{-| Module  : FiniteCategories
Description : Functions to convert all functor types.
Copyright   : Guillaume Sabbagh 2021
License     : GPL-3
Maintainer  : guillaumesabbagh@protonmail.com
Stability   : experimental
Portability : portable

Functions to convert all functor types.
-}

module Diagram.Conversion
(
    -- * Diagram to something
    diagramToFinFunctor,
    diagramToPartialFunctor,
    -- * FinFunctor to something
    finFunctorToDiagram,
    finFunctorToPartialFunctor,
    -- * PartialFunctor to something
    partialFunctorToDiagram,
    partialFunctorToFinFunctor
)
where
    import FiniteCategory.FiniteCategory
    import Diagram.Diagram
    import Cat.FinCat
    import Cat.PartialFinCat
    import Utils.SetList
    import Utils.AssociationList
    
    -- | Converts a homogeneous `Diagram` to a `FinFunctor`.
    diagramToFinFunctor :: (FiniteCategory c m o, Morphism m o) => Diagram c m o c m o -> FinFunctor c m o
    diagramToFinFunctor Diagram{src=s,tgt=t,omap=om,mmap=fm} = FinFunctor{srcF=s,tgtF=t,omapF=om,mmapF=fm}
    
    -- | Converts a homogeneous `Diagram` to a `PartialFunctor`
    diagramToPartialFunctor :: (FiniteCategory c m o, Morphism m o) => Diagram c m o c m o -> PartialFunctor c m o
    diagramToPartialFunctor Diagram{src=s,tgt=t,omap=om,mmap=fm} = PartialFunctor{srcPF=s,tgtPF=t,omapPF=om,mmapPF=fm}
    
    -- | Converts a `FinFunctor` into a `Diagram`.
    --
    -- A `FinFunctor` is a morphism of the `FinCat` category, it is a homogeneous FinFunctor. This functions casts it to a heterogeneous FinFunctor (i.e. a `Diagram`).
    finFunctorToDiagram :: FinFunctor c m o -> Diagram c m o c m o
    finFunctorToDiagram FinFunctor{srcF=s,tgtF=t,omapF=om,mmapF=fm} = Diagram {src=s,tgt=t,omap=om,mmap=fm}
    
    -- | Converts a total functor to a partial functor.
    finFunctorToPartialFunctor :: (FiniteCategory c m o, Morphism m o) => (FinFunctor c m o) -> (PartialFunctor c m o)
    finFunctorToPartialFunctor FinFunctor{srcF=s,tgtF=t,omapF=om,mmapF=fm} = PartialFunctor{srcPF=s,tgtPF=t,omapPF=om,mmapPF=fm}
    
    -- | Try to convert a `PartialFunctor` into a `Diagram` if it can (if it is total).
    partialFunctorToDiagram :: (FiniteCategory c m o, Morphism m o, Eq m, Eq o, Show o, Show m) => PartialFunctor c m o -> Maybe (Diagram c m o c m o)
    partialFunctorToDiagram x = finFunctorToDiagram <$> partialFunctorToFinFunctor x
    
    -- | Try to convert a partial functor to a total functor if it is possible.
    partialFunctorToFinFunctor :: (FiniteCategory c m o, Morphism m o, Eq m, Eq o, Show o, Show m) => (PartialFunctor c m o) -> Maybe (FinFunctor c m o)
    partialFunctorToFinFunctor PartialFunctor{srcPF=s,tgtPF=t,omapPF=om,mmapPF=fm}
        | not ((keys om) `doubleInclusion` (ob s)) = error $ (show $ ob s) ++"," ++ (show $ keys om)--Nothing
        | not ((keys fm) `doubleInclusion` (arrows s)) = error $ (show $ arrows s) ++"," ++ (show $ keys fm)--Nothing
        | otherwise = Just FinFunctor{srcF=s,tgtF=t,omapF=om,mmapF=fm}