{-
Below is a *specification* of a queue.
If possible I would like to write the equations in type class.
Does the type class need two type variables?
How do I represent the constructors?
Can the equations be written in the type class rather than the instance?
-}

module QUEUE_SPEC where
data Queue e = New | Insert (Queue e) e deriving Show

isEmpty :: Queue e -> Bool
isEmpty New = True
isEmpty (Insert q e) = False

first :: Queue e -> e
first (Insert q e) = if (isEmpty q) then e else (first q)

rest :: Queue e -> Queue e
rest (Insert q e ) = if (isEmpty q) then New else (Insert (rest q) e)

size :: Queue e -> Int
size New = 0
size (Insert q e) = succ (size q)

{-
some tests of above code
size (Insert (Insert (Insert New 5) 6) 3)
rest (Insert (Insert (Insert New 5) 6) 3)

My first stab at a class
class QUEUE_SPEC q e where
new :: q e
insert :: q e -> q e
isEmpty :: q e -> Bool
first :: q e -> e
rest :: q e -> q e
size :: q e -> Int

-}

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