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Require Import Coq.FSets.FMapPositive Coq.PArith.BinPos Coq.Lists.List.
Set Asymmetric Patterns.
Notation eta x := (fst x, snd x).
Inductive expr {var : Type} : Type :=
| Const : expr
| LetIn : expr -> (var -> expr) -> expr.
Definition Expr := forall var, @expr var.
Fixpoint count_binders (e : @expr unit) : nat :=
match e with
| LetIn _ eC => 1 + @count_binders (eC tt)
| _ => 0
end.
Definition CountBinders (e : Expr) : nat := count_binders (e _).
Class Context (Name : Type) (var : Type) :=
{ ContextT : Type;
extendb : ContextT -> Name -> var -> ContextT;
empty : ContextT }.
Coercion ContextT : Context >-> Sortclass.
Arguments ContextT {_ _ _}, {_ _} _.
Arguments extendb {_ _ _} _ _ _.
Arguments empty {_ _ _}.
Module Export Named.
Inductive expr Name : Type :=
| Const : expr Name
| LetIn : Name -> expr Name -> expr Name -> expr Name.
End Named.
Global Arguments Const {_}.
Global Arguments LetIn {_} _ _ _.
Definition split_onames {Name : Type} (ls : list (option Name))
: option (Name) * list (option Name)
:= match ls with
| cons n ls'
=> (n, ls')
| nil => (None, nil)
end.
Section internal.
Context (InName OutName : Type)
{InContext : Context InName (OutName)}
{ReverseContext : Context OutName (InName)}
(InName_beq : InName -> InName -> bool).
Fixpoint register_reassign (ctxi : InContext) (ctxr : ReverseContext)
(e : expr InName) (new_names : list (option OutName))
: option (expr OutName)
:= match e in Named.expr _ return option (expr _) with
| Const => Some Const
| LetIn n ex eC
=> let '(n', new_names') := eta (split_onames new_names) in
match n', @register_reassign ctxi ctxr ex nil with
| Some n', Some x
=> let ctxi := @extendb _ _ _ ctxi n n' in
let ctxr := @extendb _ _ _ ctxr n' n in
option_map (LetIn n' x) (@register_reassign ctxi ctxr eC new_names')
| None, Some x
=> let ctxi := ctxi in
@register_reassign ctxi ctxr eC new_names'
| _, None => None
end
end.
End internal.
Global Instance pos_context (var : Type) : Context positive var
:= { ContextT := PositiveMap.t var;
extendb ctx key v := PositiveMap.add key v ctx;
empty := PositiveMap.empty _ }.
Global Arguments register_reassign {_ _ _ _} ctxi ctxr e _.
Section language5.
Context (Name : Type).
Local Notation expr := (@Top.expr Name).
Local Notation nexpr := (@Named.expr Name).
Fixpoint ocompile (e : expr) (ls : list (option Name)) {struct e}
: option (nexpr)
:= match e in @Top.expr _ return option (nexpr) with
| Top.Const => Some Named.Const
| Top.LetIn ex eC
=> match @ocompile ex nil, split_onames ls with
| Some x, (Some n, ls')%core
=> option_map (fun C => Named.LetIn n x C) (@ocompile (eC n) ls')
| _, _ => None
end
end.
Definition compile (e : expr) (ls : list Name) := @ocompile e (List.map (@Some _) ls).
End language5.
Global Arguments compile {_} e ls.
Fixpoint merge_liveness (ls1 ls2 : list unit) :=
match ls1, ls2 with
| cons x xs, cons y ys => cons tt (@merge_liveness xs ys)
| nil, ls | ls, nil => ls
end.
Section internal1.
Context (Name : Type)
(OutName : Type)
{Context : Context Name (list unit)}.
Definition compute_livenessf_step
(compute_livenessf : forall (ctx : Context) (e : expr Name) (prefix : list unit), list unit)
(ctx : Context)
(e : expr Name) (prefix : list unit)
: list unit
:= match e with
| Const => prefix
| LetIn n ex eC
=> let lx := @compute_livenessf ctx ex prefix in
let lx := merge_liveness lx (prefix ++ repeat tt 1) in
let ctx := @extendb _ _ _ ctx n (lx) in
@compute_livenessf ctx eC (prefix ++ repeat tt 1)
end.
Fixpoint compute_liveness ctx e prefix
:= @compute_livenessf_step (@compute_liveness) ctx e prefix.
Fixpoint insert_dead_names_gen def (ls : list unit) (lsn : list OutName)
: list (option OutName)
:= match ls with
| nil => nil
| cons live xs
=> match lsn with
| cons n lsn' => Some n :: @insert_dead_names_gen def xs lsn'
| nil => def :: @insert_dead_names_gen def xs nil
end
end.
Definition insert_dead_names def (e : expr Name)
:= insert_dead_names_gen def (compute_liveness empty e nil).
End internal1.
Global Arguments insert_dead_names {_ _ _} def e lsn.
Definition Let_In {A P} (x : A) (f : forall a : A, P a) : P x := let y := x in f y.
Section language7.
Context {Context : Context unit (positive)}.
Local Notation nexpr := (@Named.expr unit).
Definition CompileAndEliminateDeadCode (e : Expr) (ls : list unit)
: option (nexpr)
:= let e := compile (Name:=positive) (e _) (List.map Pos.of_nat (seq 1 (CountBinders e))) in
match e with
| Some e => Let_In (insert_dead_names None e ls) (* help vm_compute by factoring this out *)
(fun names => register_reassign empty empty e names)
| None => None
end.
End language7.
Global Arguments CompileAndEliminateDeadCode {_} e ls.
Definition ContextOn {Name1 Name2} f {var} (Ctx : Context Name1 var) : Context Name2 var
:= {| ContextT := Ctx;
extendb ctx n v := extendb ctx (f n) v;
empty := empty |}.
Definition Register := Datatypes.unit.
Global Instance RegisterContext {var : Type} : Context Register var
:= ContextOn (fun _ => 1%positive) (pos_context var).
Definition syntax := Named.expr Register.
Definition AssembleSyntax e ls (res := CompileAndEliminateDeadCode e ls)
:= match res return match res with None => _ | _ => _ end with
| Some v => v
| None => I
end.
Definition dummy_registers (n : nat) : list Register
:= List.map (fun _ => tt) (seq 0 n).
Definition DefaultRegisters (e : Expr) : list Register
:= dummy_registers (CountBinders e).
Definition DefaultAssembleSyntax e := @AssembleSyntax e (DefaultRegisters e).
Notation "'slet' x := A 'in' b" := (Top.LetIn A (fun x => b)) (at level 200, b at level 200).
Notation "#[ var ]#" := (@Top.Const var).
Definition compiled_syntax : Expr := fun (var : Type) =>
(
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
slet x1 := #[ var ]# in
@Top.Const var).
Definition v :=
Eval cbv [compiled_syntax] in (DefaultAssembleSyntax (compiled_syntax)).
Timeout 2 Eval vm_compute in v.
|
