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Require Import QhasmEvalCommon QhasmUtil.
Require Import Language.
Require Import List.
Module Type PseudoMachine.
Parameter width: nat.
Parameter vars: nat.
Parameter width_spec: ISize width.
End PseudoMachine.
Module Pseudo (M: PseudoMachine) <: Language.
Import ListNotations State Util M.
Definition const: Type := word width.
(* Program Types *)
Definition State := list const.
Inductive Pseudo: nat -> nat -> Type :=
| PVar: forall n, Index n -> Pseudo n 1
| PConst: forall n, const -> Pseudo n 1
| PBin: forall n, IntOp -> Pseudo n 2 -> Pseudo n 1
| PDual: forall n, DualOp -> Pseudo n 2 -> Pseudo n 2
| PShift: forall n, RotOp -> Index width -> Pseudo n 1 -> Pseudo n 1
| PLet: forall n k m, Pseudo n k -> Pseudo (n + k) m -> Pseudo n m
| PComb: forall n a b, Pseudo n a -> Pseudo n b -> Pseudo n (a + b)
| PIf: forall n m, TestOp -> Index n -> Index n -> Pseudo n m -> Pseudo n m -> Pseudo n m
| PFunExp: forall n, Pseudo n n -> nat -> Pseudo n n.
Hint Constructors Pseudo.
Definition Program := Pseudo vars vars.
Definition applyBin (op: IntOp) (a b: word width): const :=
match op with
| IPlus => wplus a b
| IMinus => wminus a b
| IAnd => wand a b
| IXor => wxor a b
| IOr => wor a b
end.
Definition applyDual (op: DualOp) (a b: word width): list const :=
match op with
| Wmult =>
let wres := natToWord (width + width)
(N.to_nat ((wordToN a) * (wordToN b))) in
[split1 _ _ wres; split2 _ _ wres]
end.
Definition applyShift (op: RotOp) (v: const) (n: Index width): const.
refine match op with
| Shl => convert (Word.combine (wzero n) (split1 (width - n) n (convert v _))) _
| Shr => convert (Word.combine (split2 n (width - n) (convert v _)) (wzero n)) _
end; abstract (
unfold const;
destruct n; simpl;
replace (width - x + x) with width;
replace (x + (width - x)) with width;
intuition ).
Defined.
Fixpoint pseudoEval {n m} (prog: Pseudo n m) (st: State): option State :=
let option_map' := fun {A B: Type} (x: option A) (f: A -> option B) =>
match x with
| Some x' =>
match (f x') with
| Some res => Some res
| None => None
end
| _ => None
end in
match prog with
| PVar n i => option_map' (nth_error st i) (fun x => Some [x])
| PConst n c => Some ([c])
| PBin n o p =>
option_map' (pseudoEval p st) (fun sp =>
match sp with
| [wa; wb] => Some [applyBin o wa wb]
| _ => None
end)
| PDual n o p =>
option_map' (pseudoEval p st) (fun sp =>
match sp with
| [wa; wb] => Some (applyDual o wa wb)
| _ => None
end)
| PShift n o a x =>
option_map' (pseudoEval x st) (fun sx =>
match sx with
| [wx] => Some [applyShift o wx a]
| _ => None
end)
| PLet n k m f g =>
option_map' (pseudoEval f st) (fun sf =>
option_map' (pseudoEval g (st ++ sf))
(fun sg => Some sg))
| PComb n a b f g =>
option_map' (pseudoEval f st) (fun sf =>
option_map' (pseudoEval g st) (fun sg =>
Some (sf ++ sg)))
| PIf n m t i0 i1 l r =>
option_map' (nth_error st i0) (fun v0 =>
option_map' (nth_error st i1) (fun v1 =>
if (evalTest t v0 v1)
then pseudoEval l st
else pseudoEval r st ))
| PFunExp n p e =>
(fix funexpseudo (e': nat) (st': State) :=
match e' with
| O => Some st'
| S e'' =>
option_map' (pseudoEval p st') (fun st'' =>
funexpseudo e'' st'')
end) e st
end.
Definition evaluatesTo := fun (p: Program) (st st': State) => (pseudoEval p st = Some st').
(* world peace *)
End Pseudo.
Module PseudoUnary32 <: PseudoMachine.
Definition width := 32.
Definition vars := 1.
Definition width_spec := I32.
Definition const: Type := word width.
End PseudoUnary32.
Module PseudoUnary64 <: PseudoMachine.
Definition width := 64.
Definition vars := 1.
Definition width_spec := I64.
Definition const: Type := word width.
End PseudoUnary64.
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