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forked from GitHub/gf-core

tutorial semantics example works except one rul

This commit is contained in:
aarne
2008-06-20 10:38:03 +00:00
parent c3bb8267e6
commit e4119186fa
14 changed files with 783 additions and 0 deletions

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module Main where
import GSyntax
import AnswerBase
import GF.GFCC.API
main :: IO ()
main = do
gr <- file2grammar "base.gfcc"
loop gr
loop :: MultiGrammar -> IO ()
loop gr = do
s <- getLine
case parse gr "BaseEng" "Question" s of
[] -> putStrLn "no parse"
ts -> mapM_ answer ts
loop gr
where
answer t = putStrLn $ linearize gr "BaseEng" $ gf $ question2answer $ fg t

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module AnswerBase where
import GSyntax
-- interpretation of Base
type Prop = Bool
type Ent = Int
domain = [0 .. 100]
iS :: GS -> Prop
iS s = case s of
GPredAP np ap -> iNP np (iAP ap)
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 -> not (any (\x -> p x) domain)
GMany pns -> and (map p (iListPN pns))
GConjNP c np1 np2 -> iConj c (iNP np1 p) (iNP np2 p)
GUsePN a -> p (iPN a)
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 -> odd e
GPrime -> prime e
iCN :: GCN -> Ent -> Prop
iCN cn e = case cn of
GModCN ap cn0 -> (iCN cn0 e) && (iAP ap e)
GNumber -> True
iConj :: GConj -> Prop -> Prop -> Prop
iConj c = case c of
GAnd -> (&&)
GOr -> (||)
iA2 :: GA2 -> Ent -> Ent -> Prop
iA2 a2 e1 e2 = case a2 of
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
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 [] = []

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-- abstract syntax of a query language
abstract Base = {
cat
S ;
NP ;
PN ;
CN ;
AP ;
A2 ;
Conj ;
fun
-- sentence syntax
PredAP : NP -> AP -> S ;
ComplA2 : A2 -> NP -> AP ;
ModCN : AP -> CN -> CN ;
ConjAP : Conj -> AP -> AP -> AP ;
ConjNP : Conj -> NP -> NP -> NP ;
UsePN : PN -> NP ;
Every : CN -> NP ;
Some : CN -> NP ;
And, Or : Conj ;
-- lexicon
UseInt : Int -> PN ;
Number : CN ;
Even, Odd, Prime : AP ;
Equal, Greater, Smaller, Divisible : A2 ;
Sum, Product, GCD : ListPN -> PN ;
-- adding questions
cat
Question ;
Answer ;
ListPN ;
fun
WhatIs : PN -> Question ;
WhichAre : CN -> AP -> Question ;
QuestS : S -> Question ;
Yes : Answer ;
No : Answer ;
Value : NP -> Answer ;
None : NP ;
Many : ListPN -> NP ;
BasePN : PN -> PN -> ListPN ;
ConsPN : PN -> ListPN -> ListPN ;
}

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--# -path=.:prelude
concrete BaseEng of Base = open Prelude in {
flags lexer=literals ; unlexer=text ;
-- English concrete syntax; greatly simplified - just for demo purposes
lin
PredAP = infixSS "is" ;
ComplA2 = cc2 ;
ModCN = cc2 ;
ConjAP c = infixSS c.s ;
ConjNP c = infixSS c.s ;
UsePN a = a ;
Every = prefixSS "every" ;
Some = prefixSS "some" ;
And = ss "and" ;
Or = ss "or" ;
UseInt n = n ;
Number = ss "number" ;
Even = ss "even" ;
Odd = ss "odd" ;
Prime = ss "prime" ;
Equal = ss ("equal" ++ "to") ;
Greater = ss ("greater" ++ "than") ;
Smaller = ss ("smaller" ++ "than") ;
Divisible = ss ("divisible" ++ "by") ;
Sum = prefixSS ["the sum of"] ;
Product = prefixSS ["the product of"] ;
GCD = prefixSS ["the greatest common divisor of"] ;
WhatIs = prefixSS ["what is"] ;
WhichAre cn ap = ss ("which" ++ cn.s ++ "is" ++ ap.s) ; ---- are
QuestS s = s ; ---- inversion
Yes = ss "yes" ;
No = ss "no" ;
Value np = np ;
None = ss "none" ;
Many list = list ;
BasePN = infixSS "and" ;
ConsPN = infixSS "," ;
}

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incomplete concrete BaseI of Base =
open Syntax, (G = Grammar), Symbolic, LexBase in {
flags lexer=literals ; unlexer=text ;
lincat
Question = G.Phr ;
Answer = G.Phr ;
S = G.Cl ;
NP = G.NP ;
PN = G.NP ;
CN = G.CN ;
AP = G.AP ;
A2 = G.A2 ;
Conj = G.Conj ;
ListPN = G.ListNP ;
lin
PredAP = mkCl ;
ComplA2 = mkAP ;
ModCN = mkCN ;
ConjAP = mkAP ;
ConjNP = mkNP ;
UsePN p = p ;
Every = mkNP every_Det ;
Some = mkNP someSg_Det ;
And = and_Conj ;
Or = or_Conj ;
UseInt i = symb (i ** {lock_Int = <>}) ; ---- terrible to need this
Number = mkCN number_N ;
Even = mkAP even_A ;
Odd = mkAP odd_A ;
Prime = mkAP prime_A ;
Equal = equal_A2 ;
Greater = greater_A2 ;
Smaller = smaller_A2 ;
Divisible = divisible_A2 ;
Sum = prefix sum_N2 ;
Product = prefix product_N2 ;
GCD nps = mkNP (mkDet DefArt (mkOrd great_A))
(mkCN common_A (mkCN divisor_N2 (mkNP and_Conj nps))) ;
WhatIs np = mkPhr (mkQS (mkQCl whatSg_IP (mkVP np))) ;
-- WhichAre cn ap = mkPhr (mkQS (mkQCl (mkIP (mkIDet which_IQuant plNum) cn) (mkVP ap))) ;
QuestS s = mkPhr (mkQS (mkQCl s)) ;
Yes = mkPhr yes_Utt ;
No = mkPhr no_Utt ;
Value np = mkPhr (mkUtt np) ;
Many list = mkNP and_Conj list ;
None = none_NP ;
BasePN = G.BaseNP ;
ConsPN = G.ConsNP ;
oper
prefix : G.N2 -> G.ListNP -> G.NP = \n2,nps ->
mkNP DefArt (mkCN n2 (mkNP and_Conj nps)) ;
}

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--# -path=.:prelude:present:api:mathematical
concrete BaseIEng of Base = BaseI with
(Syntax = SyntaxEng),
(Grammar = GrammarEng),
(G = GrammarEng),
(Symbolic = SymbolicEng),
(LexBase = LexBaseEng) ;

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--# -path=.:prelude:present:api:mathematical
concrete BaseSwe of Base = BaseI with
(Syntax = SyntaxSwe),
(Grammar = GrammarSwe),
(G = GrammarSwe),
(Symbolic = SymbolicSwe),
(LexBase = LexBaseSwe) ;

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module GSyntax where
import GF.GFCC.DataGFCC
import GF.GFCC.AbsGFCC
----------------------------------------------------
-- automatic translation from GF to Haskell
----------------------------------------------------
class Gf a where gf :: a -> Exp
class Fg a where fg :: Exp -> a
newtype GString = GString String deriving Show
instance Gf GString where
gf (GString s) = DTr [] (AS s) []
instance Fg GString where
fg t =
case t of
DTr [] (AS s) [] -> GString s
_ -> error ("no GString " ++ show t)
newtype GInt = GInt Integer deriving Show
instance Gf GInt where
gf (GInt s) = DTr [] (AI s) []
instance Fg GInt where
fg t =
case t of
DTr [] (AI s) [] -> GInt s
_ -> error ("no GInt " ++ show t)
newtype GFloat = GFloat Double deriving Show
instance Gf GFloat where
gf (GFloat s) = DTr [] (AF s) []
instance Fg GFloat where
fg t =
case t of
DTr [] (AF s) [] -> GFloat s
_ -> error ("no GFloat " ++ show t)
----------------------------------------------------
-- below this line machine-generated
----------------------------------------------------
data GA2 =
GDivisible
| GEqual
| GGreater
| GSmaller
deriving Show
data GAP =
GComplA2 GA2 GNP
| GConjAP GConj GAP GAP
| GEven
| GOdd
| GPrime
deriving Show
data GAnswer =
GNo
| GValue GNP
| GYes
deriving Show
data GCN =
GModCN GAP GCN
| GNumber
deriving Show
data GConj =
GAnd
| GOr
deriving Show
newtype GListPN = GListPN [GPN] deriving Show
data GNP =
GConjNP GConj GNP GNP
| GEvery GCN
| GMany GListPN
| GNone
| GSome GCN
| GUsePN GPN
deriving Show
data GPN =
GGCD GListPN
| GProduct GListPN
| GSum GListPN
| GUseInt GInt
deriving Show
data GQuestion =
GQuestS GS
| GWhatIs GPN
| GWhichAre GCN GAP
deriving Show
data GS = GPredAP GNP GAP
deriving Show
instance Gf GA2 where
gf GDivisible = DTr [] (AC (CId "Divisible")) []
gf GEqual = DTr [] (AC (CId "Equal")) []
gf GGreater = DTr [] (AC (CId "Greater")) []
gf GSmaller = DTr [] (AC (CId "Smaller")) []
instance Gf GAP where
gf (GComplA2 x1 x2) = DTr [] (AC (CId "ComplA2")) [gf x1, gf x2]
gf (GConjAP x1 x2 x3) = DTr [] (AC (CId "ConjAP")) [gf x1, gf x2, gf x3]
gf GEven = DTr [] (AC (CId "Even")) []
gf GOdd = DTr [] (AC (CId "Odd")) []
gf GPrime = DTr [] (AC (CId "Prime")) []
instance Gf GAnswer where
gf GNo = DTr [] (AC (CId "No")) []
gf (GValue x1) = DTr [] (AC (CId "Value")) [gf x1]
gf GYes = DTr [] (AC (CId "Yes")) []
instance Gf GCN where
gf (GModCN x1 x2) = DTr [] (AC (CId "ModCN")) [gf x1, gf x2]
gf GNumber = DTr [] (AC (CId "Number")) []
instance Gf GConj where
gf GAnd = DTr [] (AC (CId "And")) []
gf GOr = DTr [] (AC (CId "Or")) []
instance Gf GListPN where
gf (GListPN [x1,x2]) = DTr [] (AC (CId "BasePN")) [gf x1, gf x2]
gf (GListPN (x:xs)) = DTr [] (AC (CId "ConsPN")) [gf x, gf (GListPN xs)]
instance Gf GNP where
gf (GConjNP x1 x2 x3) = DTr [] (AC (CId "ConjNP")) [gf x1, gf x2, gf x3]
gf (GEvery x1) = DTr [] (AC (CId "Every")) [gf x1]
gf (GMany x1) = DTr [] (AC (CId "Many")) [gf x1]
gf GNone = DTr [] (AC (CId "None")) []
gf (GSome x1) = DTr [] (AC (CId "Some")) [gf x1]
gf (GUsePN x1) = DTr [] (AC (CId "UsePN")) [gf x1]
instance Gf GPN where
gf (GGCD x1) = DTr [] (AC (CId "GCD")) [gf x1]
gf (GProduct x1) = DTr [] (AC (CId "Product")) [gf x1]
gf (GSum x1) = DTr [] (AC (CId "Sum")) [gf x1]
gf (GUseInt x1) = DTr [] (AC (CId "UseInt")) [gf x1]
instance Gf GQuestion where
gf (GQuestS x1) = DTr [] (AC (CId "QuestS")) [gf x1]
gf (GWhatIs x1) = DTr [] (AC (CId "WhatIs")) [gf x1]
gf (GWhichAre x1 x2) = DTr [] (AC (CId "WhichAre")) [gf x1, gf x2]
instance Gf GS where gf (GPredAP x1 x2) = DTr [] (AC (CId "PredAP")) [gf x1, gf x2]
instance Fg GA2 where
fg t =
case t of
DTr [] (AC (CId "Divisible")) [] -> GDivisible
DTr [] (AC (CId "Equal")) [] -> GEqual
DTr [] (AC (CId "Greater")) [] -> GGreater
DTr [] (AC (CId "Smaller")) [] -> GSmaller
_ -> error ("no A2 " ++ show t)
instance Fg GAP where
fg t =
case t of
DTr [] (AC (CId "ComplA2")) [x1,x2] -> GComplA2 (fg x1) (fg x2)
DTr [] (AC (CId "ConjAP")) [x1,x2,x3] -> GConjAP (fg x1) (fg x2) (fg x3)
DTr [] (AC (CId "Even")) [] -> GEven
DTr [] (AC (CId "Odd")) [] -> GOdd
DTr [] (AC (CId "Prime")) [] -> GPrime
_ -> error ("no AP " ++ show t)
instance Fg GAnswer where
fg t =
case t of
DTr [] (AC (CId "No")) [] -> GNo
DTr [] (AC (CId "Value")) [x1] -> GValue (fg x1)
DTr [] (AC (CId "Yes")) [] -> GYes
_ -> error ("no Answer " ++ show t)
instance Fg GCN where
fg t =
case t of
DTr [] (AC (CId "ModCN")) [x1,x2] -> GModCN (fg x1) (fg x2)
DTr [] (AC (CId "Number")) [] -> GNumber
_ -> error ("no CN " ++ show t)
instance Fg GConj where
fg t =
case t of
DTr [] (AC (CId "And")) [] -> GAnd
DTr [] (AC (CId "Or")) [] -> GOr
_ -> error ("no Conj " ++ show t)
instance Fg GListPN where
fg t =
case t of
DTr [] (AC (CId "BasePN")) [x1,x2] -> GListPN [fg x1, fg x2]
DTr [] (AC (CId "ConsPN")) [x1,x2] -> let GListPN xs = fg x2 in GListPN (fg x1:xs)
_ -> error ("no ListPN " ++ show t)
instance Fg GNP where
fg t =
case t of
DTr [] (AC (CId "ConjNP")) [x1,x2,x3] -> GConjNP (fg x1) (fg x2) (fg x3)
DTr [] (AC (CId "Every")) [x1] -> GEvery (fg x1)
DTr [] (AC (CId "Many")) [x1] -> GMany (fg x1)
DTr [] (AC (CId "None")) [] -> GNone
DTr [] (AC (CId "Some")) [x1] -> GSome (fg x1)
DTr [] (AC (CId "UsePN")) [x1] -> GUsePN (fg x1)
_ -> error ("no NP " ++ show t)
instance Fg GPN where
fg t =
case t of
DTr [] (AC (CId "GCD")) [x1] -> GGCD (fg x1)
DTr [] (AC (CId "Product")) [x1] -> GProduct (fg x1)
DTr [] (AC (CId "Sum")) [x1] -> GSum (fg x1)
DTr [] (AC (CId "UseInt")) [x1] -> GUseInt (fg x1)
_ -> error ("no PN " ++ show t)
instance Fg GQuestion where
fg t =
case t of
DTr [] (AC (CId "QuestS")) [x1] -> GQuestS (fg x1)
DTr [] (AC (CId "WhatIs")) [x1] -> GWhatIs (fg x1)
DTr [] (AC (CId "WhichAre")) [x1,x2] -> GWhichAre (fg x1) (fg x2)
_ -> error ("no Question " ++ show t)
instance Fg GS where
fg t =
case t of
DTr [] (AC (CId "PredAP")) [x1,x2] -> GPredAP (fg x1) (fg x2)
_ -> error ("no S " ++ show t)

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interface LexBase = open Syntax in {
oper
even_A : A ;
odd_A : A ;
prime_A : A ;
common_A : A ;
great_A : A ;
equal_A2 : A2 ;
greater_A2 : A2 ;
smaller_A2 : A2 ;
divisible_A2 : A2 ;
number_N : N ;
sum_N2 : N2 ;
product_N2 : N2 ;
divisor_N2 : N2 ;
none_NP : NP ; ---
}

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instance LexBaseEng of LexBase = open SyntaxEng, ParadigmsEng in {
oper
even_A = mkA "even" ;
odd_A = mkA "odd" ;
prime_A = mkA "prime" ;
great_A = mkA "great" ;
common_A = mkA "common" ;
equal_A2 = mkA2 (mkA "equal") (mkPrep "to") ;
greater_A2 = mkA2 (mkA "greater") (mkPrep "than") ; ---
smaller_A2 = mkA2 (mkA "smaller") (mkPrep "than") ; ---
divisible_A2 = mkA2 (mkA "divisible") (mkPrep "by") ;
number_N = mkN "number" ;
sum_N2 = mkN2 (mkN "sum") (mkPrep "of") ;
product_N2 = mkN2 (mkN "product") (mkPrep "of") ;
divisor_N2 = mkN2 (mkN "divisor") (mkPrep "of") ;
none_NP = mkNP (mkPN "none") ; ---
}

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instance LexBaseSwe of LexBase = open SyntaxSwe, ParadigmsSwe in {
oper
even_A = mkA "jämn" ;
odd_A = invarA "udda" ;
prime_A = mkA "prim" ;
great_A = mkA "stor" "större" "störst" ;
common_A = mkA "gemensam" ;
equal_A2 = mkA2 (invarA "lika") (mkPrep "med") ;
greater_A2 = mkA2 (invarA "större") (mkPrep "än") ; ---
smaller_A2 = mkA2 (invarA "mindre") (mkPrep "än") ; ---
divisible_A2 = mkA2 (mkA "delbar") (mkPrep "med") ;
number_N = mkN "tal" "tal" ;
sum_N2 = mkN2 (mkN "summa") (mkPrep "av") ;
product_N2 = mkN2 (mkN "produkt") (mkPrep "av") ;
divisor_N2 = mkN2 (mkN "delare") (mkPrep "av") ;
none_NP = mkNP (mkPN "inget" neutrum) ; ---
invarA : Str -> A = \x -> mkA x x x x x ; ---
}

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module Logic where
data Prop =
Pred Ident [Exp]
| And Prop Prop
| Or Prop Prop
| If Prop Prop
| Not Prop
| All Prop
| Exist Prop
deriving Show
data Exp =
App Ident [Exp]
| Var Int -- de Bruijn index
deriving Show
type Ident = String
data Model a = Model {
app :: Ident -> [a] -> a,
prd :: Ident -> [a] -> Bool,
dom :: [a]
}
type Assignment a = [a]
update :: a -> Assignment a -> Assignment a
update x assign = x : assign
look :: Int -> Assignment a -> a
look i assign = assign !! i
valExp :: Model a -> Assignment a -> Exp -> a
valExp model assign exp = case exp of
App f xs -> app model f (map (valExp model assign) xs)
Var i -> look i assign
valProp :: Model a -> Assignment a -> Prop -> Bool
valProp model assign prop = case prop of
Pred f xs -> prd model f (map (valExp model assign) xs)
And a b -> v a && v b
Or a b -> v a || v b
If a b -> if v a then v b else True
Not a -> not (v a)
All p -> all (\x -> valProp model (update x assign) p) (dom model)
Exist p -> any (\x -> valProp model (update x assign) p) (dom model)
where
v = valProp model assign
liftProp :: Int -> Prop -> Prop
liftProp i p = case p of
Pred f xs -> Pred f (map liftExp xs)
And a b -> And (lift a) (lift b)
Or a b -> Or (lift a) (lift b)
If a b -> If (lift a) (lift b)
Not a -> Not (lift a)
All p -> All (liftProp (i+1) p)
Exist p -> Exist (liftProp (i+1) p)
where
lift = liftProp i
liftExp e = case e of
App f xs -> App f (map liftExp xs)
Var j -> Var (j + i)
_ -> e
-- example: initial segments of integers
intModel :: Int -> Model Int
intModel mx = Model {
app = \f xs -> case (f,xs) of
("+",_) -> sum xs
(_,[]) -> read f,
prd = \f xs -> case (f,xs) of
("E",[x]) -> even x
("<",[x,y]) -> x < y
("=",[x,y]) -> x == y
_ -> error "undefined val",
dom = [0 .. mx]
}
exModel = intModel 100
ev x = Pred "E" [x]
lt x y = Pred "<" [x,y]
eq x y = Pred "=" [x,y]
int i = App (show i) []
ex1 :: Prop
ex1 = Exist (ev (Var 0))
ex2 :: Prop
ex2 = All (Exist (lt (Var 1) (Var 0)))
ex3 :: Prop
ex3 = All (If (lt (Var 0) (int 100)) (Exist (lt (Var 1) (Var 0))))
ex4 :: Prop
ex4 = All (All (If (lt (Var 1) (Var 0)) (Not (lt (Var 0) (Var 1)))))

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module SemBase where
import GSyntax
import Logic
-- translation of Base syntax to Logic
iS :: GS -> Prop
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 np p = case np of
GEvery cn -> All (If (iCN cn var) (liftProp 0 (p var))) ----
GSome cn -> Exist (And (iCN cn var) (p var)) ----
GConjNP c np1 np2 -> iConj c (iNP np1 p) (iNP np2 p)
GUseInt (GInt i) -> p (int i)
iAP :: GAP -> Exp -> 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 -> ev e
GOdd -> Not (ev e)
iCN :: GCN -> Exp -> Prop
iCN cn e = case cn of
GModCN ap cn0 -> And (iCN cn0 e) (iAP ap e)
GNumber -> eq e e
iConj :: GConj -> Prop -> Prop -> Prop
iConj c = case c of
GAnd -> And
GOr -> Or
iA2 :: GA2 -> Exp -> Exp -> Prop
iA2 a2 e1 e2 = case a2 of
GGreater -> lt e2 e1
GSmaller -> lt e1 e2
GEqual -> eq e1 e2
var = Var 0

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module Main where
import GSyntax
import SemBase
import Logic
import GF.GFCC.API
main :: IO ()
main = do
gr <- file2grammar "base.gfcc"
loop gr
loop :: MultiGrammar -> IO ()
loop gr = do
s <- getLine
let t:_ = parse gr "BaseEng" "S" s
putStrLn $ showTree t
let p = iS $ fg t
putStrLn $ show p
let v = valProp exModel [] p
putStrLn $ show v
loop gr