module Algebraic where



------------------------------------------
-- Introduction to Algebraic Data Types --
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------------------------------------
-- Example: enumerated data types --
------------------------------------


data MyBool = MyTrue | MyFalse


-- operations on MyBool

myand :: MyBool -> MyBool -> MyBool
myand _ MyFalse     = MyFalse          --  `_` is a don't care pattern, matches anything
myand MyFalse _     = MyFalse          -- function equations are processed from top to bottom
myand _ _           = MyTrue
myand MyTrue MyTrue = MyFalse          -- this case will never happen!


myor :: MyBool -> MyBool -> MyBool
myor _ MyTrue       = MyTrue
myor MyTrue _       = MyTrue
myor _ _            = MyFalse



-----------------------------------------
-- Example: data types with parameters --
-----------------------------------------


-- see AexpExt.hs,  data Res a = ....


-----------------------------------
-- Example: recursive data types --
-----------------------------------


-- natural numbers

data Nat = Zero | Succ Nat

one = Succ Zero
two = Succ one
-- and so on


add :: Nat -> Nat -> Nat
add Zero n         = n
add (Succ n1) n2   = Succ (add n1 n2)


mult :: Nat -> Nat -> Nat
mult = error "your code"


-- lists


data List a = Nil | Cons a (List a)


myempty :: List a
myempty = Nil

myhead :: List a -> a
myhead (Cons x _) = x

mytail :: List a -> List a
mytail (Cons _ xs) = xs

mylast :: List a -> a
mylast (Cons x Nil) = x
mylast (Cons _ xs)  = mylast xs


-- note that lists are builtin
-- we write [] for Nil, and (x:xs) for Cons x xs,
-- [x] is an abbreviation for (x:[])