Difference between revisions of "FP Laboratory 9"

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* 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>  
 
* 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">
 
<div class="mw-collapsible mw-collapsed" data-collapsetext="Hide solution" data-expandtext="Show solution">

Revision as of 07:56, 23 September 2021

User defined data types and type classes

Video logo.png

Consider following representation of expressions

data Expr = Num Int
          | Add Expr Expr
          | Sub Expr Expr
          | Mul Expr Expr
          | Div Expr Expr
          | Var Char
	  deriving (Eq)
  • Create function eval that evaluates expresions.
    Video logo.png
eval :: Expr -> Int
*Main> eval (Add (Num 1) (Num 2))
3
*Main> eval (Mul (Add (Num 1) (Num 2)) (Num 3))
9
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)
Try it!
  • Create function showExpr that shows expression as a String.
    Video logo.png
showExpr :: Expr -> String
*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"
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
Try it!
  • Extend class Show to be usable with our expressions.
    Video logo.png
*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"
instance (Show Expr) where
  show = showExpr
Try it!
  • Create function derivation representing symbolic derivation of a given expression.
deriv :: Expr-> Char -> Expr
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)
Try it!