d10-0.2.1.6: Digits 0-9

Safe Haskell None Haskell2010

Data.D10.Char

Description

Defines a D10 type as a newtype for Char, where the values are restricted to characters between '0' and '9'.

The following modules define D10 types in different ways but are otherwise very similar to this one:

Synopsis

# Type

newtype D10 Source #

A Char value between '0' and '9'.

The Data.D10.Char module provides many functions for constructing D10 values, including:

• integerD10Maybe :: Integer -> Maybe D10
• integerMod10 :: Integer -> D10

With the QuasiQuotes GHC extension enabled, you can write D10 literals using the quasi-quoters d10 and d10list.

Constructors

 D10_Unsafe Char The constructor's name include the word "unsafe" as a reminder that you should generally avoid using it directly, because it allows constructing invalid D10 values.
Instances
 Source # Instance detailsDefined in Data.D10.Char Methods Source # Instance detailsDefined in Data.D10.Char Methodssucc :: D10 -> D10 #pred :: D10 -> D10 #toEnum :: Int -> D10 #fromEnum :: D10 -> Int #enumFrom :: D10 -> [D10] #enumFromThen :: D10 -> D10 -> [D10] #enumFromTo :: D10 -> D10 -> [D10] #enumFromThenTo :: D10 -> D10 -> D10 -> [D10] # Source # Instance detailsDefined in Data.D10.Char Methods(==) :: D10 -> D10 -> Bool #(/=) :: D10 -> D10 -> Bool # Source # Instance detailsDefined in Data.D10.Char Methodscompare :: D10 -> D10 -> Ordering #(<) :: D10 -> D10 -> Bool #(<=) :: D10 -> D10 -> Bool #(>) :: D10 -> D10 -> Bool #(>=) :: D10 -> D10 -> Bool #max :: D10 -> D10 -> D10 #min :: D10 -> D10 -> D10 # Source # Shows base-10 digits using the quasiquoters defined in Data.D10.Char. A single digit is displayed using d10. A list of digits is displayed using d10list. Instance detailsDefined in Data.D10.Char MethodsshowsPrec :: Int -> D10 -> ShowS #show :: D10 -> String #showList :: [D10] -> ShowS # Source # Instance detailsDefined in Data.D10.Char Methodslift :: D10 -> Q Exp #

#### Bounded

>>> minBound :: D10
[d10|0|]

>>> maxBound :: D10
[d10|9|]


#### Enum

>>> [ [d10|5|] .. ]
[d10list|56789|]

>>> [ [d10|4|] .. [d10|7|] ]
[d10list|4567|]

>>> [ [d10|5|], [d10|4|] .. ]
[d10list|543210|]

>>> [ [d10|1|], [d10|3|] .. ]
[d10list|13579|]

>>> [ minBound .. maxBound ] :: [D10]
[d10list|0123456789|]


# Quasi-quoters

A single base-10 digit.

This quasi-quoter, when used as an expression, produces a value of type D10.

>>> d10Nat [d10|5|]
5

>>> d10Nat [d10|a|]
...
... d10 must be between 0 and 9
...

>>> d10Nat [d10|58|]
...
... d10 must be a single character
...


This quasi-quoter can also be used as a pattern.

>>> :{
      case (charD10Maybe '5') of
Just [d10|4|] -> "A"
Just [d10|5|] -> "B"
_             -> "C"
>>> :}
"B"

>>> :{
      case (charD10Maybe '5') of
Just [d10|x|] -> "A"
Just [d10|5|] -> "B"
_             -> "C"
>>> :}
...
... d10 must be between 0 and 9
...


A list of base-10 digits.

This quasi-quoter, when used as an expression, produces a value of type [D10].

>>> d10Nat <$> [d10list||] []  >>> d10Nat <$> [d10list|5|]
[5]

>>> d10Nat <$> [d10list|58|] [5,8]  >>> d10Nat <$> [d10list|a|]
...
... d10 must be between 0 and 9
...


This quasi-quoter can also be used as a pattern.

>>> :{
      case [d10list|56|] of
[d10list|41|] -> "A"
[d10list|56|] -> "B"
_             -> "C"
>>> :}
"B"

>>> :{
      case [d10list|56|] of
[d10list|4x|] -> "A"
[d10list|56|] -> "B"
_             -> "C"
>>> :}
...
... d10 must be between 0 and 9
...


# Splice expressions

d10Exp :: Integral a => a -> Q Exp Source #

Produces an expression of type D10 that can be used in a Template Haskell splice.

>>> d10Nat $(d10Exp 5) 5  >>> d10Nat$(d10Exp 12)
...
... d10 must be between 0 and 9
...


You may also be interested in d10, a quasi-quoter which does something similar.

Produces an expression of type [D10] that can be used in a Template Haskell splice.

>>> d10Nat <$>$(d10ListExp "")
[]

>>> d10Nat <$>$(d10ListExp "5")
[5]

>>> d10Nat <$>$(d10ListExp "58")
[5,8]

>>> d10Nat <$>$(d10ListExp "a")
...
... d10 must be between 0 and 9
...


You may also be interested in d10list, a quasi-quoter which does something similar.

# Splice patterns

Produces a pattern that can be used in a splice to match a particular D10 value.

>>> :{
      case (charD10Maybe '5') of
Just $(d10Pat [d10|4|]) -> "A" Just$(d10Pat [d10|5|]) -> "B"
_                       -> "C"
>>> :}
"B"


You may wish to use the d10 quasi-quoter instead.

d10ListPat :: [D10] -> Q Pat Source #

Produces a pattern that can be used in a splice to match a particular list of D10 values.

>>> :{
      case (strD10ListMaybe "56") of
Just $(d10ListPat [d10list|42|]) -> "A" Just$(d10ListPat [d10list|56|]) -> "B"
_                                -> "C"
>>> :}
"B"


You may wish to use the d10list quasi-quoter instead.

# Converting between D10 and Char

Convert a D10 to its underlying Char representation.

>>> d10Char [d10|7|]
'7'


Convert a Char to a D10 if it is within the range '0' to '9', or produce Nothing otherwise.

isD10Char x = isJust (charD10Maybe x)

charD10Fail is a more general version of this function.

>>> charD10Maybe '5'
Just [d10|5|]

>>> charD10Maybe 'a'
Nothing


Convert a Char to a D10 if it is within the range '0' to '9', or Left with an error message otherwise.

>>> charD10Either '5'
Right [d10|5|]

>>> charD10Either 'a'
Left "d10 must be between 0 and 9"


charD10Fail :: MonadFail m => Char -> m D10 Source #

Convert a Char to a D10 if it is within the range '0' to '9', or fail with an error message otherwise.

charD10Maybe is a specialized version of this function.

>>> charD10Fail '5' :: IO D10
[d10|5|]

>>> charD10Fail 'a' :: IO D10
*** Exception: user error (d10 must be between 0 and 9)


# Converting between D10 and String

Convert a D10 to a String.

d10Str x = [d10Char x]
>>> d10Str [d10|7|]
"7"


Convert a String to a D10 if it consists of exactly one character and that character is within the range '0' to '9', or produce Nothing otherwise.

isD10Str x = isJust (strD10Maybe x)

strD10Fail is a more general version of this function.

>>> strD10Maybe "5"
Just [d10|5|]

>>> strD10Maybe "a"
Nothing

>>> strD10Maybe "58"
Nothing


Convert a String to a D10 if it consists of a single character and that character is within the range '0' to '9', or Left with an error message otherwise.

>>> strD10Either "5"
Right [d10|5|]

>>> strD10Either "a"
Left "d10 must be between 0 and 9"

>>> strD10Either "58"
Left "d10 must be a single character"


strD10Fail :: MonadFail m => String -> m D10 Source #

Convert a String to a D10 if it consists of a single character and that character is within the range '0' to '9', or fail with an error message otherwise.

strD10Maybe is a specialized version of this function.

>>> strD10Fail "5" :: IO D10
[d10|5|]

>>> strD10Fail "a" :: IO D10
*** Exception: user error (d10 must be between 0 and 9)

>>> strD10Fail "58" :: IO D10
*** Exception: user error (d10 must be a single character)


Determines whether a String consists of a single character and that character is within the range '0' to '9'.

# Converting between [D10] and String

Convert a String to a list of D10 if all of the characters in the string are within the range '0' to '9', or produce Nothing otherwise.

isD10Str x = isJust (strD10ListMaybe x)

strD10ListFail is a more general version of this function.

>>> strD10ListMaybe "5"
Just [d10list|5|]

>>> strD10ListMaybe "a"
Nothing

>>> strD10ListMaybe "58"
Just [d10list|58|]


Convert a String to a D10 if all of the characters in the string fall within the range '0' to '9', or Left with an error message otherwise.

>>> strD10ListEither "5"
Right [d10list|5|]

>>> strD10ListEither "a"
Left "d10 must be between 0 and 9"

>>> strD10ListEither "58"
Right [d10list|58|]


strD10ListFail :: MonadFail m => String -> m [D10] Source #

Convert a String to a D10 if all of the characters in the string fall within the range '0' to '9', or fail with an error message otherwise.

strD10ListMaybe is a specialized version of this function.

>>> strD10ListFail "5" :: IO [D10]
[d10list|5|]

>>> strD10ListFail "a" :: IO [D10]
*** Exception: user error (d10 must be between 0 and 9)

>>> strD10ListFail "58" :: IO [D10]
[d10list|58|]


# Converting between D10 and Natural

Convert a D10 to a Natural.

d10Num is a more general version of this function.

>>> d10Nat [d10|7|]
7


Convert a Natural to a D10 if it is less than 10, or produce Nothing otherwise.

isD10Nat x = isJust (natD10Maybe x)

integralD10Maybe, natD10Fail, and integralD10Fail are more general versions of this function.

>>> natD10Maybe 5
Just [d10|5|]

>>> natD10Maybe 12
Nothing


Convert a Natural to a D10 if it is less than 10, or Left with an error message otherwise.

>>> natD10Either 5
Right [d10|5|]

>>> natD10Either 12
Left "d10 must be less than 10"


natD10Fail :: MonadFail m => Natural -> m D10 Source #

Convert a Natural to a D10 if it is less than 10, or fail with an error message otherwise.

natD10Maybe is a specialized version of this function.

integralD10Fail is a more general version of this function.

>>> natD10Fail 5 :: IO D10
[d10|5|]

>>> natD10Fail 12 :: IO D10
*** Exception: user error (d10 must be less than 10)


The D10 which is uniquely congruent modulo 10 to the given Natural.

integralMod10 is a more general version of this function.

>>> natMod10 56
[d10|6|]


# Converting between D10 and Integer

Convert a D10 to an Integer.

d10Num is a more general version of this function.

>>> d10Integer [d10|7|]
7


Convert an Integer to a D10 if it is within the range 0 to 9, or produce Nothing otherwise.

isD10Integer x = isJust (integerD10Maybe x)

integralD10Maybe, integerD10Fail, and integralD10Fail are more general versions of this function.

>>> integerD10Maybe 5
Just [d10|5|]

>>> integerD10Maybe 12
Nothing

>>> integerD10Maybe (-5)
Nothing


Convert an Integer to a D10 if it is within the range 0 to 9, or Left with an error message otherwise.

>>> integerD10Either 5
Right [d10|5|]

>>> integerD10Either 12
Left "d10 must be between 0 and 9"

>>> integerD10Either (-5)
Left "d10 must be between 0 and 9"


integerD10Fail :: MonadFail m => Integer -> m D10 Source #

Convert an Integer to a D10 if it is within the range 0 to 9, or fail with an error message otherwise.

integerD10Maybe is a specialized version of this function.

integralD10Fail is a more general version of this function.

>>> integerD10Fail 5 :: IO D10
[d10|5|]

>>> integerD10Fail 12 :: IO D10
*** Exception: user error (d10 must be between 0 and 9)

>>> integerD10Fail (-5) :: IO D10
*** Exception: user error (d10 must be between 0 and 9)


The D10 which is uniquely congruent modulo 10 to the given Integer.

integralMod10 is a more general version of this function.

>>> integerMod10 56
[d10|6|]

>>> integerMod10 (-56)
[d10|4|]


# Converting between D10 and Int

Convert a D10 to an Int.

d10Num is a more general version of this function.

>>> d10Int [d10|7|]
7


Convert an Int to a D10 if it is within the range 0 to 9, or produce Nothing otherwise.

isD10Int x = isJust (intD10Maybe x)

integralD10Maybe, intD10Fail, and integralD10Fail are more general versions of this function.

>>> intD10Maybe 5
Just [d10|5|]

>>> intD10Maybe 12
Nothing

>>> intD10Maybe (-5)
Nothing


Convert an Int to a D10 if it is within the range 0 to 9, or Left with an error message otherwise.

>>> intD10Either 5
Right [d10|5|]

>>> intD10Either 12
Left "d10 must be between 0 and 9"

>>> intD10Either (-5)
Left "d10 must be between 0 and 9"


intD10Fail :: MonadFail m => Int -> m D10 Source #

Convert an Int to a D10 if it is within the range 0 to 9, or fail with an error message otherwise.

intD10Maybe is a specialized version of this function.

integralD10Fail is a more general version of this function.

>>> intD10Fail 5 :: IO D10
[d10|5|]

>>> intD10Fail 12 :: IO D10
*** Exception: user error (d10 must be between 0 and 9)

>>> intD10Fail (-5) :: IO D10
*** Exception: user error (d10 must be between 0 and 9)


The D10 which is uniquely congruent modulo 10 to the given Int.

integralMod10 is a more general version of this function.

>>> intMod10 56
[d10|6|]

>>> intMod10 (-56)
[d10|4|]


# Converting between D10 and general numeric types

d10Num :: Num a => D10 -> a Source #

Convert a D10 to any kind of number with a Num instance.

Specialized versions of this function include d10Nat, d10Integer, and d10Int.

>>> d10Num [d10|7|] :: Integer
7


integralD10Maybe :: Integral a => a -> Maybe D10 Source #

Construct a D10 from any kind of number with an Integral instance, or produce Nothing if the number falls outside the range 0 to 9.

isD10Integral x = isJust (integralD10Maybe x)

Specialized versions of this function include natD10Maybe, integerD10Maybe, and intD10Maybe.

integralD10Fail is a more general version of this function.

>>> integralD10Maybe (5 :: Integer)
Just [d10|5|]

>>> integralD10Maybe (12 :: Integer)
Nothing

>>> integralD10Maybe ((-5) :: Integer)
Nothing


Convert a number of a type that has an Integral instance to a D10 if it falls within the range 0 to 9, or Left with an error message otherwise.

>>> integralD10Either (5 :: Integer)
Right [d10|5|]

>>> integralD10Either (12 :: Integer)
Left "d10 must be between 0 and 9"

>>> integralD10Either ((-5) :: Integer)
Left "d10 must be between 0 and 9"


integralD10Fail :: (Integral a, MonadFail m) => a -> m D10 Source #

Convert a number of a type that has an Integral instance to a D10 if it falls within the range 0 to 9, or fail with an error message otherwise.

natD10Maybe, integerD10Maybe, intD10Maybe, integralD10Maybe, natD10Fail, integerD10Fail, and intD10Fail are all specialized versions of this function.

>>> integralD10Fail (5 :: Integer) :: IO D10
[d10|5|]

>>> integralD10Fail (12 :: Integer) :: IO D10
*** Exception: user error (d10 must be between 0 and 9)

>>> integralD10Fail ((-5) :: Integer) :: IO D10
*** Exception: user error (d10 must be between 0 and 9)


integralMod10 :: Integral a => a -> D10 Source #

The D10 which is uniquely congruent modulo 10 to the given number (whose type must have an instance of the Integral class).

Specialized versions of this function include natMod10, integerMod10, and intMod10.

>>> integralMod10 (56 :: Integer)
[d10|6|]

>>> integralMod10 ((-56) :: Integer)
[d10|4|]


# Modular arithmetic

(+) :: D10 -> D10 -> D10 Source #

Addition modulo 10.

>>> [d10|2|] + [d10|3|]
[d10|5|]

>>> [d10|6|] + [d10|7|]
[d10|3|]


(-) :: D10 -> D10 -> D10 Source #

Subtraction modulo 10.

>>> [d10|7|] - [d10|5|]
[d10|2|]

>>> [d10|3|] - [d10|7|]
[d10|6|]


(*) :: D10 -> D10 -> D10 Source #

Multiplication modulo 10.

>>> [d10|2|] * [d10|4|]
[d10|8|]

>>> [d10|7|] * [d10|8|]
[d10|6|]