diff options
Diffstat (limited to 'src/common/Monad.v')
| -rw-r--r-- | src/common/Monad.v | 61 |
1 files changed, 57 insertions, 4 deletions
diff --git a/src/common/Monad.v b/src/common/Monad.v index b7d97a1..cf3180b 100644 --- a/src/common/Monad.v +++ b/src/common/Monad.v @@ -18,6 +18,9 @@ From Coq Require Import Lists.List. +Declare Scope vericert_scope. +#[local] Open Scope vericert_scope. + Declare Scope monad_scope. Module Type Monad. @@ -27,10 +30,10 @@ Module Type Monad. Parameter ret : forall (A : Type) (x : A), mon A. Arguments ret [A]. - Parameter bind : forall (A B : Type) (f : mon A) (g : A -> mon B), mon B. + Parameter bind : forall (A B : Type) (g : A -> mon B) (f : mon A), mon B. Arguments bind [A B]. - Parameter bind2 : forall (A B C: Type) (f: mon (A * B)) (g: A -> B -> mon C), mon C. + Parameter bind2 : forall (A B C: Type) (g: A -> B -> mon C) (f: mon (A * B)), mon C. Arguments bind2 [A B C]. End Monad. @@ -41,10 +44,10 @@ Module MonadExtra(M : Monad). Module Import MonadNotation. Notation "'do' X <- A ; B" := - (bind A (fun X => B)) + (bind (fun X => B) A) (at level 200, X name, A at level 100, B at level 200) : monad_scope. Notation "'do' ( X , Y ) <- A ; B" := - (bind2 A (fun X Y => B)) + (bind2 (fun X Y => B) A) (at level 200, X name, Y name, A at level 100, B at level 200) : monad_scope. End MonadNotation. @@ -70,3 +73,53 @@ Module MonadExtra(M : Monad). fold_left (fun a b => do a' <- a; f a' b) l s. End MonadExtra. + +(** A [Params f n] instance forces the setoid rewriting mechanism not to +rewrite in the first [n] arguments of the function [f]. We will declare such +instances for all operational type classes in this development. *) +From Coq Require Export Morphisms RelationClasses. + +From Coq Require Setoid. + +Global Instance: Params (@Relation_Definitions.equiv) 2 := {}. + +Class MRet (M : Type -> Type) := mret: forall {A}, A -> M A. +Global Arguments mret {_ _ _} _ : assert. +Global Instance: Params (@mret) 3 := {}. +Global Hint Mode MRet ! : typeclass_instances. + +Class MBind (M : Type -> Type) := mbind : forall {A B}, (A -> M B) -> M A -> M B. +Global Arguments mbind {_ _ _ _} _ !_ / : assert. +Global Instance: Params (@mbind) 4 := {}. +Global Hint Mode MBind ! : typeclass_instances. + +Class MJoin (M : Type -> Type) := mjoin: forall {A}, M (M A) -> M A. +Global Arguments mjoin {_ _ _} !_ / : assert. +Global Instance: Params (@mjoin) 3 := {}. +Global Hint Mode MJoin ! : typeclass_instances. + +Class FMap (M : Type -> Type) := fmap : forall {A B}, (A -> B) -> M A -> M B. +Global Arguments fmap {_ _ _ _} _ !_ / : assert. +Global Instance: Params (@fmap) 4 := {}. +Global Hint Mode FMap ! : typeclass_instances. + +Class OMap (M : Type -> Type) := omap: forall {A B}, (A -> option B) -> M A -> M B. +Global Arguments omap {_ _ _ _} _ !_ / : assert. +Global Instance: Params (@omap) 4 := {}. +Global Hint Mode OMap ! : typeclass_instances. + +Notation "m ≫= f" := (mbind f m) (at level 60, right associativity) : vericert_scope. +Notation "( m ≫=.)" := (fun f => mbind f m) (only parsing) : vericert_scope. +Notation "(.≫= f )" := (mbind f) (only parsing) : vericert_scope. +Notation "(≫=)" := (fun m f => mbind f m) (only parsing) : vericert_scope. + +Notation "x ← y ; z" := (y ≫= (fun x : _ => z)) + (at level 20, y at level 100, z at level 200, only parsing) : vericert_scope. + +Notation "' x ← y ; z" := (y ≫= (fun x : _ => z)) + (at level 20, x pattern, y at level 100, z at level 200, only parsing) : vericert_scope. + +Infix "<$>" := fmap (at level 61, left associativity) : vericert_scope. + +Notation "x ;; z" := (x ≫= fun _ => z) + (at level 100, z at level 200, only parsing, right associativity): vericert_scope. |