{-| Module  : FiniteCategories
Description : Examples of Kan extensions pretty printed.
Copyright   : Guillaume Sabbagh 2023
License     : GPL-3
Maintainer  : guillaumesabbagh@protonmail.com
Stability   : experimental
Portability : portable

Examples of Kan extensions pretty printed.


-}
module Math.Functors.KanExtension.Example
(
    main
)
where
    import              Math.FiniteCategory
    import              Math.FiniteCategories
    import              Math.Functors.KanExtension
    import              Math.IO.PrettyPrint
    import              Math.FiniteCategory

    
    import              Data.WeakSet             (Set)
    import qualified    Data.WeakSet           as Set
    import              Data.WeakSet.Safe
    import              Data.WeakMap             (Map)
    import qualified    Data.WeakMap           as Map
    import              Data.WeakMap.Safe
    
    -- | Examples of Kan extensions pretty printed.

    main :: IO ()
    main :: IO ()
main = do
        String -> IO ()
putStrLn String
"Start of Math.Functors.KanExtension.Example"
        let d1 :: Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d1 = (Set
  (Diagram
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural)
-> [Diagram
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural]
forall a. Eq a => Set a -> [a]
setToList (Set
   (Diagram
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural)
 -> [Diagram
       (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
       (IsSmallerThan Natural)
       Natural
       (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
       (IsSmallerThan Natural)
       Natural])
-> Set
     (Diagram
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural)
-> [Diagram
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural]
forall a b. (a -> b) -> a -> b
$ FunctorCategory
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> Set
     (Diagram
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural)
forall c m o. FiniteCategory c m o => c -> Set o
ob (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
-> InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
-> FunctorCategory
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
forall c1 m1 o1 c2 m2 o2.
c1 -> c2 -> FunctorCategory c1 m1 o1 c2 m2 o2
FunctorCategory (Natural
-> InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
numberCategory Natural
2) (Natural
-> InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
numberCategory Natural
4)))[Diagram
   (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
   (IsSmallerThan Natural)
   Natural
   (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
   (IsSmallerThan Natural)
   Natural]
-> Int
-> Diagram
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
forall a. HasCallStack => [a] -> Int -> a
!! Int
3
        let d2 :: Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d2 = (Set
  (Diagram
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural)
-> [Diagram
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural]
forall a. Eq a => Set a -> [a]
setToList (Set
   (Diagram
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural)
 -> [Diagram
       (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
       (IsSmallerThan Natural)
       Natural
       (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
       (IsSmallerThan Natural)
       Natural])
-> Set
     (Diagram
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural)
-> [Diagram
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural
      (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
      (IsSmallerThan Natural)
      Natural]
forall a b. (a -> b) -> a -> b
$ FunctorCategory
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> Set
     (Diagram
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural)
forall c m o. FiniteCategory c m o => c -> Set o
ob (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
-> InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
-> FunctorCategory
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
forall c1 m1 o1 c2 m2 o2.
c1 -> c2 -> FunctorCategory c1 m1 o1 c2 m2 o2
FunctorCategory (Natural
-> InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
numberCategory Natural
2) (Natural
-> InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural
numberCategory Natural
3)))[Diagram
   (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
   (IsSmallerThan Natural)
   Natural
   (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
   (IsSmallerThan Natural)
   Natural]
-> Int
-> Diagram
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
forall a. HasCallStack => [a] -> Int -> a
!! Int
2
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> String
forall a. PrettyPrint a => a -> String
pprint Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d1 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> String
forall a. PrettyPrint a => a -> String
pprint Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d2 
        let Just (Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
lk,NaturalTransformation
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
lknat) = (Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> Diagram
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
-> Maybe
     (Diagram
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural,
      NaturalTransformation
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
leftKan Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d1 Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d2)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> String
forall a. PrettyPrint a => a -> String
pprint Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
lk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
lknat 
        let Just (Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
rk,NaturalTransformation
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
rknat) = (Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> Diagram
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
     (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
     (IsSmallerThan Natural)
     Natural
-> Maybe
     (Diagram
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural,
      NaturalTransformation
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural
        (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
        (IsSmallerThan Natural)
        Natural)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
rightKan Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d1 Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
d2)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> String
forall a. PrettyPrint a => a -> String
pprint Diagram
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
rk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
  (InheritedFullSubcategory Omega (IsSmallerThan Natural) Natural)
  (IsSmallerThan Natural)
  Natural
rknat 
        
        let a :: SCG
a = String -> SCG
unsafeReadSCGString String
"2\nA\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
a 
        let b :: SCG
b = String -> SCG
unsafeReadSCGString String
"2\nA -f-> B\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
b 
        let c :: SCG
c = String -> SCG
unsafeReadSCGString String
"2\nA -f-> B -g-> A = <ID>\nB -g-> A -f-> B = <ID>\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
c 
        let f :: SCGD
f = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\n</SRC>\n<TGT>\n2\nA -f-> B -g-> A = <ID>\nB -g-> A -f-> B = <ID>\n</TGT>\nA => A"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
f 
        let g :: SCGD
g = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\n</SRC>\n<TGT>\n2\nA -f-> B\n</TGT>\nA => A"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
g 
        
        let Just (SCGD
lk,NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
lknat) = (SCGD
-> SCGD
-> Maybe
     (SCGD,
      NaturalTransformation
        SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
leftKan SCGD
f SCGD
g)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
lk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
lknat 
        
        let Just (SCGD
rk,NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
rknat) = (SCGD
-> SCGD
-> Maybe
     (SCGD,
      NaturalTransformation
        SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
rightKan SCGD
f SCGD
g)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
rk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
rknat 
        
        
        let a :: SCG
a = String -> SCG
unsafeReadSCGString String
"2\nA\nB\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
a 
        let b :: SCG
b = String -> SCG
unsafeReadSCGString String
"2\nC -p1-> A\nC -p2-> B\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
b 
        let c :: SCG
c = String -> SCG
unsafeReadSCGString String
"2\n0 -abs-> 1\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
c 
        let f :: SCGD
f = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\nC -p1-> A\nC -p2-> B\n</TGT>\nA => A\nB => B\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
f 
        let x :: SCGD
x = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\n0 -abs-> 1\n</TGT>\nA => 1\nB => 1"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
x 
        
        -- let Just (lk,lknat) = (leftKan f x)

        -- putStrLn $ pprint lk 

        -- putStrLn $ pprint lknat 

        
        let Just (SCGD
rk,NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
rknat) = (SCGD
-> SCGD
-> Maybe
     (SCGD,
      NaturalTransformation
        SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
rightKan SCGD
f SCGD
x)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
rk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
rknat 
        
        
        let a :: SCG
a = String -> SCG
unsafeReadSCGString String
"2\nA\nB\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
a 
        let b :: SCG
b = String -> SCG
unsafeReadSCGString String
"2\nA -q1-> C\nB -q2-> C\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
b 
        let c :: SCG
c = String -> SCG
unsafeReadSCGString String
"2\n0 -abs-> 1\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
c 
        let f :: SCGD
f = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\nA -q1-> C\nB -q2-> C\n</TGT>\nA => A\nB => B\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
f 
        let x :: SCGD
x = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\n0 -abs-> 1\n</TGT>\nA => 1\nB => 1"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
x 
        
        let Just (SCGD
lk,NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
lknat) = (SCGD
-> SCGD
-> Maybe
     (SCGD,
      NaturalTransformation
        SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
leftKan SCGD
f SCGD
x)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
lk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
lknat 
        
        -- let Just (rk,rknat) = (rightKan f x)

        -- putStrLn $ pprint rk 

        -- putStrLn $ pprint rknat 

        
        
        let a :: SCG
a = String -> SCG
unsafeReadSCGString String
"2\nA\nB\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
a 
        let b :: SCG
b = String -> SCG
unsafeReadSCGString String
"2\nA -f-> C\nB -g-> C\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
b 
        let c :: SCG
c = String -> SCG
unsafeReadSCGString String
"2\n0 -f-> 1\n1 -g-> 2\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCG -> String
forall c m o.
(FiniteCategory c m o, Morphism m o, PrettyPrint c, PrettyPrint m,
 PrettyPrint o, Eq m, Eq o) =>
c -> String
pprintFiniteCategory SCG
c 
        let f :: SCGD
f = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\nA -f-> C\nB -g-> C\n</TGT>\nA => A\nB => B\n"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
f 
        let x :: SCGD
x = String -> SCGD
unsafeReadSCGDString String
"<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\n0 -f-> 1\n1 -g-> 2\n</TGT>\nA => 1\nB => 1"
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
x 
        
        let Just (SCGD
lk,NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
lknat) = (SCGD
-> SCGD
-> Maybe
     (SCGD,
      NaturalTransformation
        SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
leftKan SCGD
f SCGD
x)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
lk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
lknat 
        
        let Just (SCGD
rk,NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
rknat) = (SCGD
-> SCGD
-> Maybe
     (SCGD,
      NaturalTransformation
        SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text)
forall c1 m1 o1 c2 m2 o2 c3 m3 o3.
(FiniteCategory c1 m1 o1, Morphism m1 o1, Eq c1, Eq m1, Eq o1,
 FiniteCategory c2 m2 o2, Morphism m2 o2, Eq c2, Eq m2, Eq o2,
 FiniteCategory c3 m3 o3, Morphism m3 o3, Eq c3, Eq m3, Eq o3) =>
Diagram c1 m1 o1 c2 m2 o2
-> Diagram c1 m1 o1 c3 m3 o3
-> Maybe
     (Diagram c2 m2 o2 c3 m3 o3,
      NaturalTransformation c1 m1 o1 c3 m3 o3)
rightKan SCGD
f SCGD
x)
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ SCGD -> String
forall a. PrettyPrint a => a -> String
pprint SCGD
rk 
        String -> IO ()
putStrLn (String -> IO ()) -> String -> IO ()
forall a b. (a -> b) -> a -> b
$ NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
-> String
forall a. PrettyPrint a => a -> String
pprint NaturalTransformation
  SCG (SCGMorphism Text Text) Text SCG (SCGMorphism Text Text) Text
rknat 
        
        -- let a = unsafeReadSCGString "2\nA\nB\n"

        -- putStrLn $ pprintFiniteCategory a 

        -- let b = unsafeReadSCGString "2\nA -q1-> C\nB -q2-> C\n"

        -- putStrLn $ pprintFiniteCategory b 

        -- let c = unsafeReadSCGString "2\n0 -abs-> 1\n"

        -- putStrLn $ pprintFiniteCategory c 

        -- let f = unsafeReadSCGDString "<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\nA -q1-> C\nB -q2-> C\n</TGT>\nA => A\nB => B\n"

        -- putStrLn $ pprint f 

        -- let x = unsafeReadSCGDString "<SRC>\n2\nA\nB\n</SRC>\n<TGT>\n2\n0 -abs-> 1\n</TGT>\nA => 0\nB => 1"

        -- putStrLn $ pprint x 

        
        -- let Just (lk,lknat) = (leftKan f x)

        -- putStrLn $ pprint lk 

        -- putStrLn $ pprint lknat 

        
        -- let Just (rk,rknat) = (rightKan f x)

        -- putStrLn $ pprint rk 

        -- putStrLn $ pprint rknat 

        
        String -> IO ()
putStrLn String
"End of Math.Functors.KanExtension.Example"