FP Laboratory 9/cs - Revision history

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Fai0013: Created page with "* Implementujte funkci derivation reprezentující symbolickou derivaci daného výrazu."

2021-10-20T19:05:39Z

Created page with "* Implementujte funkci derivation reprezentující symbolickou derivaci daného výrazu."

Fai0013: Created page with "* Rozšiřte třídu Show tak, aby ji bylo možno využít s našimi výrazy."

2021-10-20T19:05:14Z

Created page with "* Rozšiřte třídu Show tak, aby ji bylo možno využít s našimi výrazy."

Fai0013: Created page with "* Implementujte funkci showExpr, která převede výraz na String."

2021-10-20T19:04:49Z

Created page with "* Implementujte funkci showExpr, která převede výraz na String."

Fai0013: Created page with "* Implementujte funkci eval, která vyhodnocuje výrazy."

2021-10-20T19:04:26Z

Created page with "* Implementujte funkci eval, která vyhodnocuje výrazy."

Fai0013: Created page with "Uvažujte následující reprezentaci výrazů"

2021-10-20T19:04:08Z

Created page with "Uvažujte následující reprezentaci výrazů"

Fai0013: Created page with "== Uživatelsky definované datové typy a typové třídy =="

2021-10-20T19:03:56Z

Created page with "== Uživatelsky definované datové typy a typové třídy =="

Fai0013: Created page with "FP Cvičení 9"

2021-10-20T19:03:38Z

Created page with "FP Cvičení 9"

New page

== 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>

← Older revision		Revision as of 19:03, 20 October 2021
Line 1:		Line 1:
−	== ~~User defined data types and type classes~~ ==	+	== Uživatelsky definované datové typy a typové třídy ==

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

@@ Line 115: / Line 115: @@
 <div style="clear:both"></div>
-* Create function derivation representing symbolic derivation of a given expression.
+* Implementujte funkci derivation reprezentující symbolickou derivaci daného výrazu.
 <syntaxhighlight lang="Haskell">

@@ Line 92: / Line 92: @@
 <div style="clear:both"></div>
-* Extend class Show to be usable with our expressions.
+* Rozšiřte třídu Show tak, aby ji bylo možno využít s našimi výrazy.
 <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/NCAxJx_wJxI]]</div>

@@ Line 41: / Line 41: @@
 <div style="clear:both"></div>
-* Create function showExpr that shows expression as a String.
+* Implementujte funkci showExpr, která převede výraz na String.
 <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/cPL1zEZHLh0]]</div>

@@ Line 15: / Line 15: @@
 </syntaxhighlight>
-* Create function eval that evaluates expresions.
+* Implementujte funkci eval, která vyhodnocuje výrazy.
 <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/AvThE0I4Iz8]]</div>

@@ Line 3: / Line 3: @@
 <div style="float: right"> [[File:Video logo.png|80px|link=https://youtu.be/lo0pdwWoSx4]]</div>
-Consider following representation of expressions
+Uvažujte následující reprezentaci výrazů
 <syntaxhighlight lang="Haskell">