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module Library.TermNet(
TermNet,
empty,
getLeafList,
getBranchList,
genThm,
termToTermString,
thmToTermString,
addThm,
addThmFromNode,
matchThm
) where
import Data.Maybe
import Data.List
import qualified Data.Set as Set
import Data.Graph.Inductive.Graph( Node )
import qualified Data.Graph.Inductive.Graph as Graph
import Library.ProofGraph
import Library.WriteProof
import Library.Object
import Library.Theorem
import Library.Term
import Library.Parse
import Library.Semantic
import Library.Stack( Stack, at, (<:>) )
import qualified Library.Stack as Stack
data TermNet = Leaf [(Theorem, Node)] | Branch [(String, TermNet)]
deriving (Eq, Show)
empty :: TermNet
empty = Branch []
isLeaf :: TermNet -> Bool
isLeaf (Leaf _) = True
isLeaf _ = False
isBranch :: TermNet -> Bool
isBranch (Branch _) = True
isBranch _ = False
getLeafList :: TermNet -> Maybe [(Theorem, Node)]
getLeafList net =
case net of
Leaf list -> Just list
Branch list -> Nothing
getBranchList :: TermNet -> Maybe [(String, TermNet)]
getBranchList net =
case net of
Leaf list -> Nothing
Branch list -> Just list
genThm :: PGraph -> Node -> Theorem
genThm graph node =
let gen g n num =
let edge = filter (\x -> (fst . thd3 $ x) == num) (Graph.out g n)
node = (snd3 . head $ edge)
listing = write g node
in fromJust (((\(a,_,_,_) -> a) . fromJust $ (eval listing)) `at` 0)
hypList = map (fromJust . objTerm) (fromJust . objList $ (gen graph node 2))
con = fromJust . objTerm $ (gen graph node 1)
in Theorem (Set.fromList hypList) con
termToTermString :: Term -> [String]
termToTermString term =
case term of
(TConst _ _) ->
["const"]
(TApp func arg) ->
["app"] ++ (termToTermString func) ++ (termToTermString arg)
(TAbs var body) ->
["abs", "var"] ++ (termToTermString body)
(TVar var) ->
["var"]
thmToTermString :: Theorem -> [String]
thmToTermString theorem =
let hypList = Set.toList (thmHyp theorem)
f soFar hyp = soFar ++ ["hyp"] ++ (termToTermString hyp)
in (foldl' f [] hypList) ++ ["con"] ++ (termToTermString . thmCon $ theorem)
addThm :: TermNet -> Theorem -> Node -> TermNet
addThm net theorem node =
addThmImp net (theorem,node) (thmToTermString theorem)
addThmFromNode :: TermNet -> PGraph -> Node -> TermNet
addThmFromNode net graph node =
let theorem = genThm graph node
in addThmImp net (theorem,node) (thmToTermString theorem)
addThmImp :: TermNet -> (Theorem,Node) -> [String] -> TermNet
addThmImp (Branch branchList) item (x:[]) =
let (sameKey, rest) = partition (\(y,z) -> y == x && isLeaf z) branchList
in if (sameKey == [])
then let leaf' = Leaf [item]
in Branch ((x,leaf'):rest)
else let leaf = snd . head $ sameKey
leafList = fromJust . getLeafList $ leaf
in if (item `elem` leafList)
then Branch branchList
else let leaf' = Leaf (item:leafList)
in Branch ((x,leaf'):rest)
addThmImp (Branch branchList) item (x:xs) =
let (sameKey, rest) = partition (\(y,z) -> y == x) branchList
in if (sameKey == [])
then let net' = addThmImp empty item xs
in Branch ((x,net'):rest)
else let nextStepDown = snd . head $ sameKey
net' = addThmImp nextStepDown item xs
in Branch ((x,net'):rest)
matchThm :: TermNet -> Theorem -> [(Theorem,Node)]
matchThm net theorem =
let hyp = Set.toList (thmHyp theorem)
con = thmCon theorem
(curPrefix, curTerm) = if (hyp == [])
then ("con", con)
else ("hyp", head hyp)
r = do a <- matchImp curPrefix net
let b = matchTermImp curTerm a
(branches, leaves) = partition (\x -> isBranch x) b
c <- if (hyp == [])
then getLeafList (foldl' unify (Leaf []) leaves)
else let theorem' = Theorem (Set.fromList (tail hyp)) con
in return (matchThm (foldl' unify empty branches) theorem')
return c
in if (isNothing r) then [] else fromJust r
matchImp :: String -> TermNet -> Maybe TermNet
matchImp key net =
do list <- getBranchList net
let result = filter (\(x,y) -> x == key) list
r <- if (result == []) then Nothing else Just (snd . head $ result)
return r
matchTermImp :: Term -> TermNet -> [TermNet]
matchTermImp term net =
let list = getBranchList net
var = matchImp "var" net
result =
case term of
(TConst c ty) ->
do a <- matchImp "const" net
return [a]
(TApp f x) ->
do a <- matchImp "app" net
let b = matchTermImp f a
return (concat (map (matchTermImp x) b))
(TAbs v x) ->
do a <- matchImp "abs" net
b <- matchImp "var" a
return (matchTermImp x b)
(TVar v) -> Nothing --don't need to do anything because variables are already taken care of
var' = if (isNothing var) then [] else [fromJust var]
result' = if (isNothing result) then [] else fromJust result
in var' ++ result'
unify :: TermNet -> TermNet -> TermNet
unify (Branch a) (Branch b) = Branch (a ++ b)
unify (Leaf a) (Leaf b) = Leaf (a ++ b)
|
