semantics extended to questions

examples/tutorial/semantics/AnswerBase.hs

@@ -5,7 +5,7 @@ import GSyntax
 -- interpretation of Base
 
 type Prop = Bool
-type Exp = Int
+type Ent = Int
 domain = [0 .. 100]
 
 iS :: GS -> Prop
@@ -13,21 +13,31 @@ iS s = case s of
   GPredAP np ap -> iNP np (iAP ap)
   GConjS c s t  -> iConj c (iS s) (iS t)
 
-iNP :: GNP -> (Exp -> Prop) -> Prop
+iNP :: GNP -> (Ent -> Prop) -> Prop
 iNP np p = case np of
   GEvery cn -> all (\x -> not (iCN cn x) || p x) domain
   GSome  cn -> any (\x ->      iCN cn x  && p x) domain
+  GNone  cn -> not (any (\x -> iCN cn x  && p x) domain)
+  GMany pns -> and (map p (iListPN pns))
   GConjNP c np1 np2 -> iConj c (iNP np1 p) (iNP np2 p)
-  GUseInt (GInt i) -> p (fromInteger i)
+  GUsePN a -> p (iPN a)
 
-iAP :: GAP -> Exp -> Prop
+iPN :: GPN -> Ent
+iPN pn = case pn of  
+  GUseInt i -> iInt i
+  GSum pns -> sum (iListPN pns)
+  GProduct pns -> product (iListPN pns)
+  GGCD pns -> foldl1 gcd (iListPN pns)
+
+iAP :: GAP -> Ent -> Prop
 iAP ap e = case ap of
   GComplA2 a2 np    -> iNP np (iA2 a2 e)
   GConjAP c ap1 ap2 -> iConj c (iAP ap1 e) (iAP ap2 e)
-  GEven -> even e
-  GOdd -> not (even e)
+  GEven  -> even e
+  GOdd   -> odd e
+  GPrime -> prime e
 
-iCN :: GCN -> Exp -> Prop
+iCN :: GCN -> Ent -> Prop
 iCN cn e = case cn of
   GModCN ap cn0 -> (iCN cn0 e) && (iAP ap e)
   GNumber -> True
@@ -37,8 +47,45 @@ iConj c = case c of
   GAnd -> (&&)
   GOr  -> (||)
 
-iA2 :: GA2 -> Exp -> Exp -> Prop
+iA2 :: GA2 -> Ent -> Ent -> Prop
 iA2 a2 e1 e2 = case a2 of
-  GGreater -> e1 > e1
+  GGreater -> e1 > e2
   GSmaller -> e1 < e2 
   GEqual   -> e1 == e2
+  GDivisible -> e2 /= 0 && mod e1 e2 == 0
+
+iListPN :: GListPN -> [Ent]
+iListPN gls = case gls of
+  GListPN pns -> map iPN pns
+
+iInt :: GInt -> Ent
+iInt gi = case gi of
+  GInt i -> fromInteger i
+
+-- questions and answers
+
+iQuestion :: GQuestion -> Either Bool [Ent]
+iQuestion q = case q of
+  GWhatIs pn      -> Right [iPN pn]  -- computes the value
+  GWhichAre cn ap -> Right [e | e <- domain, iCN cn e, iAP ap e]
+  GQuestS s       -> Left  (iS s)
+
+question2answer :: GQuestion -> GAnswer
+question2answer q = case iQuestion q of
+  Left True  -> GYes
+  Left False -> GNo
+  Right []   -> GValue (GNone GNumber)
+  Right [v]  -> GValue (GUsePN (ent2pn v))
+  Right vs   -> GValue (GMany (GListPN (map ent2pn vs)))
+
+ent2pn :: Ent -> GPN
+ent2pn e = GUseInt (GInt (toInteger e))
+
+
+-- auxiliary
+
+prime :: Int -> Bool
+prime x = elem x primes where
+  primes = sieve [2 .. x]
+  sieve (p:xs) = p : sieve [ n | n <- xs, n `mod` p > 0 ]
+  sieve [] = []