similar to <$>

>>> pl @(FMap Succ) (Right 'a')
Present Right 'b' (FMap Succ 'b' | 'a')
Val (Right 'b')

>>> pl @(FMap Succ) (Left "Sf")
Present Left "Sf" (FMap <skipped>)
Val (Left "Sf")

>>> pz @(FMap (MkDay Id) >> Join) (Just (2020,01,01))
Val (Just 2020-01-01)

>>> pz @(FMap (MkDay Id) >> Join) (Just (2020,01,32))
Val Nothing

>>> pz @(FMap Succ) (Just LT)
Val (Just EQ)

>>> pz @(FMap Pred) (Just LT)
Fail "Pred IO e=Prelude.Enum.Ordering.pred: bad argument"

>>> pz @(FMap (ShowP Id)) (Just 10)
Val (Just "10")

>>> pan @(FMap $ FMap $ FMap Succ) [Just "abcdefG",Nothing,Just "X"]
P FMap FMap FMap Succ 'b' | Succ 'c' | Succ 'd' | Succ 'e' | Succ 'f' | Succ 'g' | Succ 'H' | FMap <skipped> | FMap FMap Succ 'Y'
|
+- P FMap FMap Succ 'b' | Succ 'c' | Succ 'd' | Succ 'e' | Succ 'f' | Succ 'g' | Succ 'H'
|  |
|  `- P FMap Succ 'b' | Succ 'c' | Succ 'd' | Succ 'e' | Succ 'f' | Succ 'g' | Succ 'H'
|     |
|     +- P Succ 'b'
|     |
|     +- P Succ 'c'
|     |
|     +- P Succ 'd'
|     |
|     +- P Succ 'e'
|     |
|     +- P Succ 'f'
|     |
|     +- P Succ 'g'
|     |
|     `- P Succ 'H'
|
+- P FMap <skipped>
|
`- P FMap FMap Succ 'Y'
   |
   `- P FMap Succ 'Y'
      |
      `- P Succ 'Y'
Val [Just "bcdefgH",Nothing,Just "Y"]

>>> pan @(FMap (FromEnum > 97)) "abc"
P FMap 97 > 97 | 98 > 97 | 99 > 97
|
+- False 97 > 97
|  |
|  +- P FromEnum 97
|  |
|  `- P '97
|
+- True 98 > 97
|  |
|  +- P FromEnum 98
|  |
|  `- P '97
|
`- True 99 > 97
   |
   +- P FromEnum 99
   |
   `- P '97
Val [False,True,True]

>>> pan @(FMap (FromEnum > 97 >> Id)) "abc"
P FMap (>>) False | (>>) True | (>>) True
|
+- P (>>) False
|  |
|  +- False 97 > 97
|  |  |
|  |  +- P FromEnum 97
|  |  |
|  |  `- P '97
|  |
|  `- P Id False
|
+- P (>>) True
|  |
|  +- True 98 > 97
|  |  |
|  |  +- P FromEnum 98
|  |  |
|  |  `- P '97
|  |
|  `- P Id True
|
`- P (>>) True
   |
   +- True 99 > 97
   |  |
   |  +- P FromEnum 99
   |  |
   |  `- P '97
   |
   `- P Id True
Val [False,True,True]

>>> pan @(FMap IdBool) (Just True)
P FMap IdBool
|
`- True IdBool
Val (Just True)

>>> pz @(FMap (Pure (Either String) Id)) [1,2,4]
Val [Right 1,Right 2,Right 4]

>>> pl @(FMap (Pure [] Id)) (Just 10)
Present Just [10] (FMap Pure [10] | 10)
Val (Just [10])

>>> pl @(FMap (Pure SG.Sum Id)) (Just 20)
Present Just (Sum {getSum = 20}) (FMap Pure Sum {getSum = 20} | 20)
Val (Just (Sum {getSum = 20}))

>>> pz @(FMap (Coerce (SG.Sum Integer))) [Identity (-13), Identity 4, Identity 99]
Val [Sum {getSum = -13},Sum {getSum = 4},Sum {getSum = 99}]

>>> pz @(FMap (Coerce (SG.Sum Integer))) (Just (Identity (-13)))
Val (Just (Sum {getSum = -13}))

>>> pz @(FMap (Coerce (SG.Sum Int))) (Nothing @(Identity Int))
Val Nothing

>>> pl @(FMap (Coerce (SG.Sum Int))) (Just (10 :: Int))
Present Just (Sum {getSum = 10}) (FMap Coerce Sum {getSum = 10} | 10)
Val (Just (Sum {getSum = 10}))

>>> pz @(Proxy Char >> FMap Succ) () ^!? acts . _Val . to typeRep
Just Char

similar to <$>

>>> pz @(Len <$> Snd) (1,Just "abcdef")
Val (Just 6)

>>> pz @(Len <$> (Id <> Id <> "extra" <$> Snd)) (1,Just "abcdef")
Val (Just 17)

>>> pz @(Len <$> (Id <> Id <> "extra" <$> Snd)) (1,Right "abcdef")
Val (Right 17)

>>> pz @(FMap $ FMap (Succ <$> Id)) (True,Just (These 12 'c'))
Val (True,Just (These 12 'd'))

>>> pz @(FMap (Second (Succ <$> Id))) [(True, (These 12 'c'))]
Val [(True,These 12 'd')]

similar to <&>

>>> pz @('[1,2,3] <&> Succ) ()
Val [2,3,4]

similar to pure

>>> pz @(Pure Maybe Id) 4
Val (Just 4)

>>> pz @(Pure [] Id) 4
Val [4]

>>> pz @(Pure (Either String) Fst) (13,True)
Val (Right 13)

>>> pl @(Pure Maybe Id) 'x'
Present Just 'x' (Pure Just 'x' | 'x')
Val (Just 'x')

>>> pl @(Pure (Either _) Id) 'x'
Present Right 'x' (Pure Right 'x' | 'x')
Val (Right 'x')

>>> pl @(Pure (Either _) Id >> Swap) 'x'
Present Left 'x' ((>>) Left 'x' | {Swap Left 'x' | Right 'x'})
Val (Left 'x')

>>> pl @(Pure (Either ()) Id >> Swap) 'x'
Present Left 'x' ((>>) Left 'x' | {Swap Left 'x' | Right 'x'})
Val (Left 'x')

>>> pl @(Pure (Either String) Id >> Swap) 123
Present Left 123 ((>>) Left 123 | {Swap Left 123 | Right 123})
Val (Left 123)

applicative bind similar to <*> but functions have to be fully saturated: ie Len is ok but not Length can use Proxy to delay evaluation until Pop0

>>> pz @(MkJust '("sdf",Id) <*> MkJust 4) ()
Val (Just ("sdf",4))

>>> pz @(MkJust Succ <*> MkJust 4) ()
Val (Just 5)

>>> pz @('[Succ,Id,Pred] <*> "abcdef") undefined
Val "ba`cbadcbedcfedgfe"

>>> pz @(MkJust "abc" <*> MkJust "def") () -- no function to apply so has to choose ie first one
Val (Just "abc")

>>> pz @('[1,2] <*> "abcdef") () -- [1,2] <* "abcdef" -- ie skips rhs "abcdef" but still runs the effects
Val [1,2,1,2,1,2,1,2,1,2,1,2]

>>> pz @(MkJust ((*) 3 Id) <*> MkJust 4) ()
Val (Just 12)

>>> pz @(MkJust ((*) 3 Len) <*> MkJust '["aa","bb","c","d","e"]) ()
Val (Just 15)

>>> pz @(ShowP Id <$> MkJust Succ <*> MkJust 4) ()
Val (Just "5")

>>> pz @('["x","y"] <*> '[1,2,3]) ()
Val ["x","y","x","y","x","y"]

similar to liftA2

>>> pan @(LiftA2 Id (MkJust 12) (MkJust "abc")) ()
P LiftA2 Id (12,"abc")
|
+- P MkJust Just 12
|  |
|  `- P '12
|
+- P MkJust Just "abc"
|  |
|  `- P '"abc"
|
`- P Id (12,"abc")
Val (Just (12,"abc"))

>>> pan @(LiftA2 Swap (MkJust 12) (MkNothing _)) ()
P LiftA2 <skipped>
|
+- P MkJust Just 12
|  |
|  `- P '12
|
`- P MkNothing
Val Nothing

>>> pz @(LiftA2 (ShowP Fst <> "---" <> ShowP Snd) Fst Snd) (Just 10, Just True)
Val (Just "10---True")

>>> pz @(LiftA2 (Fst + Snd) Fst Snd) (Just 10, Just 13)
Val (Just 23)

>>> pz @(LiftA2 Fst '["x","y"] '[1,2,3]) ()
Val ["x","x","x","y","y","y"]

>>> pz @(LiftA2 Snd '["x","y"] '[1,2,3]) ()
Val [1,2,3,1,2,3]

>>> pz @(LiftA2 (Pop0 Fst Snd) '[ Proxy Len ] '[ "abc", "def", "aaaaaaaaaaa"]) ()
Val [3,3,11]

>>> pz @(LiftA2 (Fst * Snd) (FromList (ZipList _) << (10...15)) (FromList (ZipList _) << (1...10))) ()
Val (ZipList {getZipList = [10,22,36,52,70,90]})

runs liftA2 (,) against two values: LiftA2 is traversable and provides better debugging

>>> pz @(FPair Fst Snd) (Just 10, Just True)
Val (Just (10,True))

>>> pz @(FPair Fst Snd >> FMap (ShowP Fst <> "---" <> ShowP Snd)) (Just 10, Just True)
Val (Just "10---True")

>>> pz @(FPair Fst Snd >> FMap (Fst + Snd)) (Just 10, Just 13)
Val (Just 23)

>>> pz @(FPair (EnumFromTo Fst Snd) ('LT ... 'GT)) (10,11)
Val [(10,LT),(10,EQ),(10,GT),(11,LT),(11,EQ),(11,GT)]

>>> pz @(FPair '[ '() ] (1 ... 5)) True
Val [((),1),((),2),((),3),((),4),((),5)]

see FPair

>>> pz @(Fst <:> Snd) (Just 10, Just True)
Val (Just (10,True))

>>> pz @(Fst <:> Snd) ("abc",[10,12,14])
Val [('a',10),('a',12),('a',14),('b',10),('b',12),('b',14),('c',10),('c',12),('c',14)]

>>> pz @('[1,2] <:> "abcdef") ()
Val [(1,'a'),(1,'b'),(1,'c'),(1,'d'),(1,'e'),(1,'f'),(2,'a'),(2,'b'),(2,'c'),(2,'d'),(2,'e'),(2,'f')]

>>> pz @(EnumFromTo Fst Snd <:> ('LT ... 'GT)) (10,11)
Val [(10,LT),(10,EQ),(10,GT),(11,LT),(11,EQ),(11,GT)]

>>> pz @(MkJust Succ <:> MkJust 4) ()   -- uses Succ on (): instead use LiftA2 with Pop0 or <*>  (see next 2 tests)
Fail "Succ IO e=Prelude.Enum.().succ: bad argument"

>>> pz @(LiftA2 (Pop0 Fst Snd) (MkJust (Proxy Succ)) (MkJust 4)) ()
Val (Just 5)

>>> pz @(MkJust Succ <*> MkJust 4) ()
Val (Just 5)

similar to <$

>>> pz @(Fst <$ Snd) ("abc",Just 20)
Val (Just "abc")

>>> pl @(Fst <$ Snd) (4,These "xxx" 'a')
Present These "xxx" 4 ((<$) 4)
Val (These "xxx" 4)

>>> pl @(Fst <$ Snd) (4,This 'a')
Present This 'a' ((<$) 4)
Val (This 'a')

>>> pl @(Fst <$ Snd) (4,Just 'a')
Present Just 4 ((<$) 4)
Val (Just 4)

>>> pl @(Fst <$ Snd) (4,Nothing @Int)
Present Nothing ((<$) 4)
Val Nothing

>>> pl @('True <$ Id) [1..4]
Present [True,True,True,True] ((<$) True)
Val [True,True,True,True]

>>> import Data.Functor.Compose
>>> pl @(C "ab" <$ Id) (Compose $ Just [1..4])
Present Compose (Just "aaaa") ((<$) 'a')
Val (Compose (Just "aaaa"))

>>> pl @(Snd <$ Fst) (Just 10,'x')
Present Just 'x' ((<$) 'x')
Val (Just 'x')

similar to Applicative <*

>>> pl @(Fst <* Snd) (Just 4,Just 'a')
Present Just 4 ((<*) Just 4 | p=Just 4 | q=Just 'a')
Val (Just 4)

>>> pz @(Fst <* Snd) (Just "abc",Just 20)
Val (Just "abc")

>>> pz @('["x","y"] <* '[1,2,3]) ()
Val ["x","x","x","y","y","y"]

similar to Applicative *>

>>> pl @(Fst *> Snd) (Just 4,Just 'a')
Present Just 'a' ((*>) Just 4 | p=Just 4 | q=Just 'a')
Val (Just 'a')

>>> pz @('["x","y"] *> '[1,2,3]) ()
Val [1,2,3,1,2,3]

similar to monad operator >=>

>>> pz @(FFish Uncons (Snd >> Uncons) "abcdef") ()
Val (Just ('b',"cdef"))

>>> :m + Data.Time
>>> pz @(FFish (ReadMaybe Day Id >> FMap Fst) (MkJust Succ) "2020-02-02") ()
Val (Just 2020-02-03)

>>> pz @(FFish Uncons (Lookup Fst "abcdef") [3,14,12]) ()
Val (Just 'd')

similar to monad bind operator >>=

>>> pz @(Id >>= HeadMay) (Just "abcdef")
Val (Just 'a')

>>> pz @(Uncons >>= (Snd >> HeadMay)) "abcdef"
Val (Just 'b')

>>> pz @((1 ... 10) >>= EmptyBool [] Even '[Id,Id]) ()
Val [[2,2],[4,4],[6,6],[8,8],[10,10]]

>>> pz @((1 ... 10) >>= If Even '[Id,Id] (EmptyT [] _)) ()
Val [2,2,4,4,6,6,8,8,10,10]

>>> pz @(Lookup 0 Id >>= Lookup 1 Id) [[1,2,3]]
Val (Just 2)

>>> pz @(Lookup 4 Id >>= Lookup 1 Id) [[1,2,3]]
Val Nothing

>>> pz @(Lookup 0 Id >>= Lookup 5 Id) [[1,2,3]]
Val Nothing

>>> pz @(Lookup 0 Id >>= Lookup 1 Id >>= MaybeBool Even '(Id,"is even!")) [[1,2,3]]
Val (Just (2,"is even!"))

>>> pz @(Lookup 0 Id >>= Lookup 1 Id >>= MaybeBool Even '(Id,"is even!")) [[1,5,3]]
Val Nothing

>>> pz @((48...55) >>= '[ '[ToEnum Char << Id,ToEnum Char << (Id+3),ToEnum Char << (Id+6)] ]) ()
Val ["036","147","258","369","47:","58;","69<","7:="]

>>> pz @((48...55) >>= '[ Map (ToEnum Char) << '[ Id, Id+3 ,Id+6 ] ]) ()
Val ["036","147","258","369","47:","58;","69<","7:="]

similar to sequenceA

>>> pz @Sequence [Just 10, Just 20, Just 30]
Val (Just [10,20,30])

>>> pz @Sequence [Just 10, Just 20, Just 30, Nothing, Just 40]
Val Nothing

like traverse

>>> pl @(Traverse (If (Gt 3) (Pure Maybe Id) (EmptyT Maybe _))) [1..5]
Present Nothing ((>>) Nothing | {Sequence Nothing | [Nothing,Nothing,Nothing,Just 4,Just 5]})
Val Nothing

>>> pl @(Traverse (MaybeBool (Le 3) Id)) [1..5]
Present Nothing ((>>) Nothing | {Sequence Nothing | [Just 1,Just 2,Just 3,Nothing,Nothing]})
Val Nothing

>>> pl @(Traverse (If (Gt 0) (Pure Maybe Id) (EmptyT Maybe _))) [1..5]
Present Just [1,2,3,4,5] ((>>) Just [1,2,3,4,5] | {Sequence Just [1,2,3,4,5] | [Just 1,Just 2,Just 3,Just 4,Just 5]})
Val (Just [1,2,3,4,5])

>>> pl @(Traverse (If (Gt 0) (Pure Maybe Id) (MkNothing _))) [1..5]
Present Just [1,2,3,4,5] ((>>) Just [1,2,3,4,5] | {Sequence Just [1,2,3,4,5] | [Just 1,Just 2,Just 3,Just 4,Just 5]})
Val (Just [1,2,3,4,5])

>>> pl @(Traverse (MaybeBool (Id >= 0) Id)) [1..5]
Present Just [1,2,3,4,5] ((>>) Just [1,2,3,4,5] | {Sequence Just [1,2,3,4,5] | [Just 1,Just 2,Just 3,Just 4,Just 5]})
Val (Just [1,2,3,4,5])

>>> pl @(Traverse (MaybeBool (Id <= 3) Id)) [1..5]
Present Nothing ((>>) Nothing | {Sequence Nothing | [Just 1,Just 2,Just 3,Nothing,Nothing]})
Val Nothing

similar to join

>>> pz @Join (Just (Just 20))
Val (Just 20)

>>> pz @Join ["ab","cd","","ef"]
Val "abcdef"

similar to <|>

>>> pz @(Fst <|> Snd) (Nothing,Just 20)
Val (Just 20)

>>> pz @(Fst <|> Snd) (Just 10,Just 20)
Val (Just 10)

>>> pz @(Fst <|> Snd) (Nothing,Nothing)
Val Nothing

>>> pl @(Fst <|> Snd) (Just "cdef",Just "ab")
Present Just "cdef" ((<|>) Just "cdef" | p=Just "cdef" | q=Just "ab")
Val (Just "cdef")

>>> pl @(Fst <|> Snd) ("cdef","ab"::String)
Present "cdefab" ((<|>) "cdefab" | p="cdef" | q="ab")
Val "cdefab"

similar to empty

>>> pz @(EmptyT Maybe _) ()
Val Nothing

>>> pz @(EmptyT [] _) ()
Val []

>>> pz @(C "x" >> EmptyT [] String) (13,True)
Val []

>>> pz @(Fst >> EmptyT (Either String) _) (13,True)
Val (Left "")

>>> pz @(If 'True (MkJust 11) (EmptyT _ _)) ()
Val (Just 11)

>>> pz @(EmptyT [] _ <> "123") ()
Val "123"

similar to empty where t is the type of the container and t1 is a reference to the type of the items in the container

>>> pz @(EmptyT' [] "x") ()
Val []

>>> pz @(EmptyT' (Either String) (1 % 1)) ()
Val (Left "")

>>> pl @(If 'True (MkJust 11) (EmptyT' _ 0)) ()
Present Just 11 (If 'True Just 11)
Val (Just 11)

>>> pz @(If 'True (MkJust 11) (EmptyT' _ (Hole Int))) ()
Val (Just 11)

>>> pz @(If 'False (MkJust 11) (EmptyT' _ (Hole Int))) ()
Val Nothing

creates an empty list for the given type

>>> pz @(Id :+ EmptyList _) 99
Val [99]

creates an empty list for the given pointer to a type t

>>> pz @(EmptyList' 123 +: Id) 99
Val [99]

Convenient method to convert a value p to an Alternative based on a predicate b

if b is True then pure p else empty

>>> pz @(EmptyBool [] (Id > 4) 'True) 24
Val [True]

>>> pz @(EmptyBool [] (Id > 4) 'True) 1
Val []

Convenient method to convert a value p to an Alternative based on a predicate b the value of p drives the choice of Alternative to use for the empty similar to EmptyBool but no need to provide t as it is inferred from the resulting type of p

if b is True then run p else empty

>>> pz @(EmptyBool' (Id > 4) (MkJust (Id * 3))) 24
Val (Just 72)

>>> pz @(EmptyBool' (Id > 4) (MkJust (Id * 3))) 2
Val Nothing

>>> pz @(EmptyBool' (Len > 0) Head) ["Abcd","def","g"::String]
Val "Abcd"

>>> pz @(EmptyBool' (Len > 0) Head) ([] :: [String])
Val ""

similar to bimap

>>> pz @(BiMap Succ Head) (Left @_ @String 12) -- needs a type signature for Right
Val (Left 13)

>>> pz @(BiMap Succ Head) (Right "xyz")
Val (Right 'x')

>>> pz @(FMap (BiMap Succ Head)) [Right "xyz",Left 'a',Right "ab",Left 'x']
Val [Right 'x',Left 'b',Right 'a',Left 'y']

>>> pz @(FMap (BiMap Succ Pred)) [These 12 'b', This 1, That 'd',That 'e']
Val [These 13 'a',This 2,That 'c',That 'd']

>>> pz @(BiMap Succ Pred) (True,12,'b')
Val (True,13,'a')

>>> pl @(FMap $ BiMap Succ (Not Id)) [This @Int @Bool 1, This 2,That True,These 4 False]
Present [This 2,This 3,That False,These 5 True] (FMap BiMap(L) Succ 2 | 1 | BiMap(L) Succ 3 | 2 | BiMap(R) Not (Id True) | BiMap(B) Succ 5 | 4 | Not (Id False))
Val [This 2,This 3,That False,These 5 True]

>>> pl @(BiMap Succ (Not Id)) (This @Int @Bool 1)
Present This 2 (BiMap(L) Succ 2 | 1)
Val (This 2)

>>> pl @(BiMap Succ (Not Id)) (That @Int @Bool True)
Present That False (BiMap(R) Not (Id True))
Val (That False)

>>> pl @(BiMap Succ (Not Id)) (These @Int @Bool 1 True)
Present These 2 False (BiMap(B) Succ 2 | 1 | Not (Id True))
Val (These 2 False)

>>> pan @(FMap $ BiMap Succ (Not Id)) [This @Int @Bool 1, This 2,That True,These 4 False]
P FMap BiMap(L) Succ 2 | BiMap(L) Succ 3 | BiMap(R) Not | BiMap(B) Succ 5 | Not
|
+- P BiMap(L) Succ 2
|  |
|  `- P Succ 2
|
+- P BiMap(L) Succ 3
|  |
|  `- P Succ 3
|
+- P BiMap(R) Not
|  |
|  `- False Not
|     |
|     `- True Id True
|
`- P BiMap(B) Succ 5 | Not
   |
   +- P Succ 5
   |
   `- True Not
      |
      `- False Id False
Val [This 2,This 3,That False,These 5 True]

>>> pl @(BiMap Succ Head) (ENone @Int @String)
Present ENone (BiMap <skipped>)
Val ENone

>>> pl @(BiMap Succ Head) (ELeft @Int @String 10)
Present ELeft 11 (BiMap(L) Succ 11 | 10)
Val (ELeft 11)

>>> pl @(BiMap Succ Head) (ERight @Int @String "xyz")
Present ERight 'x' (BiMap(R) Head 'x' | "xyz")
Val (ERight 'x')

>>> pl @(BiMap Succ Head) (EBoth @Int @String 10 "xyz")
Present EBoth 11 'x' (BiMap(B) Succ 11 | 10 | Head 'x' | "xyz")
Val (EBoth 11 'x')

>>> pan @(FMap $ BiMap Succ Head) [ENone,ELeft 10,ERight "abc",EBoth 10 "xyz"]
P FMap BiMap <skipped> | BiMap(L) Succ 11 | BiMap(R) Head 'a' | BiMap(B) Succ 11 | Head 'x'
|
+- P BiMap <skipped>
|
+- P BiMap(L) Succ 11
|  |
|  `- P Succ 11
|
+- P BiMap(R) Head 'a'
|  |
|  `- P Head 'a'
|
`- P BiMap(B) Succ 11 | Head 'x'
   |
   +- P Succ 11
   |
   `- P Head 'x'
Val [ENone,ELeft 11,ERight 'a',EBoth 11 'x']

a version of bifoldMap

>>> pl @(BiFoldMap Id Id) (Right [10..13])
Present [10,11,12,13] (BiFoldMap(R) Id [10,11,12,13])
Val [10,11,12,13]

>>> pl @(BiFoldMap Id Id) (Left [10..13])
Present [10,11,12,13] (BiFoldMap(L) Id [10,11,12,13])
Val [10,11,12,13]

>>> pl @(BiFoldMap Id Id) (SG.Arg [1..5] [10..13])
Present [1,2,3,4,5,10,11,12,13] (BiFoldMap(B) Id [1,2,3,4,5] | Id [10,11,12,13])
Val [1,2,3,4,5,10,11,12,13]

>>> pz @(BiFoldMap (Wrap (SG.Sum _) Id) (Wrap (SG.Sum _) Id)) (SG.Arg 1 4)
Val (Sum {getSum = 5})

>>> pl @(BiFoldMap '( '[Id], '[]) '( '[], '[Id])) (SG.Arg "hap" "bcd")
Present (["hap"],["bcd"]) (BiFoldMap(B) '(["hap"],[]) | '([],["bcd"]))
Val (["hap"],["bcd"])

>>> pz @(BiFoldMap '(Wrap (SG.Sum _) Id, MEmptyT _) '(MEmptyT _, Id)) (SG.Arg 123 "xyz")
Val (Sum {getSum = 123},"xyz")

>>> pl @(BiFoldMap '(Wrap (SG.Sum _) Id, MEmptyT _) '(MEmptyT _, Id)) (Left 123)
Present (Sum {getSum = 123},()) (BiFoldMap(L) '(Sum {getSum = 123},()))
Val (Sum {getSum = 123},())

>>> pz @(BiFoldMap (MEmptyT _) $ FoldMap (FoldMap (Wrap (SG.Sum _) Id))) (Right (Just [1..10]))
Val (Sum {getSum = 55})

similar to extract

>>> pz @Extract (Nothing,Just 20)
Val (Just 20)

>>> pz @Extract (Identity 20)
Val 20

>>> pl @Extract (10,"hello")
Present "hello" (Extract "hello" | (10,"hello"))
Val "hello"

similar to duplicate

>>> pz @Duplicate (20,"abc")
Val (20,(20,"abc"))

function application for pure functions appearing on the rhs: similar to $

>>> :m + Text.Show.Functions
>>> pz @(Fst $$ Snd) ((*16),4)
Val 64

>>> pz @(Id $$ "def") ("abc"<>)
Val "abcdef"

>>> pz @(Id $$ 12) (*13)
Val 156

>>> pz @(Id $$ 7 $$ 3) (*)
Val 21

>>> pz @(Id $$ 7 $$ 3) (,)
Val (7,3)

>>> pz @(Id $$ "abc" $$ 'True) (,)
Val ("abc",True)

>>> pz @(Id $$ "asdf" $$ 99 $$ C "A") (,,)
Val ("asdf",99,'A')

>>> (fmap.fmap) ($ 9999) $ pz @Id (*33)
Val 329967

>>> (fmap.fmap) ($ 9999) $ pz @(Id $$ 1 $$ 'True) (,,)
Val (1,True,9999)

>>> (fmap.fmap.fmap) ($ 8) $ pz @'("xxx",Id) (*33)
Val ("xxx",264)

>>> pz @('True $& 4 $& Id $$ "aa") (,,)
Val (4,True,"aa")

>>> pz @((Id $$ "abc" $$ Wrap (SG.Sum _) 14) >> Id <> Id) These
Val (These "abcabc" (Sum {getSum = 28}))

flipped function application for expressions: similar to &

>>> :m + Text.Show.Functions
>>> pz @(Snd $& Fst) ((*16),4)
Val 64

>>> pz @("def" $& Id) ("abc"<>)
Val "abcdef"

>>> pz @('True $& 4 $& Id) (,)
Val (4,True)

just run the effect ignoring the result passing the original value through

for example for use with Stdout so it doesnt interfere with the a on the rhs unless it fails

run p for the effect and then run q using that original value

run run p and then q for the effect but using the result from p

run both p and q for their effects but ignoring the results

similar to flip:see also FlipT

>>> pz @(Flip Map' Id Succ) [1..5]
Val [2,3,4,5,6]

>>> pz @(Flip '(,) 'True 2) ()
Val (2,True)

>>> pz @(Flip ('(,,) 1) 2 Id) "ab"
Val (1,"ab",2)

compose simple functions

>>> pl @(Dot '[L3,L2,L1] Id) ((1,(2,9,10)),(3,4))
Present 10 (Thd 10 | (2,9,10))
Val 10

reversed version of Dot

>>> pl @(RDot '[L1,L2,L3] Id) ((1,(2,9,10)),(3,4))
Present 10 (Thd 10 | (2,9,10))
Val 10

>>> pl @(RDot '[L1,L2] Id) (('a',2),(True,"zy"))
Present 2 (Snd 2 | ('a',2))
Val 2

similar to const:types dont need to match on rhs!

>>> pl @(RDot '[L1,L2,L3,K "xxx"] Id) 12345
Present "xxx" (K '"xxx")
Val "xxx"

>>> pl @(RDot '[L1,L2,L3,K '("abc",Id)] Id) ()
Present ("abc",()) (K '("abc",()))
Val ("abc",())

>>> pl @(Dot '[K "skip",L6,Lift Dup,Lift Succ] Id) ()
Present "skip" (K '"skip")
Val "skip"

>>> pl @(L3 $ L2 $ L1 $ K Id "dud") ((1,("X",9,'a')),(3,4))
Present 'a' (Thd 'a' | ("X",9,'a'))
Val 'a'

>>> pl @((L3 $ L2 $ L1 $ K Id "dud") >> Pred) ((1,("X",9,'a')),(3,4))
Present '`' ((>>) '`' | {Pred '`' | 'a'})
Val '`'

>>> pl @(K "ss" $ L3 $ L3 $ Fst) ()
Present "ss" (K '"ss")
Val "ss"

Lift a no arg Adt to a function of one argument (for use with Dot and RDot)

>>> pl @(Lift Len Snd) (True,"abcdef")
Present 6 ((>>) 6 | {Len 6 | "abcdef"})
Val 6

similar to coerce

>>> pz @(Coerce (SG.Sum Integer)) (Identity (-13))
Val (Sum {getSum = -13})

>>> pl @(Coerce SG.Any) True
Present Any {getAny = True} (Coerce Any {getAny = True} | True)
Val (Any {getAny = True})

>>> pl @(Coerce Bool) (SG.Any True)
Present True (Coerce True | Any {getAny = True})
Val True

>>> pz @(Proxy 'True >> Coerce (Proxy 'False)) () ^!? acts . _Val . to typeRep
Just 'False

>>> pz @(Proxy Int >> Coerce (Proxy (String,Char))) () ^!? acts . _Val . to typeRep
Just ([Char],Char)

>>> import qualified GHC.Exts as GE
>>> pz @(Proxy GE.Any >> Coerce (Proxy Int)) () ^!? acts . _Val . to typeRep
Just Int

>>> pz @(Proxy '(_,_) >> Coerce (Proxy '(Float,Int))) () ^!? acts . _Val . to typeRep
Just ('(,) * * Float Int)

run an expression p and on failure run q

>>> pz @(Catch Succ (Fst >> Second (ShowP Id) >> PrintT "%s %s" Id >> 'LT)) GT
Val LT

>>> pz @(Len > 1 && Catch (Id !! 3 == 66) 'False) [1,2]
Val False

>>> pl @(Catch (Resplit "\\d+(") (Snd >> MEmptyP)) "123"
Present [] (Catch caught exception[Regex failed to compile])
Val []

>>> pl @(Catch OneP 99) [10,11]
Present 99 (Catch caught exception[OneP:expected one element(2)])
Val 99

>>> pl @(Catch OneP 99) [10]
Present 10 (Catch did not fire)
Val 10

>>> pl @(Catch OneP 'True) [False]
Present False (Catch did not fire)
Val False

>>> pl @(Catch OneP 'False) [True,True,False]
False (Catch caught exception[OneP:expected one element(3)])
Val False

>>> pl @(Catch OneP 'True) []
True (Catch caught exception[OneP:expected one element(empty)])
Val True

run an expression p and on failure print a custom error s using the error string and the input value

>>> pz @(Catch' Succ (Second (ShowP Id) >> PrintT "%s %s" Id)) GT
Fail "Succ IO e=Prelude.Enum.Ordering.succ: bad argument GT"

>>> pz @(Catch' Succ (Second (ShowP Id) >> PrintT "%s %s" Id)) LT
Val EQ

>>> pl @(Catch' (FailT Int "someval") (PrintT "msg=%s caught(%03d)" Id)) 44
Error msg=someval caught(044) (Catch default condition failed)
Fail "msg=someval caught(044)"

>>> pl @(Catch' OneP (Second (ShowP Id) >> PrintT "msg=%s caught(%s)" Id)) [10,12,13]
Error msg=OneP:expected one element(3) caught([10,12,13]) (Catch default condition failed)
Fail "msg=OneP:expected one element(3) caught([10,12,13])"

>>> pl @(Catch' OneP (PrintT "msg=%s caught(%s)" (Second (ShowP Id)))) [10]
Present 10 (Catch did not fire)
Val 10

>>> pl @(Catch' OneP (PrintT "msg=%s err s=%s" (Second (ShowP Id)))) [10,11]
Error msg=OneP:expected one element(2) err s=[10,11] (Catch default condition failed)
Fail "msg=OneP:expected one element(2) err s=[10,11]"

calculates the return type for Dot

calculates the return type for RDot