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(** * Linearize: Place all and only operations in let binders *)
Require Import Crypto.Reflection.Syntax.
Require Import Crypto.Reflection.SmartMap.
Require Import Crypto.Util.Tactics.
Local Open Scope ctype_scope.
Section language.
Context {base_type_code : Type}
{op : flat_type base_type_code -> flat_type base_type_code -> Type}.
Local Notation flat_type := (flat_type base_type_code).
Local Notation type := (type base_type_code).
Local Notation Tbase := (@Tbase base_type_code).
Local Notation Expr := (@Expr base_type_code op).
Section with_var.
Context {var : base_type_code -> Type}.
Local Notation exprf := (@exprf base_type_code op var).
Local Notation expr := (@expr base_type_code op var).
Section under_lets.
Fixpoint under_letsf {t} (e : exprf t)
: forall {tC} (C : interp_flat_type var t -> exprf tC), exprf tC
:= match e in Syntax.exprf _ _ t return forall {tC} (C : interp_flat_type var t -> exprf tC), exprf tC with
| LetIn _ ex _ eC
=> fun _ C => @under_letsf _ ex _ (fun v => @under_letsf _ (eC v) _ C)
| TT => fun _ C => C tt
| Var _ x => fun _ C => C x
| Op _ _ op args as e => fun _ C => LetIn e C
| Pair A x B y => fun _ C => @under_letsf A x _ (fun x =>
@under_letsf B y _ (fun y =>
C (x, y)))
end.
End under_lets.
Fixpoint linearizef {t} (e : exprf t) : exprf t
:= match e in Syntax.exprf _ _ t return exprf t with
| LetIn _ ex _ eC
=> under_letsf (@linearizef _ ex) (fun x => @linearizef _ (eC x))
| TT => TT
| Var _ x => Var x
| Op _ _ op args
=> under_letsf (@linearizef _ args) (fun args => LetIn (Op op (SmartVarf args)) SmartVarf)
| Pair A ex B ey
=> under_letsf (@linearizef _ ex) (fun x =>
under_letsf (@linearizef _ ey) (fun y =>
SmartVarf (t:=Prod A B) (x, y)))
end.
Definition linearize {t} (e : expr t) : expr t
:= match e in Syntax.expr _ _ t return expr t with
| Abs _ _ f => Abs (fun x => linearizef (f x))
end.
End with_var.
Definition Linearize {t} (e : Expr t) : Expr t
:= fun var => linearize (e _).
End language.
Global Arguments under_letsf {_ _ _ _} _ {tC} _.
Global Arguments linearizef {_ _ _ _} _.
Global Arguments linearize {_ _ _ _} _.
Global Arguments Linearize {_ _ _} _ var.
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