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7shi/Main.hs

Last active Aug 29, 2015
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module Main where
import Test.HUnit
import System.IO
data Expr = N Int
| Var String Int Int
| Add [Expr]
| Mul [Expr]
deriving (Show, Eq)
x a n = Var "x" a n
eval (N x ) = x
eval (Add xs) = sum [eval x | x <- xs]
eval (Mul xs) = product [eval x | x <- xs]
isneg (N n) | n < 0 = True
isneg (Var _ a _) | a < 0 = True
isneg _ = False
str (N x) = show x
str (Var x 1 1) = x
str (Var x(-1)1) = "-" ++ x
str (Var x a 1) = show a ++ x
str (Var x a n) = str (Var x a 1) ++ "^" ++ show n
str (Add []) = ""
str (Add [Add xs]) = "(" ++ str (Add xs) ++ ")"
str (Add [x]) = str x
str (Add (x:y:zs))
| isneg y = str (Add [x]) ++ str (Add (y:zs))
str (Add (x:xs)) = str (Add [x]) ++ "+" ++ str (Add xs)
str (Mul []) = ""
str (Mul [Add xs]) = "(" ++ str (Add xs) ++ ")"
str (Mul [Mul xs]) = "(" ++ str (Mul xs) ++ ")"
str (Mul [x]) = str x
str (Mul (x:xs)) = str (Mul [x]) ++ "*" ++ str (Mul xs)
xlt (Var "x" _ n1) (Var "x" _ n2) = n1 < n2
xlt (Var "x" _ _ ) _ = False
xlt _ (Var "x" _ _ ) = True
xlt _ _ = True -- ignore
xsort (Add xs) = Add $ f xs
where
f [] = []
f (x:xs) = f xs1 ++ [x] ++ f xs2
where
xs1 = [xsort x' | x' <- xs, not $ x' `xlt` x]
xs2 = [xsort x' | x' <- xs, x' `xlt` x]
xsort (Mul xs) = Mul [xsort x | x <- xs]
xsort x = x
flatten [] = []
flatten ((Add xs1):xs2) = flatten (xs1 ++ xs2)
flatten (x:xs) = x : flatten xs
add [] = N 0
add [x] = x
add xs = Add xs
xsimplify (Add xs) = add $ f $ getxs $ xsort $ Add $ flatten xs
where
getxs (Add xs) = xs
f [] = []
f ((N 0 ):xs) = f xs
f ((Var _ 0 _):xs) = f xs
f [x] = [xsimplify x]
f ((N a1):(N a2):zs) = f $ N (a1 + a2) : zs
f ((Var "x" a1 n1):(Var "x" a2 n2):zs)
| n1 == n2 = f $ (a1 + a2)`x`n1 : zs
f (x:xs) = xsimplify x : f xs
xsimplify (Mul xs) = Mul [xsimplify x | x <- xs]
xsimplify x = x
multiply (N n1) (N n2) = N $ n1 * n2
multiply (N n1) (Var x a2 n2) = Var x (n1 * a2) n2
multiply (Var x a1 n1) (N n2) = Var x (a1 * n2) n1
multiply (Var x a1 n1) (Var y a2 n2)
| x == y = Var x (a1 * a2) (n1 + n2)
| otherwise = Mul [Var x a1 n1, Var y a2 n2]
multiply (Add xs1) (Add xs2) = Add [multiply x1 x2 | x1 <- xs1, x2 <- xs2]
multiply (Add xs1) x2 = Add [multiply x1 x2 | x1 <- xs1 ]
multiply x1 (Add xs2) = Add [multiply x1 x2 | x2 <- xs2]
multiply (Mul xs1) (Mul xs2) = Mul (xs1 ++ xs2)
multiply (Mul xs1) x2 = Mul (xs1 ++ [x2])
multiply x1 (Mul xs2) = Mul (x1:xs2)
tests = TestList
[ "eval 1" ~: eval (Add[N 1,N 1 ]) ~?= 1+1
, "eval 2" ~: eval (Add[N 2,N 3 ]) ~?= 2+3
, "eval 3" ~: eval (Add[N 5,N(-3)]) ~?= 5-3
, "eval 4" ~: eval (Mul[N 3,N 4 ]) ~?= 3*4
, "eval 5" ~: eval (Add[N 1,Mul[N 2,N 3]]) ~?= 1+2*3
, "eval 6" ~: eval (Mul[Add[N 1,N 2],N 3]) ~?= (1+2)*3
, "str 1" ~: str (Add[N 1,N 2 ,N 3 ]) ~?= "1+2+3"
, "str 2" ~: str (Add[N 1,N(-2),N(-3)]) ~?= "1-2-3"
, "str 3" ~: str (Mul[N 1,N 2 ,N 3 ]) ~?= "1*2*3"
, "str 4" ~: str (Add[N 1,Mul[N 2,N 3]]) ~?= "1+2*3"
, "str 5" ~: str (Add[Add[N 1,N 2],N 3]) ~?= "(1+2)+3"
, "str 6" ~: str (Mul[Add[N 1,N 2],N 3]) ~?= "(1+2)*3"
, "str 7" ~: str (Mul[Mul[N 1,N 2],N 3]) ~?= "(1*2)*3"
, "equal" ~: Add[N 1,N 2] ~?= Add[N 1,N 2]
, "x 1" ~: str (Add [1`x`1,N 1]) ~?= "x+1"
, "x 2" ~: str (Add [1`x`3,(-1)`x`2,(-2)`x`1,N 1]) ~?= "x^3-x^2-2x+1"
, "xlt 1" ~: (1`x`1) `xlt` (1`x`2) ~?= True
, "xlt 2" ~: (N 1) `xlt` (1`x`1) ~?= True
, "xsort 1" ~:
let f = Add[1`x`1,N 1,1`x`2]
in (str f, str $ xsort f)
~?= ("x+1+x^2", "x^2+x+1")
, "xsort 2" ~:
let f = Mul[Add[N 5,2`x`1],Add[1`x`1,N 1,1`x`2]]
in (str f, str $ xsort f)
~?= ("(5+2x)*(x+1+x^2)", "(2x+5)*(x^2+x+1)")
, "xsimplify 1" ~:
let f = Add[2`x`1,N 3,4`x`2,1`x`1,N 1,1`x`2]
in (str f, str $ xsimplify f)
~?= ("2x+3+4x^2+x+1+x^2", "5x^2+3x+4")
, "xsimplify 2" ~:
let f = Mul[Add[1`x`1,N 0,2`x`1],Add[1`x`2,Add[N 1,2`x`2],N 2]]
in (str f, str $ xsimplify f)
~?= ("(x+0+2x)*(x^2+(1+2x^2)+2)", "3x*(3x^2+3)")
, "xsimplify 3" ~:
let f = Add[1`x`1,N 1,0`x`2,1`x`1,N 1,(-2)`x`1,N(-2)]
in (str f, str $ xsimplify f)
~?= ("x+1+0x^2+x+1-2x-2", "0")
, "multiply 1" ~:
let f1 = N 2
f2 = N 3
in (str f1, str f2, str $ f1 `multiply` f2)
~?= ("2", "3", "6")
, "multiply 2" ~:
let f1 = N 2
f2 = 3`x`2
in (str f1, str f2, str $ f1 `multiply` f2)
~?= ("2", "3x^2", "6x^2")
, "multiply 3" ~:
let f1 = 2`x`3
f2 = 3`x`4
in (str f1, str f2, str $ f1 `multiply` f2)
~?= ("2x^3", "3x^4", "6x^7")
, "multiply 4" ~:
let f1 = N 2
f2 = Add[1`x`1,2`x`2,N 3]
in (str f1, str f2, str $ f1 `multiply` f2)
~?= ("2", "x+2x^2+3", "2x+4x^2+6")
, "multiply 5" ~:
let f1 = Add[1`x`1,N 1]
f2 = Add[2`x`1,N 3]
f3 = f1 `multiply` f2
f4 = xsimplify f3
in (str f1, str f2, str f3, str f4)
~?= ("x+1", "2x+3", "2x^2+3x+2x+3", "2x^2+5x+3")
]
main = do
runTestText (putTextToHandle stderr False) tests
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