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(** * Linearize: Place all and only operations in let binders *)
Require Import Crypto.Reflection.Syntax.
Require Import Crypto.Util.Tactics.
Local Open Scope ctype_scope.
Section language.
Context (base_type_code : Type).
Context (interp_base_type : base_type_code -> Type).
Context (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).
Let Tbase := @Tbase base_type_code.
Local Coercion Tbase : base_type_code >-> Syntax.flat_type.
Local Notation interp_type := (interp_type interp_base_type).
Local Notation interp_flat_type_gen := interp_flat_type.
Local Notation interp_flat_type := (interp_flat_type interp_base_type).
Local Notation Expr := (@Expr base_type_code interp_base_type op).
Section with_var.
Context {var : base_type_code -> Type}.
Local Notation exprf := (@exprf base_type_code interp_base_type op var).
Local Notation expr := (@expr base_type_code interp_base_type op var).
Section under_lets.
Fixpoint let_bind_const {t} (e : interp_flat_type t) {struct t}
: forall {tC} (C : interp_flat_type_gen var t -> exprf tC), exprf tC
:= match t return forall (e : interp_flat_type t) {tC} (C : interp_flat_type_gen var t -> exprf tC), exprf tC with
| Prod A B => fun e _ C => @let_bind_const A (fst e) _ (fun x =>
@let_bind_const B (snd e) _ (fun y =>
C (x, y)))
| Syntax.Tbase _ => fun e _ C => LetIn (Const e) C
end e.
Fixpoint under_letsf {t} (e : exprf t)
: forall {tC} (C : interp_flat_type_gen var t -> exprf tC), exprf tC
:= match e in Syntax.exprf _ _ _ t return forall {tC} (C : interp_flat_type_gen var t -> exprf tC), exprf tC with
| LetIn _ ex _ eC
=> fun _ C => @under_letsf _ ex _ (fun v => @under_letsf _ (eC v) _ C)
| Const _ x => fun _ C => let_bind_const x C
| 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))
| Const _ x => Const x
| 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.
Fixpoint linearize {t} (e : expr t) : expr t
:= match e in Syntax.expr _ _ _ t return expr t with
| Return _ x => linearizef x
| Abs _ _ f => Abs (fun x => @linearize _ (f x))
end.
End with_var.
Definition Linearize {t} (e : Expr t) : Expr t
:= fun var => linearize (e _).
End language.
Global Arguments let_bind_const {_ _ _ _ t} _ {tC} _.
Global Arguments under_letsf {_ _ _ _ _} _ {tC} _.
Global Arguments linearizef {_ _ _ _ _} _.
Global Arguments linearize {_ _ _ _ _} _.
Global Arguments Linearize {_ _ _ _} _ var.
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