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module Internal.Tools.RationalOrder exposing (..)
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{-|
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# Rational order
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The rational order module simulates the properties of the order of rational
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numbers: all values have a clear direct ordering, but one can always gain a
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new number in-between two existing numbers.
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While this property is similarly achievable with floats, the Float type has a
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precision limit and it is therefor more desirable to achieve the same property
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using an Elm type that uses Int types for comparison.
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Given the design of the order, the best case comparison design is O(1), and the
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worst case comparison is O(log(n)). The worst case relies on recursively
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creating two values a and b, create two new numbers in-between, and repeat.
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-}
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import Recursion exposing (base, recurse, recurseThen)
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{-| The RationalOrder consists of two items: a number for ordering and a
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tie-breaking next RationalOrder type for when two RationalOrders have the same
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number.
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When the next RationalOrder is Nothing, it should be considered -infinite.
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-}
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type RationalOrder
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= With Int (Maybe RationalOrder)
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{-| Find a new value that comes after a given value. For optimization reasons,
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this will find the nearest number at the highest level.
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-}
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after : RationalOrder -> RationalOrder
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after (With i _) =
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With (i + 1) Nothing
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{-| Find a new value that comes before a given value. For optimization reasons,
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this will find the nearest number at the highest level.
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-}
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before : RationalOrder -> RationalOrder
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before (With i _) =
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With (i - 1) Nothing
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{-| Find a new value in-between two existing values. The inputs don't need to be
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ordered.
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-}
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between : RationalOrder -> RationalOrder -> RationalOrder
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between x y =
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Recursion.runRecursion
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(\orders ->
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case orders of
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( Nothing, Nothing ) ->
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base (With 0 Nothing)
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( Just o1, Nothing ) ->
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base (before o1)
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( Nothing, Just o2 ) ->
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base (before o2)
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( Just ((With i1 n1) as o1), Just ((With i2 n2) as o2) ) ->
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case Basics.compare i1 i2 of
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EQ ->
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recurseThen ( n1, n2 )
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(base << With i1 << Maybe.Just)
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LT ->
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case compare (after o1) o2 of
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LT ->
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base (after o1)
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_ ->
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Maybe.map after n1
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|> Maybe.withDefault (With 0 Nothing)
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|> Maybe.Just
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|> With i1
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|> base
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GT ->
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case compare (after o2) o1 of
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LT ->
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base (after o2)
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_ ->
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Maybe.map after n2
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|> Maybe.withDefault (With 0 Nothing)
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|> Maybe.Just
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|> With i2
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|> base
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)
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( Just x, Just y )
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compare : RationalOrder -> RationalOrder -> Basics.Order
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compare x y =
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Recursion.runRecursion
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(\( With i1 n1, With i2 n2 ) ->
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case ( Basics.compare i1 i2, n1, n2 ) of
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( EQ, Just o1, Just o2 ) ->
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recurse ( o1, o2 )
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( EQ, Just _, Nothing ) ->
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base GT
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( EQ, Nothing, Just _ ) ->
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base LT
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( EQ, Nothing, Nothing ) ->
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base EQ
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( LT, _, _ ) ->
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base LT
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( GT, _, _ ) ->
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base GT
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)
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( x, y )
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fromList : List Int -> Maybe RationalOrder
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fromList =
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Recursion.runRecursion
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(\items ->
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case items of
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[] ->
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base Nothing
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head :: tail ->
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recurseThen tail (With head >> Maybe.Just >> base)
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)
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toList : RationalOrder -> List Int
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toList =
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Recursion.runRecursion
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(\(With i next) ->
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case next of
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Nothing ->
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base [ i ]
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Just n ->
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recurseThen n ((::) i >> base)
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)
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@ -1,256 +0,0 @@
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module Test.Tools.RationalOrder exposing (..)
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import Expect
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import Fuzz exposing (Fuzzer)
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import Internal.Tools.RationalOrder as RO exposing (RationalOrder(..))
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import Test exposing (..)
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fuzzer : Fuzzer RationalOrder
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fuzzer =
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Fuzz.map2 With Fuzz.int (Fuzz.lazy (\_ -> Fuzz.maybe fuzzer))
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twoUnequal : Fuzzer ( RationalOrder, RationalOrder )
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twoUnequal =
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fuzzer
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|> Fuzz.andThen
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(\o ->
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Fuzz.map2
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(\o1 o2 ->
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if RO.compare o1 o2 == LT then
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( o1, o2 )
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else
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( o2, o1 )
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)
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(Fuzz.constant o)
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(Fuzz.filter ((/=) o) fuzzer)
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)
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suite : Test
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suite =
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describe "RationalOrder"
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[ describe "Semantic truths"
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[ describe "After is always greater"
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[ fuzz fuzzer
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"Forwards"
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(\o ->
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Expect.equal LT (RO.compare o (RO.after o))
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)
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, fuzz fuzzer
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"Backwards"
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(\o ->
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Expect.equal GT (RO.compare (RO.after o) o)
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)
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]
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, describe "Before is always lesser"
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[ fuzz fuzzer
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"Forwards"
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(\o ->
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Expect.equal GT (RO.compare o (RO.before o))
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)
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, fuzz fuzzer
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"Backwards"
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(\o ->
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Expect.equal LT (RO.compare (RO.before o) o)
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)
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]
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, describe "Two unequal == two unequal"
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[ fuzz twoUnequal
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"Forwards"
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(\( small, big ) ->
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Expect.equal LT (RO.compare small big)
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)
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, fuzz twoUnequal
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"Backwards"
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(\( small, big ) ->
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Expect.equal GT (RO.compare big small)
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)
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]
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, describe "compare"
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[ fuzz2 fuzzer
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fuzzer
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"EQ iff same value"
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(\o1 o2 ->
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Expect.equal
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(o1 == o2)
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(RO.compare o1 o2 == EQ)
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)
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, fuzz2 fuzzer
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fuzzer
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"LT iff opposite GT"
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(\o1 o2 ->
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Expect.equal
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(RO.compare o1 o2 == LT)
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(RO.compare o2 o1 == GT)
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)
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]
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, describe "Between is always between"
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[ fuzz twoUnequal
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"Less than first - forwards"
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(\( small, big ) ->
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RO.between small big
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|> RO.compare small
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|> Expect.equal LT
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)
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, fuzz twoUnequal
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"Less than first - backwards"
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(\( small, big ) ->
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small
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|> RO.compare (RO.between small big)
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|> Expect.equal GT
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)
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, fuzz twoUnequal
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"Less than second - forwards"
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(\( small, big ) ->
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RO.between small big
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|> RO.compare big
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|> Expect.equal GT
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)
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, fuzz twoUnequal
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"Less than second - backwards"
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(\( small, big ) ->
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big
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|> RO.compare (RO.between small big)
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|> Expect.equal LT
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)
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]
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]
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, describe "Between creates between"
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[ test "With 0 Nothing <--> With 1 Nothing"
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(\() ->
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RO.between (With 0 Nothing) (With 1 Nothing)
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|> Expect.equal (With 0 (Just (With 0 Nothing)))
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)
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, test "With 1 Nothing <--> With 0 Nothing"
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(\() ->
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RO.between (With 1 Nothing) (With 0 Nothing)
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|> Expect.equal (With 0 (Just (With 0 Nothing)))
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)
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, test "With 0 is filled between With 1 Nothing"
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(\() ->
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With 0 Nothing
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> Expect.equal (With 0 (Just (With 5 Nothing)))
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)
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, test "Will start counting high level as soon as possible"
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(\() ->
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With 0 Nothing
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> Expect.equal (With 2 Nothing)
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)
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, test "Will start counting high level, then return lower level"
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(\() ->
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With 0 Nothing
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 1 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> RO.between (With 5 Nothing)
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|> Expect.equal (With 4 (Just (With 6 Nothing)))
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)
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, fuzz2 fuzzer
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fuzzer
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"Between is commutative"
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(\o1 o2 ->
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Expect.equal (RO.between o1 o2) (RO.between o2 o1)
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)
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]
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, describe "After"
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[ fuzz Fuzz.int
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"One more - level 1"
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(\a ->
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Expect.equal
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(RO.after <| With a Nothing)
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(With (a + 1) Nothing)
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)
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, fuzz2 Fuzz.int
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Fuzz.int
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"One more - level 2"
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(\a b ->
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Expect.equal
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(RO.after <| With a <| Just <| With b Nothing)
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(With (a + 1) Nothing)
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)
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, fuzz3 Fuzz.int
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Fuzz.int
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Fuzz.int
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"One more - level 3"
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(\a b c ->
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Expect.equal
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(RO.after <| With a <| Just <| With b <| Just <| With c Nothing)
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(With (a + 1) Nothing)
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)
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]
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, describe "Before"
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[ fuzz Fuzz.int
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"One less - level 1"
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(\a ->
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Expect.equal
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(RO.before <| With a Nothing)
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(With (a - 1) Nothing)
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)
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, fuzz2 Fuzz.int
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Fuzz.int
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"One less - level 2"
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(\a b ->
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Expect.equal
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(RO.before <| With a <| Just <| With b Nothing)
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(With (a - 1) Nothing)
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)
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, fuzz3 Fuzz.int
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Fuzz.int
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Fuzz.int
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"One less - level 3"
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(\a b c ->
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Expect.equal
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(RO.before <| With a <| Just <| With b <| Just <| With c Nothing)
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(With (a - 1) Nothing)
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)
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]
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, describe "Compare vs. list compare"
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[ fuzz2
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(Fuzz.listOfLengthBetween 1 32 Fuzz.int)
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(Fuzz.listOfLengthBetween 1 32 Fuzz.int)
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"Compares the same between normal lists and orders"
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(\l1 l2 ->
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Expect.equal
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(Just <| Basics.compare l1 l2)
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(Maybe.map2 RO.compare (RO.fromList l1) (RO.fromList l2))
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)
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, fuzz2 fuzzer
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fuzzer
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"Compares the same when converted to list"
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(\o1 o2 ->
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Expect.equal
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(RO.compare o1 o2)
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(Basics.compare (RO.toList o1) (RO.toList o2))
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)
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]
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]
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