forked from GitHub/gf-core
92 lines
2.2 KiB
Haskell
92 lines
2.2 KiB
Haskell
module AnswerBase where
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import GSyntax
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-- interpretation of Base
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type Prop = Bool
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type Ent = Int
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domain = [0 .. 100]
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iS :: GS -> Prop
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iS s = case s of
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GPredAP np ap -> iNP np (iAP ap)
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GConjS c s t -> iConj c (iS s) (iS t)
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iNP :: GNP -> (Ent -> Prop) -> Prop
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iNP np p = case np of
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GEvery cn -> all (\x -> not (iCN cn x) || p x) domain
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GSome cn -> any (\x -> iCN cn x && p x) domain
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GNone cn -> not (any (\x -> iCN cn x && p x) domain)
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GMany pns -> and (map p (iListPN pns))
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GConjNP c np1 np2 -> iConj c (iNP np1 p) (iNP np2 p)
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GUsePN a -> p (iPN a)
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iPN :: GPN -> Ent
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iPN pn = case pn of
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GUseInt i -> iInt i
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GSum pns -> sum (iListPN pns)
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GProduct pns -> product (iListPN pns)
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GGCD pns -> foldl1 gcd (iListPN pns)
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iAP :: GAP -> Ent -> Prop
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iAP ap e = case ap of
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GComplA2 a2 np -> iNP np (iA2 a2 e)
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GConjAP c ap1 ap2 -> iConj c (iAP ap1 e) (iAP ap2 e)
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GEven -> even e
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GOdd -> odd e
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GPrime -> prime e
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iCN :: GCN -> Ent -> Prop
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iCN cn e = case cn of
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GModCN ap cn0 -> (iCN cn0 e) && (iAP ap e)
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GNumber -> True
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iConj :: GConj -> Prop -> Prop -> Prop
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iConj c = case c of
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GAnd -> (&&)
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GOr -> (||)
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iA2 :: GA2 -> Ent -> Ent -> Prop
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iA2 a2 e1 e2 = case a2 of
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GGreater -> e1 > e2
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GSmaller -> e1 < e2
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GEqual -> e1 == e2
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GDivisible -> e2 /= 0 && mod e1 e2 == 0
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iListPN :: GListPN -> [Ent]
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iListPN gls = case gls of
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GListPN pns -> map iPN pns
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iInt :: GInt -> Ent
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iInt gi = case gi of
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GInt i -> fromInteger i
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-- questions and answers
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iQuestion :: GQuestion -> Either Bool [Ent]
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iQuestion q = case q of
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GWhatIs pn -> Right [iPN pn] -- computes the value
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GWhichAre cn ap -> Right [e | e <- domain, iCN cn e, iAP ap e]
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GQuestS s -> Left (iS s)
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question2answer :: GQuestion -> GAnswer
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question2answer q = case iQuestion q of
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Left True -> GYes
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Left False -> GNo
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Right [] -> GValue (GNone GNumber)
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Right [v] -> GValue (GUsePN (ent2pn v))
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Right vs -> GValue (GMany (GListPN (map ent2pn vs)))
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ent2pn :: Ent -> GPN
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ent2pn e = GUseInt (GInt (toInteger e))
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-- auxiliary
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prime :: Int -> Bool
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prime x = elem x primes where
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primes = sieve [2 .. x]
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sieve (p:xs) = p : sieve [ n | n <- xs, n `mod` p > 0 ]
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sieve [] = []
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