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Fix tmOptimizedBind to avoid quadratic blowup #936

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Apr 12, 2023
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Fix tmOptimizedBind to avoid quadratic blowup #936

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12 changes: 10 additions & 2 deletions template-coq/theories/TemplateMonad/Core.v
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Original file line number Diff line number Diff line change
Expand Up @@ -70,17 +70,25 @@ Cumulative Inductive TemplateMonad@{t u} : Type@{t} -> Prop :=
.

(** This version of [tmBind] flattens nesting structure; using it in deeply recursive template programs can speed things up drastically *)
(** We use [tmBind] in the recursive position to avoid quadratic blowup in the number of [tmOptimizedBind]s *)
Fixpoint tmOptimizedBind@{t u} {A B : Type@{t}} (v : TemplateMonad@{t u} A) : (A -> TemplateMonad@{t u} B) -> TemplateMonad@{t u} B
:= match v with
| tmReturn x => fun f => f x
| tmBind v k => fun f => tmOptimizedBind v (fun v => tmOptimizedBind (k v) f)
| tmBind v k => fun f => tmOptimizedBind v (fun v => tmBind (k v) f)
| tmFail msg => fun _ => tmFail msg
| v => tmBind v
end.

(** Flatten nested [tmBind] *)
Fixpoint tmOptimize'@{t u} {A B : Type@{t}} (v : TemplateMonad@{t u} A) : (A -> TemplateMonad@{t u} B) -> TemplateMonad@{t u} B
:= match v with
| tmReturn x => fun f => f x
| tmBind v k => fun f => tmOptimize' v (fun v => tmOptimize' (k v) f)
| tmFail msg => fun _ => tmFail msg
| v => tmBind v
end.
Definition tmOptimize@{t u} {A : Type@{t}} (v : TemplateMonad@{t u} A) : TemplateMonad@{t u} A
:= tmOptimizedBind v tmReturn.
:= tmOptimize' v tmReturn.

(** This allow to use notations of MonadNotation *)
Definition TemplateMonad_UnoptimizedMonad@{t u} : Monad@{t u} TemplateMonad@{t u} :=
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