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Require Export Language Conversion QhasmCommon QhasmEvalCommon QhasmUtil.
Require Export Pseudo AlmostQhasm State.
Require Import Bedrock.Word NArith NPeano Euclid.
Require Import List Sumbool Vector.
Module PseudoConversion <: Conversion Pseudo AlmostQhasm.
Import AlmostQhasm EvalUtil ListState Pseudo ListNotations.
Section Conv.
Variable w: nat.
Variable s: Width w.
Definition MMap := NatM.t (Mapping w).
Definition mempty := NatM.empty (Mapping w).
Definition FMap := NatM.t (AlmostProgram * (list (Mapping w))).
Definition fempty := NatM.empty (AlmostProgram * (list (Mapping w))).
Transparent MMap FMap.
Definition getStart {n m} (prog: @Pseudo w s n m) :=
let ns := (fix getStart' {n' m'} (prog': @Pseudo w s n' m') :=
match prog' with
| PVar _ _ i => [proj1_sig i]
| PBin _ _ p => getStart' p
| PDual _ _ p => getStart' p
| PCarry _ _ p => getStart' p
| PShift _ _ _ p => getStart' p
| PFunExp _ p _ => getStart' p
| PCall _ _ _ p => getStart' p
| PIf _ _ _ _ _ l r => (getStart' l) ++ (getStart' r)
| PLet _ k _ a b => (n + k) :: (getStart' a) ++ (getStart' b)
| PComb _ _ _ a b => (getStart' a) ++ (getStart' b)
| _ => []
end) _ _ prog in
(fix maxN (lst: list nat) :=
match lst with
| [] => O
| x :: xs => max x (maxN xs)
end) (n :: m :: ns).
Definition addMap {T} (a b: (NatM.t T)) : NatM.t T :=
(fix add' (m: NatM.t T) (elts: list (nat * T)%type) :=
match elts with
| [] => m
| (k, v) :: elts' => add' (NatM.add k v m) elts'
end) a (NatM.elements b).
Fixpoint convertProgram' {n m} (prog: @Pseudo w s n m) (start: nat) (M: MMap) (F: FMap) :
option (AlmostProgram * (list (Mapping w)) * MMap * FMap) :=
let rM := fun (x: nat) => regM _ (reg s x) in
let sM := fun (x: nat) => stackM _ (stack s x) in
let reg' := reg s in
let stack' := stack s in
let const' := constant s in
let get := fun (k: nat) (default: nat -> Mapping w) (M': MMap) =>
match (NatM.find k M') with
| Some v => v
| _ => default k
end in
let madd := fun (a: nat) (default: nat -> Mapping w) (M': MMap) =>
NatM.add a (get a default M') M' in
let fadd := fun (k: nat) (f: AlmostProgram) (r: list (Mapping w)) =>
NatM.add k (f, r) in
let updateM := (
fix updateM' (k: nat) (mtmp: list (Mapping w)) (Miter: MMap) : MMap :=
match mtmp with
| [] => Miter
| a :: mtmp' => NatM.add k a (updateM' (S k) mtmp' Miter)
end) in
match prog with
| PVar n (Some true) i =>
Some (ASkip, [get i rM M], madd i rM M, F)
| PVar n (Some false) i =>
Some (ASkip, [get i sM M], madd i sM M, F)
| PVar n None i => (* assign to register by default *)
Some (ASkip, [get i rM M], madd i rM M, F)
| PConst n c =>
Some (AAssign (AConstInt (reg' start) (const' c)),
[get start rM M], madd start rM M, F)
| PMem n m v i =>
Some (AAssign (ARegMem (reg' start) (mem s v) i),
[get start rM M], madd start rM M, F)
| PBin n o p =>
match (convertProgram' p start M F) with
| Some (p', [regM (reg _ _ a); regM (reg _ _ b)], M', F') =>
Some (ASeq p' (AOp (IOpReg o (reg' a) (reg' b))),
[get a rM M'], madd a rM (madd b rM M'), F')
| Some (p', [regM (reg _ _ a); constM c], M', F') =>
Some (ASeq p' (AOp (IOpConst o (reg' a) c)),
[get a rM M'], madd a rM M', F')
| Some (p', [regM (reg _ _ a); memM _ b i], M', F') =>
Some (ASeq p' (AOp (IOpMem o (reg' a) b i)),
[get a rM M'], madd a rM M', F')
| Some (p', [regM (reg _ _ a); stackM (stack _ _ b)], M', F') =>
Some (ASeq p' (AOp (IOpStack o (reg' a) (stack' b))),
[get a rM M'], madd a rM (madd b sM M'), F')
| _ => None
end
| PCarry n o p =>
match (convertProgram' p start M F) with
| Some (p', [regM (reg _ _ a); regM (reg _ _ b)], M', F') =>
Some (ASeq p' (AOp (COp o (reg' a) (reg' b))),
[get a rM M'], madd a rM (madd b rM M'), F')
| _ => None
end
| PDual n o p =>
match (convertProgram' p (S start) M F) with
| Some (p', [regM (reg _ _ a); regM (reg _ _ b)], M', F') =>
Some (ASeq p' (AOp (DOp o (reg' a) (reg' b) (Some (reg' start)))),
[get a rM M'; get start rM M'],
madd a rM (madd b rM (madd start rM M')), F')
| _ => None
end
| PShift n o x p =>
match (convertProgram' p start M F) with
| Some (p', [regM (reg _ _ a)], M', F') =>
Some (ASeq p' (AOp (ROp o (reg' a) x)),
[get a rM M'], madd a rM M', F')
| _ => None
end
| PLet n k m f g =>
match (convertProgram' f start M F) with
| None => None
| Some (fp, fm, M', F') =>
(* Make sure all of the new variables are bound to their results *)
let M'' := updateM start fm M' in
(* Then convert the second program *)
match (convertProgram' g (start + (length fm)) M'' F') with
| None => None
| Some (gp, gm, M''', F'') => Some (ASeq fp gp, gm, M''', F'')
end
end
| PComb n a b f g =>
match (convertProgram' f start M F) with
| None => None
| Some (fp, fm, M', F') =>
match (convertProgram' g (start + (length fm)) M' F') with
| None => None
| Some (gp, gm, M'', F'') => Some (ASeq fp gp, fm ++ gm, M'', F'')
end
end
| PIf n m o i0 i1 l r =>
match (convertProgram' l start M F) with
| None => None
| Some (lp, lr, lM, lF) =>
match (convertProgram' r start lM lF) with
| None => None
| Some (rp, rr, M', F') =>
if (list_eq_dec mapping_dec lr rr)
then
match (get (proj1_sig i0) rM M, get (proj1_sig i1) rM M) with
| (regM r0, regM r1) => Some (ACond (CReg _ o r0 r1) lp rp, lr, M', F')
| (regM r, constM c) => Some (ACond (CConst _ o r c) lp rp, lr, M', F')
| _ => None
end
else None
end
end
| PFunExp n f e =>
match (convertProgram' f (S start) M F) with
| Some (fp, fr, M', F') =>
let a := start in
Some (ASeq
(AAssign (AConstInt (reg' a) (const' (natToWord _ O))))
(AWhile (CConst _ TLt (reg' a) (const' (natToWord _ e)))
(ASeq fp (AOp (IOpConst IAdd (reg' a) (const' (natToWord _ 1)))))),
fr, madd a rM M', F')
| _ => None
end
| PCall n m lbl f =>
match (convertProgram' f start M F) with
| Some (fp, fr, M', F') =>
let F'' := NatM.add lbl (fp, fr) F' in
Some (ACall lbl, fr, M', F'')
| None => None
end
end.
End Conv.
Definition convertProgram x y (prog: Program x) : option (AlmostQhasm.Program y) :=
let vs := max (inputs x) (outputs x) in
let M0 := mempty (width x) in
let F0 := fempty (width x) in
match (convertProgram' (width x) (spec x) prog vs M0 F0) with
| Some (prog', _, M, F) =>
Some (fold_left
(fun p0 t => match t with | (k, (v, _)) => ADef k v p0 end)
prog'
(of_list (NatM.elements F)))
| _ => None
end.
Fixpoint convertState x y (st: AlmostQhasm.State y) : option (State x) :=
let vars := max (inputs x) (outputs x) in
let try_cons := fun {T} (x: option T) (l: list T) =>
match x with | Some x' => x' :: l | _ => l end in
let get := fun i =>
match (FullState.getReg (reg (spec x) i) st,
FullState.getStack (stack (spec x) i) st) with
| (Some v, _) => Some v
| (_, Some v) => Some v
| _ => None
end in
let varList := (fix cs' (n: nat) :=
try_cons (get (vars - n)) (match n with | O => [] | S m => cs' m end)) vars in
match st with
| FullState.fullState _ _ memState _ carry =>
if (Nat.eq_dec (length varList) vars)
then Some (varList, memState, carry)
else None
end.
Lemma convert_spec: forall pa pb a a' b b' prog prog',
convertProgram pa pb prog = Some prog' ->
convertState pa pb a = Some a' ->
convertState pa pb b = Some b' ->
AlmostQhasm.evaluatesTo pb prog' a b <-> evaluatesTo pa prog a' b'.
Admitted.
End PseudoConversion.
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