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Require Import QhasmEvalCommon QhasmUtil State.
Require Import Language.
Require Import List.
Module Type PseudoMachine.
Parameter width: nat.
Parameter vars: nat.
Parameter width_spec: Width width.
End PseudoMachine.
Module Pseudo (M: PseudoMachine) <: Language.
Import EvalUtil ListState Util M.
Definition const: Type := word width.
(* Program Types *)
Inductive Pseudo: nat -> nat -> Type :=
(* Some true for registers, false for stack, None for default *)
| PVar: forall n, option bool -> Index n -> Pseudo n 1
| PMem: forall n m, Index n -> Index m -> 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
| PCarry: forall n, CarryOp -> Pseudo n 2 -> Pseudo n 1
| PShift: forall n, RotOp -> Index width -> Pseudo n 1 -> Pseudo n 1
| 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
| 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)
| PCall: forall n m, Label -> Pseudo n m -> Pseudo n m.
Hint Constructors Pseudo.
Definition Program := Pseudo vars vars.
Definition State := ListState width.
Fixpoint pseudoEval {n m} (prog: Pseudo n m) (st: State): option State :=
match prog with
| PVar n _ i => omap (getVar i st) (fun x => Some (setList [x] st))
| PMem n m v i => omap (getMem v i st) (fun x => Some (setList [x] st))
| PConst n c => Some (setList [c] st)
| PBin n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp) with
| [wa; wb] =>
let (v, c) := evalIntOp o wa wb in
Some (setList [v] (setCarryOpt c sp))
| _ => None
end)
| PCarry n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp, getCarry sp) with
| ([wa; wb], Some c) =>
let (v, c') := evalCarryOp o wa wb c in
Some (setList [v] (setCarry c' sp))
| _ => None
end)
| PDual n o p =>
omap (pseudoEval p st) (fun sp =>
match (getList sp) with
| [wa; wb] =>
let (low, high) := evalDualOp o wa wb in
Some (setList [low; high] sp)
| _ => None
end)
| PShift n o a x =>
omap (pseudoEval x st) (fun sx =>
match (getList sx) with
| [wx] => Some (setList [evalRotOp o wx a] sx)
| _ => None
end)
| PLet n k m f g =>
omap (pseudoEval f st) (fun sf =>
omap (pseudoEval g (setList ((getList st) ++ (getList sf)) sf))
(fun sg => Some sg))
| PComb n a b f g =>
omap (pseudoEval f st) (fun sf =>
omap (pseudoEval g st) (fun sg =>
Some (setList ((getList sf) ++ (getList sg)) sg)))
| PIf n m t i0 i1 l r =>
omap (getVar i0 st) (fun v0 =>
omap (getVar i1 st) (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'' =>
omap (pseudoEval p st') (fun st'' =>
funexpseudo e'' st'')
end) e st
| PCall n m _ p => pseudoEval p st
end.
Definition evaluatesTo := fun (p: Program) (st st': State) => (pseudoEval p st = Some st').
Module Notations.
Delimit Scope pseudo_notations with p.
Open Scope pseudo_notations.
Definition indexize (n: nat) (p: (n > 0)%nat) (x: nat): Index n.
intros; exists (x mod n);
abstract (pose proof (mod_bound_pos x n); omega).
Defined.
Notation "% A" := (PVar _ (Some false) (indexize _ _ A))
(at level 20, right associativity) : pseudo_notations.
Notation "$ A" := (PVar _ (Some true) (indexize _ _ A))
(at level 20, right associativity) : pseudo_notations.
Notation "'MEM' ( A , B )" := (PMem _ _ (indexize _ _ A) (indexize _ _ B))
(at level 20, right associativity) : pseudo_notations.
Notation "# A" := (PConst _ (natToWord _ A))
(at level 20, right associativity) : pseudo_notations.
Notation "A :+: B" := (PBin _ Add (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :+c: B" := (PCarry _ AddWithCarry (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :-: B" := (PBin _ Sub (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :&: B" := (PBin _ And (PComb _ _ _ A B))
(at level 45, right associativity) : pseudo_notations.
Notation "A :^: B" := (PBin _ Xor (PComb _ _ _ A B))
(at level 45, right associativity) : pseudo_notations.
Notation "A :|: B" := (PBin _ Or (PComb _ _ _ A B))
(at level 60, right associativity) : pseudo_notations.
Notation "A :>>: B" := (PShift _ Shr (indexize _ _ B) A)
(at level 60, right associativity) : pseudo_notations.
Notation "A :<<: B" := (PShift _ Shl (indexize _ _ B) A)
(at level 60, right associativity) : pseudo_notations.
Notation "A :**: B" := (PDual _ Mult (PComb _ _ _ A B))
(at level 55, right associativity) : pseudo_notations.
Notation "'IF' O ( A , B ) 'THEN' L 'ELSE' R" :=
(PIf _ _ O (indexize _ _ A) (indexize _ _ B) L R)
(at level 70, left associativity) : pseudo_notations.
Notation "'EXP' ( e ) ( F )" :=
(PFunExp _ F e)
(at level 70, left associativity) : pseudo_notations.
Notation "'LET' E 'IN' F" :=
(PLet _ _ _ E F)
(at level 70, left associativity) : pseudo_notations.
Notation "A | B" :=
(PComb _ _ _ A B)
(at level 65, left associativity) : pseudo_notations.
Notation "'CALL' n ::: A" :=
(PCall _ _ n A)
(at level 65, left associativity) : pseudo_notations.
Definition p0: Pseudo 1 2.
refine (CALL 0 ::: %0 :**: $0); intuition.
Defined.
End Notations.
(* world peace *)
End Pseudo.
Module PseudoUnary32 <: PseudoMachine.
Definition width := 32.
Definition vars := 1.
Definition width_spec := W32.
Definition const: Type := word width.
End PseudoUnary32.
Module PseudoUnary64 <: PseudoMachine.
Definition width := 64.
Definition vars := 1.
Definition width_spec := W64.
Definition const: Type := word width.
End PseudoUnary64.
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