module Domain.Math.Polynomial.BuggyBalance
( buggyBalanceRules, buggyBalanceExprRules, buggyPriority
) where
import Control.Monad
import Data.Ratio
import Domain.Math.Data.Relation
import Domain.Math.Expr
import Domain.Math.Numeric.Views
import Domain.Math.Polynomial.BalanceUtils
import Domain.Math.Polynomial.Views
import Ideas.Common.Library
buggyBalanceRules :: [Rule (Equation Expr)]
buggyBalanceRules =
[ rule1234, rule201, rule2111, rule2112, rule2113, rule2114
, rule2121, rule2122, rule2131, rule2132, rule2133, rule2134
, rule2135, rule2136, rule2137, rule2138, rule2141, rule2142
, rule221, rule222, rule2232, rule2233
, rule311, rule322, rule2231, rule227, rule321, rule323
]
buggyBalanceExprRules :: [Rule Expr]
buggyBalanceExprRules =
[ rule121, rule122, rule1231, rule1232, rule1311, rule1312
, rule1314, rule1321, rule1322, rule133, rule134, rule135
, rule136, rule137
]
buggyPriority :: [Id]
buggyPriority =
[ getId rule1312, getId rule121, getId rule221, getId rule222
, getId rule2232, getId rule2233, getId rule227, getId rule323
]
rule121 :: Rule Expr
rule121 = describe "1.2.1: fout bij vermenigvuldigen" $
buggyBalanceExprRule "multiply1" f
where
f (expr :/: c) = do
(a, b) <- match timesView expr
return $ a/(b*c)
f _ = Nothing
rule122 :: Rule Expr
rule122 = describe "1.2.2: fout bij vermenigvuldigen" $
buggyBalanceExprRule "multiply2" f
where
f (a :*: expr) = do
((b, x), c) <- match (plusView >>> first timesView) expr
return $ x/(a*b) + a*c
f _ = Nothing
rule1231 :: Rule Expr
rule1231 = describe "1.2.3.1: fout bij vermenigvuldigen; min raakt kwijt" $
buggyBalanceExprRule "multiply3" f
where
f (a :*: expr) = do
(b, (c, x)) <- match (minusView >>> second timesView) expr
return $ a*b+a*c*x
f _ = Nothing
rule1232 :: Rule Expr
rule1232 = describe "1.2.3.2: fout bij vermenigvuldigen; min te veel" $
buggyBalanceExprRule "multiply4" f
where
f expr = do
(a, (x, b)) <- match (timesView >>> negView *** minusView) expr
return $ -a*x-a*b
rule1234 :: Rule (Equation Expr)
rule1234 = describe "1.2.3.4: fout bij vermenigvuldigen; delen door negatief getal" $
buggyBalanceRule "multiply5" f
where
f (expr :==: b) = do
(a, x) <- match (timesView >>> first negView) expr
return $ x :==: b/a
rule1311 :: Rule Expr
rule1311 = describe "1.3.1.1: fout bij haakjes wegwerken; haakjes staan er niet voor niets" $
buggyBalanceExprRule "par1" f
where
f expr = do
(a, (x, b)) <- match (timesView >>> second plusView) expr
return $ a*x+b
rule1312 :: Rule Expr
rule1312 = describe "1.3.1.2: fout bij haakjes wegwerken; haakjes staan er niet voor niets" $
buggyBalanceExprRule "par2" f
where
f (e1 :*: e2) = do
(n, a) <- match (divView >>> first integerView) e1
guard (n==1)
(x, b) <- match plusView e2
return $ 1/a*x+b
f _ = Nothing
rule1314 :: Rule Expr
rule1314 = describe "1.3.1.4: fout bij haakjes wegwerken met unaire min; haakjes staan er niet voor niets" $
buggyBalanceExprRule "par11" f
where
f expr = do
(a, b) <- match (negView >>> plusView) expr
return $ -a+b
rule1321 :: Rule Expr
rule1321 = describe "1.3.2.1: fout bij haakjes wegwerken; haakjes goed uitwerken" $
buggyBalanceExprRule "par4" f
where
f (a :*: expr) = do
((_, x), c) <- match (plusView >>> first timesView) expr
return $ a*x+a*c
f _ = Nothing
rule1322 :: Rule Expr
rule1322 = describe "1.3.2.2: fout bij haakjes wegwerken; haakjes goed uitwerken" $
buggyBalanceExprRule "par5" f
where
f (a :*: expr) = do
(b, (_, x)) <- match (minusView >>> second timesView) expr
return $ a*b-a*x
f _ = Nothing
rule133 :: Rule Expr
rule133 = describe "1.3.3: fout bij haakjes wegwerken; haakjes goed uitwerken" $
buggyBalanceExprRule "par6" f
where
f (a :*: expr) = do
((b, x), c) <- match (plusView >>> first timesView) expr
return $ b*x+a*c
f _ = Nothing
rule134 :: Rule Expr
rule134 = describe "1.3.4: fout bij haakjes wegwerken; haakjes goed uitwerken" $
buggyBalanceExprRule "par7" f
where
f expr = do
(a, (b, c)) <- match (minusView >>> second plusView) expr
return $ a-b+c
rule135 :: Rule Expr
rule135 = describe "1.3.5: fout bij haakjes wegwerken; kijk goed waar de haakjes staan" $
buggyBalanceExprRule "par8" f
where
f expr = do
((a, (b, c)), d) <- match (minusView >>> first (timesView >>> second minusView)) expr
return $ a*b-a*c-a*d
rule136 :: Rule Expr
rule136 = describe "1.3.6: fout bij haakjes wegwerken; haakjes goed uitwerken" $
buggyBalanceExprRule "par9" f
where
f (a :*: expr) = do
((b, x), c) <- match (plusView >>> first timesView) expr
return $ (a+b)*x+a*c
f _ = Nothing
rule137 :: Rule Expr
rule137 = describe "1.3.7: fout bij haakjes wegwerken; denk aan 'voorrangsregels'" $
buggyBalanceExprRule "par10" f
where
f (a :+: expr) = do
(b, (x, c)) <- match (timesView >>> second plusView) expr
return $ (a+b)*(x+c)
f _ = Nothing
rule201 :: Rule (Equation Expr)
rule201 = describe "2.0.1: Links en rechts alleen maar verwisseld?" $
buggyBalanceRule "flip1" f
where
f (a :==: rhs) = do
(b, c) <- match minusView rhs
return $ c-b :==: a
rule2111 :: Rule (Equation Expr)
rule2111 = describe "2.1.1.1: Links en rechts hetzelfde optellen; links +b en rechts -b" $
buggyBalanceRuleArg "addbal1" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(ax, b) <- matchPlusCon lhs
guard (b>0)
return (ax :==: rhs+fromRational b, fromRational b)
rule2112 :: Rule (Equation Expr)
rule2112 = describe "2.1.1.2: Links en rechts hetzelfde optellen; links -b en rechts +b" $
buggyBalanceRuleArg "addbal2" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(ax, b) <- matchPlusCon lhs
guard (b<0)
return (ax :==: rhs+fromRational b, fromRational (abs b))
rule2113 :: Rule (Equation Expr)
rule2113 = describe "2.1.1.3: Je trekt er rechts {?} vanaf, maar links tel je {?} erbij op." $
buggyBalanceRuleArg "addbal9" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(cx, d) <- matchPlusCon rhs
guard (d>0)
return (lhs+fromRational d :==: cx, fromRational d)
rule2114 :: Rule (Equation Expr)
rule2114 = describe "2.1.1.4: Je telt er rechts {?} bij op, maar links trek je {?} er vanaf." $
buggyBalanceRuleArg "addbal10" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(cx, d) <- matchPlusCon rhs
guard (d<0)
return (lhs+fromRational d :==: cx, fromRational (abs d))
rule2121 :: Rule (Equation Expr)
rule2121 = describe "2.1.2.1: Links en rechts hetzelfde optellen; links +cx en rechts -cx" $
buggyBalanceRuleArg "addbal3" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin lhs
~(y, c, d) <- matchLin rhs
guard (c>0 && x==y)
return (fromRational (a+c)*x+fromRational b :==: fromRational d, fromRational c*x)
rule2122 :: Rule (Equation Expr)
rule2122 = describe "2.1.2.2: Links en rechts hetzelfde optellen; links -cx en rechts +cx" $
buggyBalanceRuleArg "addbal4" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin lhs
~(y, c, d) <- matchLin rhs
guard (c<0 && x==y)
return (fromRational (a+c)*x+fromRational b :==: fromRational d, fromRational (abs c)*x)
rule2141 :: Rule (Equation Expr)
rule2141 = describe "2.1.4.1: Links en rechts hetzelfde optellen; links -ax en rechts +ax" $
buggyBalanceRuleArg "addbal7" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin lhs
~(y, c, d) <- matchLin rhs
guard (a>0 && x==y)
return (fromRational b :==: fromRational (a+c)*x+fromRational d, fromRational a*x)
rule2142 :: Rule (Equation Expr)
rule2142 = describe "2.1.4.2: Links en rechts hetzelfde optellen; links -cx en rechts +cx" $
buggyBalanceRuleArg "addbal8" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin lhs
~(y, c, d) <- matchLin rhs
guard (a<0 && x==y)
return (fromRational b :==: fromRational (a+c)*x+fromRational d, fromRational (abs a)*x)
rule2131 :: Rule (Equation Expr)
rule2131 = describe "2.1.3.1: Links en rechts hetzelfde optellen; links -b rechts niet(s)" $
buggyBalanceRuleArg "addbal5" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(ax, b) <- matchPlusCon lhs
guard (b > 0)
return (ax :==: rhs, fromRational b)
rule2132 :: Rule (Equation Expr)
rule2132 = describe "2.1.3.2: Links en rechts hetzelfde optellen; links +b en rechts niet(s)" $
buggyBalanceRuleArg "addbal6" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(ax, b) <- matchPlusCon lhs
guard (b < 0)
return (ax :==: rhs, fromRational (abs b))
rule2133 :: Rule (Equation Expr)
rule2133 = describe "2.1.3.3: Links en rechts hetzelfde optellen; rechts -b links niet(s)" $
buggyBalanceRuleArg "addbal11" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(ax, b) <- matchPlusCon rhs
guard (b > 0)
return (lhs :==: ax, fromRational b)
rule2134 :: Rule (Equation Expr)
rule2134 = describe "2.1.3.4: Links en rechts hetzelfde optellen; rechts +b en links niet(s)" $
buggyBalanceRuleArg "addbal12" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(ax, b) <- matchPlusCon rhs
guard (b < 0)
return (lhs :==: ax, fromRational (abs b))
rule2135 :: Rule (Equation Expr)
rule2135 = describe "2.1.3.5: Links en rechts hetzelfde optellen; links -ax rechts niet(s)" $
buggyBalanceRuleArg "addbal13" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin lhs
guard (a > 0)
return (fromRational b :==: rhs, fromRational a*x)
rule2136 :: Rule (Equation Expr)
rule2136 = describe "2.1.3.6: Links en rechts hetzelfde optellen; links +ax en rechts niet(s)" $
buggyBalanceRuleArg "addbal14" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin lhs
guard (a < 0)
return (fromRational b :==: rhs, fromRational (abs a)*x)
rule2137 :: Rule (Equation Expr)
rule2137 = describe "2.1.3.7: Links en rechts hetzelfde optellen; rechts -ax links niet(s)" $
buggyBalanceRuleArg "addbal15" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin rhs
guard (a > 0)
return (lhs :==: fromRational b, fromRational a*x)
rule2138 :: Rule (Equation Expr)
rule2138 = describe "2.1.3.8: Links en rechts hetzelfde optellen; rechts +ax en links niet(s)" $
buggyBalanceRuleArg "addbal16" (writeTerm f)
where
f ~(lhs :==: rhs) = do
~(x, a, b) <- matchLin rhs
guard (a < 0)
return (lhs :==: fromRational b, fromRational (abs a)*x)
rule221 :: Rule (Equation Expr)
rule221 = describe "2.2.1: Links en rechts hetzelfde vermenigvuldigen; verkeerd om gedeeld" $
buggyBalanceRule "mulbal1" f
where
f (expr :==: c) = do
(a, x) <- match timesView expr
return $ x :==: a/c
rule222 :: Rule (Equation Expr)
rule222 = describe "2.2.2: Links en rechts hetzelfde vermenigvuldigen; links *a; rechts *b" $
buggyBalanceRuleArg "mulbal2" t
where
t = writeWith (writeRef2_ factor1Ref factor2Ref) f
f ~(lhs :==: rhs) = do
~(x, ra, b) <- matchLin lhs
~(y, rc, d) <- matchLin rhs
let a = denom ra
c = denom rc
denom = fromInteger . denominator
num = fromInteger . numerator
guard (a /= c && (a /= 1 || c /= 1))
return (num ra*x+fromRational b*a :==: num rc*y+c*fromRational d, (a, c))
rule2231 :: Rule (Equation Expr)
rule2231 = describe "2.2.3.1: Links en rechts hetzelfde vermenigvuldigen; links *p, rechts niet (of andersom)" $
buggyBalanceRecognizer "mulbal3" t
where
t = transMaybe (uncurry p) >>> writeRef_ factorRef
p ~(a1 :==: a2) ~(b1 :==: b2) = do
dl <- diffTimes a1 b1
dr <- diffTimes a2 b2
guard ((dl==1) /= (dr==1))
return (if dr/=1 then dr else dl)
rule2232 :: Rule (Equation Expr)
rule2232 = describe "2.2.3.2: Links en rechts hetzelfde vermenigvuldigen; links /p, rechts niet" $
buggyBalanceRuleArg "mulbal4" t
where
t = writeWith (writeRef_ factorRef) f
f ~(expr :==: c) = do
~(a, b) <- matchM divView expr
return (a :==: c, b)
rule2233 :: Rule (Equation Expr)
rule2233 = describe "2.2.3.3: Links en rechts hetzelfde vermenigvuldigen; links en rechts *-1" $
buggyBalanceRule "mulbal5" f
where
f (expr :==: c) = do
(a, b) <- match plusView expr
return $ -a-b :==: c
rule227 :: Rule (Equation Expr)
rule227 = describe "2.2.7: Links en rechts hetzelfde vermenigvuldigen; een kant door p delen, andere kant niets" $
buggyBalanceRecognizer "mulbal6" t
where
t = transMaybe (uncurry p) >>> writeRef_ factorRef
p ~(a1 :==: a2) ~(b1 :==: b2) = do
dl <- diffTimes a1 b1
dr <- diffTimes a2 b2
rl <- matchM rationalView dl
rr <- matchM rationalView dr
guard ( rl == 1 && rr /= 1 && numerator rr == 1 ||
rl /= 1 && rr == 1 && numerator rl == 1 )
return (fromIntegral (denominator (if rr /= 1 then rr else rl)))
rule311 :: Rule (Equation Expr)
rule311 = describe "3.1.1: Doe je wat je wilt doen?" $
buggyBalanceRule "misc1" f
where
f (lhs :==: rhs) = do
(x, a, b) <- matchLin lhs
(y, c, d) <- matchLin rhs
guard (x==y)
return (fromRational (c-a)*x+fromRational b :==: fromRational d)
rule321 :: Rule (Equation Expr)
rule321 = describe "3.2.1: Doe je wat je wilt doen? vermenigvuldig de hele linkerkant met p" $
buggyBalanceRecognizer "misc2" t
where
t = transMaybe (uncurry p) >>> writeRef_ factorRef
p ~(a1 :==: a2) ~(b1 :==: b2) = do
d <- diffTimes a2 b2
let as = from simpleSumView a1
guard (d `notElem` [1, -1] && length as > 1)
guard $ flip any (take (length as) [0..]) $ \i ->
let (xs,y:ys) = splitAt i as
aps = to sumView $ map (d*) xs ++ [y] ++ map (d*) ys
in viewEquivalent (polyViewWith rationalView) aps b1
return d
rule322 :: Rule (Equation Expr)
rule322 = describe "3.2.2: Doe je wat je wilt doen? neem het tegengestelde van de hele linkerkant" $
buggyBalanceRule "misc3" f
where
f (expr :==: c) = do
(a, b) <- match minusView expr
return $ -a-b :==: -c
rule323 :: Rule (Equation Expr)
rule323 = describe "3.2.3: Doe je wat je wilt doen? Deel de hele linkerkant door p" $
buggyBalanceRecognizer "misc4" t
where
t = transMaybe (uncurry p) >>> writeRef_ factorRef
p ~(a1 :==: a2) ~(b1 :==: b2) = do
d <- diffTimes a2 b2
dr <- matchM rationalView d
let as = from simpleSumView a1
guard (dr `notElem` [0, 1, -1] && numerator dr == 1 && length as > 1)
guard $ flip any (take (length as) [0..]) $ \i ->
let (xs,y:ys) = splitAt i as
aps = to sumView $ map (d*) xs ++ [y] ++ map (d*) ys
in viewEquivalent (polyViewWith rationalView) aps b1
return (fromRational (1/dr))