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Require Import Crypto.Language.
Require Import Crypto.Util.Notations.
Module Compilers.
Export Language.Compilers.
Import invert_expr.
Module SubstVarLike.
Section with_ident.
Context {base_type : Type}.
Local Notation type := (type.type base_type).
Context {ident : type -> Type}.
Local Notation expr := (@expr.expr base_type ident).
Section with_var.
Context {var : type -> Type}.
Section with_var_like.
Context (is_var_like : forall t, @expr var t -> bool).
Fixpoint subst_var_like {t} (e : @expr (@expr var) t) : @expr var t
:= match e with
| expr.LetIn tx tC ex eC
=> let ex' := @subst_var_like tx ex in
let eC' := fun v => @subst_var_like tC (eC v) in
if is_var_like _ ex'
then eC' ex'
else expr.LetIn ex' (fun v => eC' ($v))
| expr.App s d f x
=> let f' := @subst_var_like _ f in
let x' := @subst_var_like _ x in
expr.App f' x'
| expr.Abs s d f
=> expr.Abs (fun v => @subst_var_like _ (f ($v)))
| expr.Var t v => v
| expr.Ident t idc => expr.Ident idc
end%expr.
End with_var_like.
Section with_ident_like.
Context (ident_is_good : forall t, ident t -> bool).
Fixpoint is_recursively_var_or_ident {t} (e : @expr var t) : bool
:= match e with
| expr.Ident t idc => ident_is_good _ idc
| expr.Var t v => true
| expr.Abs s d f => false
| expr.App s d f x
=> andb (@is_recursively_var_or_ident _ f)
(@is_recursively_var_or_ident _ x)
| expr.LetIn A B x f => false
end.
End with_ident_like.
End with_var.
Definition SubstVarLike (is_var_like : forall var t, @expr var t -> bool)
{t} (e : expr.Expr t) : expr.Expr t
:= fun var => subst_var_like (is_var_like _) (e _).
Definition SubstVar {t} (e : expr.Expr t) : expr.Expr t
:= SubstVarLike (fun _ _ e => match invert_Var e with Some _ => true | None => false end) e.
Definition SubstVarOrIdent (should_subst_ident : forall t, ident t -> bool)
{t} (e : expr.Expr t) : expr.Expr t
:= SubstVarLike (fun var t => is_recursively_var_or_ident should_subst_ident) e.
End with_ident.
Definition ident_is_var_like {t} (idc : ident t) : bool
:= match idc with
| ident.Literal _ _
| ident.nil _
| ident.cons _
| ident.pair _ _
| ident.fst _ _
| ident.snd _ _
| ident.Z_opp
| ident.Z_cast _
| ident.Z_cast2 _
=> true
| _ => false
end.
Definition is_var_fst_snd_pair_opp_cast {var} {t} (e : expr (var:=var) t) : bool
:= @is_recursively_var_or_ident base.type ident var (@ident_is_var_like) t e.
Definition IsVarFstSndPairOppCast {t} (e : expr.Expr t) : bool
:= @is_var_fst_snd_pair_opp_cast (fun _ => unit) t (e _).
Definition SubstVarFstSndPairOppCast {t} (e : expr.Expr t) : expr.Expr t
:= @SubstVarOrIdent base.type ident (@ident_is_var_like) t e.
End SubstVarLike.
Module UnderLets.
Section with_var.
Context {base_type : Type}.
Local Notation type := (type base_type).
Context {ident : type -> Type}
{var : type -> Type}.
Local Notation expr := (@expr base_type ident var).
Inductive UnderLets {T : Type} :=
| Base (v : T)
| UnderLet {A} (x : expr A) (f : var A -> UnderLets).
Fixpoint splice {A B} (x : @UnderLets A) (e : A -> @UnderLets B) : @UnderLets B
:= match x with
| Base v => e v
| UnderLet A x f => UnderLet x (fun v => @splice _ _ (f v) e)
end.
Fixpoint splice_list {A B} (ls : list (@UnderLets A)) (e : list A -> @UnderLets B) : @UnderLets B
:= match ls with
| nil => e nil
| cons x xs
=> splice x (fun x => @splice_list A B xs (fun xs => e (cons x xs)))
end.
Definition splice_option {A B} (v : option (@UnderLets A)) (e : option A -> @UnderLets B) : @UnderLets B
:= match v with
| None => e None
| Some x
=> splice x (fun x => e (Some x))
end.
Fixpoint to_expr {t} (x : @UnderLets (expr t)) : expr t
:= match x with
| Base v => v
| UnderLet A x f
=> expr.LetIn x (fun v => @to_expr _ (f v))
end.
Fixpoint of_expr {t} (x : expr t) : @UnderLets (expr t)
:= match x in expr.expr t return @UnderLets (expr t) with
| expr.LetIn A B x f
=> UnderLet x (fun v => @of_expr B (f v))
| e => Base e
end.
End with_var.
Module Export Notations.
Global Arguments UnderLets : clear implicits.
Delimit Scope under_lets_scope with under_lets.
Bind Scope under_lets_scope with UnderLets.UnderLets.
Notation "x <-- y ; f" := (UnderLets.splice y (fun x => f%under_lets)) : under_lets_scope.
Notation "x <---- y ; f" := (UnderLets.splice_list y (fun x => f%under_lets)) : under_lets_scope.
Notation "x <----- y ; f" := (UnderLets.splice_option y (fun x => f%under_lets)) : under_lets_scope.
End Notations.
Section with_var2.
Context {base_type : Type}.
Local Notation type := (type base_type).
Context {ident1 var1 ident2 var2 : type -> Type}.
Section map.
Context (f : forall t, @expr base_type ident1 var1 t -> @expr base_type ident2 var2 t)
(f' : forall t, var2 t -> var1 t)
{T : Type}.
Fixpoint map (x : @UnderLets base_type ident1 var1 T) : @UnderLets base_type ident2 var2 T
:= match x with
| UnderLet A x F
=> UnderLet (f A x) (fun v => map (F (f' A v)))
| Base x => Base x
end.
End map.
Section flat_map.
Context (f : forall t, @expr base_type ident1 var1 t -> @UnderLets base_type ident2 var2 (@expr base_type ident2 var2 t))
(f' : forall t, var2 t -> var1 t)
{T : Type}.
Fixpoint flat_map (x : @UnderLets base_type ident1 var1 T) : @UnderLets base_type ident2 var2 T
:= match x with
| UnderLet A x F
=> splice (f A x) (fun v => UnderLet v (fun v => flat_map (F (f' A v))))
| Base x => Base x
end.
End flat_map.
End with_var2.
Section reify.
Context {var : type.type base.type -> Type}.
Local Notation type := (type.type base.type).
Local Notation expr := (@expr.expr base.type ident var).
Local Notation UnderLets := (@UnderLets.UnderLets base.type ident var).
Let type_base (t : base.type) : type := type.base t.
Coercion type_base : base.type >-> type.
Let default_reify_and_let_binds_base_cps {t : base.type} : expr t -> forall T, (expr t -> UnderLets T) -> UnderLets T
:= fun e T k
=> match invert_expr.invert_Var e with
| Some v => k ($v)%expr
| None => if SubstVarLike.is_var_fst_snd_pair_opp_cast e
then k e
else UnderLets.UnderLet e (fun v => k ($v)%expr)
end.
Fixpoint reify_and_let_binds_base_cps {t : base.type} : expr t -> forall T, (expr t -> UnderLets T) -> UnderLets T
:= match t return expr t -> forall T, (expr t -> UnderLets T) -> UnderLets T with
| base.type.type_base t
=> fun e T k
=> match invert_Literal e with
| Some v => k (expr.Ident (ident.Literal v))
| None => @default_reify_and_let_binds_base_cps _ e T k
end
| base.type.prod A B
=> fun e T k
=> match invert_pair e with
| Some (a, b)
=> @reify_and_let_binds_base_cps
A a _
(fun ae
=> @reify_and_let_binds_base_cps
B b _
(fun be
=> k (ae, be)%expr))
| None => @default_reify_and_let_binds_base_cps _ e T k
end
| base.type.list A
=> fun e T k
=> match reflect_list e with
| Some ls
=> list_rect
_
(fun k => k []%expr)
(fun x _ rec k
=> @reify_and_let_binds_base_cps
A x _
(fun xe
=> rec (fun xse => k (xe :: xse)%expr)))
ls
k
| None => @default_reify_and_let_binds_base_cps _ e T k
end
| base.type.option A
=> fun e T k
=> match reflect_option e with
| Some ls
=> option_rect
_
(fun x k
=> @reify_and_let_binds_base_cps
A x _
(fun xe
=> k (#ident.Some @ xe)%expr))
(fun k => k (#ident.None)%expr)
ls
k
| None => @default_reify_and_let_binds_base_cps _ e T k
end
end%under_lets.
Fixpoint let_bind_return {t} : expr t -> expr t
:= match t return expr t -> expr t with
| type.base t
=> fun e => to_expr (v <-- of_expr e; reify_and_let_binds_base_cps v _ Base)
| type.arrow s d
=> fun e
=> expr.Abs (fun v => @let_bind_return
d
match invert_Abs e with
| Some f => f v
| None => e @ $v
end%expr)
end.
End reify.
Definition LetBindReturn {t} (e : expr.Expr t) : expr.Expr t
:= fun var => let_bind_return (e _).
End UnderLets.
Export UnderLets.Notations.
End Compilers.
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