Difference between revisions of "FP Laboratory 9"
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Line 230: | Line 230: | ||
| If BExpr Expr Expr | | If BExpr Expr Expr | ||
deriving (Eq) | deriving (Eq) | ||
+ | </syntaxhighlight> | ||
+ | |||
+ | * Modify function eval to evaluate If-Then-Else statements. | ||
+ | <syntaxhighlight lang="Haskell"> | ||
+ | *Main> eval (If (Greater (Num 5)(Num 1)) (Num 5) (Num 6)) | ||
+ | 5 | ||
+ | *Main> eval (Mul (If (Greater (Add (Num 0) (Num 1))(Num 1)) (Num 5) (Num 6)) (Num 7)) | ||
+ | 42 | ||
</syntaxhighlight> | </syntaxhighlight> |
Revision as of 09:58, 18 August 2023
User defined data types and type classes
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.
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)
- Create function showExpr that shows expression as a String.
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 HiDiv
in if op == HiDiv
then "(" ++ x ++")"
else x
- Extend class Show to be usable with our expressions.
*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"
- Create function derivation representing symbolic derivation of a given expression.
deriv :: Expr -> Char -> Expr
*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)
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)
Additional exercises
- Define a function that counts the number of operators in an expression.
size :: Expr -> Int
*Main> size (Add (Num 1) (Num 2))
1
*Main> size (Mul (Add (Num 1) (Mul (Num 2) (Var 'x'))) (Mul (Num 3) (Var 'x')))
4
- It is possible to extend the type Expr so that it contains conditional expressions. Consider the following representation of boolean expressions:
data BExpr = Val Bool
| And BExpr BExpr
| Not BExpr
| Equal Expr Expr
| Greater Expr Expr
deriving (Eq)
- Define a function that evaluates boolean expressions.
bEval :: BExpr -> Bool
*Main> bEval (And (Equal (Num 4) (Num 5)) (Greater (Num 5) (Num 1)))
False
*Main> bEval (And (Equal (Add (Num 1) (Num 4)) (Num 5)) (Greater (Num 5) (Num 1)))
True
- Define a function that shows a boolean expression as a string. Use symbols "/\","!","=",">" for logical conjunction, negation, equality, and comparison respectively.
showBExpr :: BExpr -> String
*Main> showBExpr((And (Val True) (Not (Greater (Num 5) (Num 1)))))
"(True/\\~(5>1))"
*Main> showBExpr(And (Equal (Add (Num 1) (Num 4)) (Num 5)) (Greater (Num 5) (Num 1)))
"(((1+4)=5)/\\(5>1))"
- Extend class Show to be usable with our boolean expressions.
*Main> (And (Val True) (Not (Greater (Num 5) (Num 1))))
(True/\~(5>1))
*Main> And (Equal (Add (Num 1) (Num 4)) (Num 5)) (Greater (Num 5) (Num 1))
(((1+4)=5)/\(5>1))
- Extend the Expr type with the If-Then-Else statement as follows:
data Expr = Num Int
| Add Expr Expr
| Sub Expr Expr
| Mul Expr Expr
| Div Expr Expr
| If BExpr Expr Expr
deriving (Eq)
- Modify function eval to evaluate If-Then-Else statements.
*Main> eval (If (Greater (Num 5)(Num 1)) (Num 5) (Num 6))
5
*Main> eval (Mul (If (Greater (Add (Num 0) (Num 1))(Num 1)) (Num 5) (Num 6)) (Num 7))
42