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+From Coq Require Export Morphisms RelationClasses List Bool Utf8 Setoid.
+Set Default Proof Using "Type".
+Export ListNotations.
+From Coq.Program Require Export Basics Syntax.
+Global Generalizable All Variables.
+
+(** * Type classes *)
+(** ** Decidable propositions *)
+(** This type class by (Spitters/van der Weegen, 2011) collects decidable
+propositions. *)
+Class Decision (P : Prop) := decide : {P} + {¬P}.
+Hint Mode Decision ! : typeclass_instances.
+Arguments decide _ {_} : simpl never, assert.
+
+(** ** Proof irrelevant types *)
+(** This type class collects types that are proof irrelevant. That means, all
+elements of the type are equal. We use this notion only used for propositions,
+but by universe polymorphism we can generalize it. *)
+Class ProofIrrel (A : Type) : Prop := proof_irrel (x y : A) : x = y.
+Hint Mode ProofIrrel ! : typeclass_instances.
+
+Class MGuard (M : Type → Type) :=
+  mguard: ∀ P {dec : Decision P} {A}, (P → M A) → M A.
+Arguments mguard _ _ _ !_ _ _ / : assert.
+Notation "'guard' P ; z" := (mguard P (λ _, z))
+  (at level 20, z at level 200, only parsing, right associativity) .
+Notation "'guard' P 'as' H ; z" := (mguard P (λ H, z))
+  (at level 20, z at level 200, only parsing, right associativity) .