File size: 2,469 Bytes
2f887db | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 | import Mathlib
namespace OAI
section
open scoped BigOperators
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
end
end OAI
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