Modules

categorical-crypto

  • Prelude

CategoricalCrypto

  • CategoricalCrypto
  • Abstract
  • Abstract2
  • Abstract2.Equivalence
  • Abstract2.Morphism
  • Abstract2.OAPEmulation
  • Abstract2.WideSubcategory
  • Channel.Category
  • Channel.Core
  • Channel.Selection
  • Examples.Basic
  • Examples.Commitment
  • Examples.RelSetup
  • Examples.Signatures
  • FamilyCategory
  • Machine.Constraints
  • Machine.Core
  • MachineAxioms
  • RandomOracle
  • RandomOracle2
  • SFunM
  • Standard
  • Standard2
  • Standard2.Morphism
  • StandardTV
  • UCSetup
  • UCSetup.Morphism
  • VanishingTV

Categories

  • Actegory
  • Actegory.Underlying
  • Category.EquivClosureHelper
  • Coherence.Monoidal
  • Coherence.Monoidal.Compare
  • Coherence.Monoidal.Diagram
  • Coherence.Monoidal.Frontend
  • Coherence.Monoidal.Frontend.Core
  • Coherence.Monoidal.Frontend.Sigma
  • Coherence.Monoidal.MacLane
  • Coherence.Monoidal.Normalize
  • Coherence.Monoidal.Reflect
  • Coherence.Monoidal.Sigma
  • Coherence.Monoidal.Test.Frontend
  • Coherence.Monoidal.Test.InterchangeStress
  • Coherence.Monoidal.Test.Limitations
  • Coherence.Monoidal.Test.SigmaFrontend
  • Coherence.Monoidal.WireCoherence
  • CoherenceIsos
  • Diagram.Coend.Ext.Setoids
  • Discrete
  • FreeMonoidal
  • FreeStrictMonoidal
  • Functor.Monoidal.CurriedTensor
  • Functor.Monoidal.CurriedTensor.Properties
  • Functor.Monoidal.Properties.Ext
  • Functor.Presheaf.Morphism
  • GradedKleisli
  • GradedKleisli.Functorial
  • GradedKleisli.Functorial.Category
  • GradedKleisli.Regrade
  • KernelCongruence
  • KernelCongruence.Reindex
  • LocallyGraded
  • LocallyGraded.FreeActegory
  • LocallyGraded.FreeActegory.Kleisli
  • LocallyGraded.Kleisli
  • Monad.Graded.Ext
  • Monad.Graded.Morphism
  • Monad.Graded.Pullback
  • Monad.Graded.Uncurried
  • Morphism.Reasoning.Ext
  • NaturalTransformationHelper
  • Properties

Class

  • Monad.Ext

Data

  • List.Properties.Ext
  • Maybe.Ext
  • Nat.Poly

LibExt

  • LibExt
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{-# OPTIONS --cubical-compatible #-}
module Class.Monad.Instances where
 
open import Class.Prelude
open import Class.Functor.Core
open import Class.Applicative
open import Class.Monad.Core
open import Class.Monad.Id
 
instance
Monad-TC : Monad TC
Monad-TC = record {R}
where import Reflection as R renaming (pure to return)
 
Monad-List : Monad List
Monad-List = λ where
.return → _∷ []
._>>=_ → flip concatMap
 
Monad-Maybe : Monad Maybe
Monad-Maybe = λ where
.return → just
._>>=_ → Maybe._>>=_
where import Data.Maybe as Maybe
 
MonadLaws-Maybe : MonadLaws Maybe
MonadLaws-Maybe = λ where
.>>=-identityˡ → refl
.>>=-identityʳ → λ where
(just _) → refl
nothing → refl
.>>=-assoc → λ where
(just _) → refl
nothing → refl