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== User defined data types and type classes ==

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/lo0pdwWoSx4]]</div>

Consider following representation of expressions

<syntaxhighlight lang="Haskell">
data Expr = Num Int
| Add Expr Expr
| Sub Expr Expr
| Mul Expr Expr
| Div Expr Expr
| Var Char
deriving (Eq)
</syntaxhighlight>

* Create function eval that evaluates expresions.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/AvThE0I4Iz8]]</div>
<syntaxhighlight lang="Haskell">
eval :: Expr -> Int
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> eval (Add (Num 1) (Num 2))
3
*Main> eval (Mul (Add (Num 1) (Num 2)) (Num 3))
9
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
eval :: Expr -> Int
eval (Num x) = x
eval (Add l r) = (eval l) + (eval r)
eval (Sub l r) = (eval l) - (eval r)
eval (Mul l r) = (eval l) * (eval r)
eval (Div l r) = (eval l) `div` (eval r)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

* Create function showExpr that shows expression as a String.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/cPL1zEZHLh0]]</div>
<syntaxhighlight lang="Haskell">
showExpr :: Expr -> String
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> showExpr (Add (Num 1) (Num 2))
"1+2"
*Main> showExpr (Mul (Add (Num 1) (Num 2)) (Num 3))
"(1+2)*3"
*Main> showExpr (Mul (Add (Num 1) (Mul (Num 2) (Var 'x'))) (Mul (Num 3) (Var 'x')))
"(1+2*x)*3*x"
*Main> showExpr (Mul (Num 2) (Mul (Var 'x') (Var 'x')))
"2*x*x"
</syntaxhighlight>
<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
showExpr :: Expr -> String
showExpr expr = showExpr' expr NoOp

data Operation = Hi | HiDiv | Lo | LoSub | NoOp deriving (Eq)

showExpr' :: Expr -> Operation -> String
showExpr' (Num x) _ = show x
showExpr' (Var x) _ = [x]
showExpr' (Add l r) op = let
x = showExpr' l Lo ++"+"++showExpr' r Lo
in if op == Hi || op == HiDiv || op==LoSub
then "(" ++ x ++")"
else x
showExpr' (Sub l r) op = let
x = showExpr' l Lo ++"-"++showExpr' r LoSub
in if op == Hi || op == HiDiv || op==LoSub
then "(" ++ x ++")"
else x
showExpr' (Mul l r) op = let
x = showExpr' l Hi ++"*"++showExpr' r Hi
in if op == HiDiv
then "(" ++ x ++")"
else x
showExpr' (Div l r) op = let
x = showExpr' l Hi ++"/"++showExpr' r Hi
in if op == HiDiv
then "(" ++ x ++")"
else x
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

* Extend class Show to be usable with our expressions.

<div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/NCAxJx_wJxI]]</div>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> Add (Num 1) (Num 2)
"1+2"
*Main> Mul (Add (Num 1) (Num 2)) (Num 3)
"(1+2)*3"
*Main> Mul (Add (Num 1) (Mul (Num 2) (Var 'x'))) (Mul (Num 3) (Var 'x'))
"(1+2*x)*3*x"
*Main> Mul (Num 2) (Mul (Var 'x') (Var 'x'))
"2*x*x"
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
instance (Show Expr) where
show = showExpr
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

* Create function derivation representing symbolic derivation of a given expression.

<syntaxhighlight lang="Haskell">
deriv :: Expr-> Char -> Expr
</syntaxhighlight>
<syntaxhighlight lang="Haskell" class="myDark">
*Main> deriv (Add (Num 1) (Num 2)) 'x'
0+0
*Main> deriv (Mul (Num 2) (Mul (Var 'x') (Var 'x'))) 'x'
0*x*x+2*(1*x+x*1)
*Main> deriv (Mul (Num 2) (Mul (Var 'x') (Var 'x'))) 'x'
0*x*x+2*(1*x+x*1)
</syntaxhighlight>

<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">
<syntaxhighlight lang="Haskell">
deriv :: Expr-> Char -> Expr
deriv (Num _) _ = (Num 0)
deriv (Var x) y | x==y = (Num 1)
| otherwise = (Num 0)
deriv (Add l r) x = Add (deriv l x) (deriv r x)
deriv (Sub l r) x = Sub (deriv l x) (deriv r x)
deriv (Mul l r) x = Add (Mul (deriv l x) r) (Mul l (deriv r x))
deriv (Div l r) x =
Div
(Sub (Mul (deriv l x) r) (Mul l (deriv r x)))
(Mul r r)
</syntaxhighlight>
[[File:Tryit.png|center|60px|Try it!|link=https://rextester.com/BHV96059]]
</div>
<div style="clear:both"></div>

@@ Line 83: / Line 83: @@
       else x
 showExpr' (Div l r) op = let
-   x = showExpr' l Hi ++"/"++showExpr' r Hi
+   x = showExpr' l Hi ++"/"++showExpr' r HiDiv
    in if op == HiDiv
       then "(" ++ x ++")"

FP Laboratory 9/en - Revision history

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