fun j => ?_) i |
| · simp only [inputsPrefix, Fin.snoc_last] |
| change AIG.denote x ((inputsPrefix n k (by omega)).1.mkAtom ⟨k, by omega⟩) = _ |
| rw [AIG.denote_mkAtom] |
| rfl |
| · simp only [inputsPrefix, Fin.snoc_castSucc] |
| rw [AIG.LawfulOperator.denote_cast_entry (f := @AIG.mkAtom (Fin n) _ _) |
| (entry := ⟨(inputsPrefix n k (by omega)).1, (inputsPrefix n k (by omega)).2 j⟩)] |
| exact ih (by omega) j |
|
|
| def inputs (n : ℕ) := inputsPrefix n n le_rfl |
|
|
| lemma inputs_size (n : ℕ) : (inputs n).1.decls.size = n+1 := inputsPrefix_size .. |
|
|
| lemma inputs_correct (n : ℕ) (x : Fin n → Bool) (i : Fin n) : |
| AIG.denote x ⟨(inputs n).1, (inputs n).2 i⟩ = x i := inputsPrefix_correct .. |
|
|
| /-- A vector of ordinary references; this constructor emits no graph nodes. -/ |
| def refVector {α : Type} [Hashable α] [DecidableEq α] {g : AIG α} {w : ℕ} |
| (f : Fin w → AIG.Ref g) : AIG.RefVec g w where |
| refs := Vector.ofFn (fun i => AIG.Fanin.mk (f i).gate (f i).invert) |
| hrefs := by intro i hi; simpa using (f ⟨i,hi⟩).hgate |
|
|
| lemma refVector_get {α : Type} [Hashable α] [DecidableEq α] {g : AIG α} {w : ℕ} |
| (f : Fin w → AIG.Ref g) (i : ℕ) (hi : i < w) : |
| (refVector f).get i hi = f ⟨i,hi⟩ := by |
| simp [refVector, AIG.RefVec.get, AIG.Fanin.gate_mk, AIG.Fanin.invert_mk] |
|
|
| end ExactQuantumFactoring.AIGCompiler |
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| end |
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| end OAI |
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|
