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module Library.ProofGraph (
PGraph,
doGraphGen,
checkDupe,
nodeEquals,
resolveNodeClash
) where
import Data.Maybe
import Data.List
import Data.Set( Set )
import qualified Data.Set as Set
import Data.Map( Map, (!) )
import qualified Data.Map as Map
import Data.Graph.Inductive.Graph( Node, LNode, LEdge, (&) )
import qualified Data.Graph.Inductive.Graph as Graph
import Data.Graph.Inductive.Tree
import Library.Stack( Stack, at, (<:>) )
import qualified Library.Stack as Stack
import Library.Parse( isNumber, isName )
type PGraph = Gr String (Int,Int)
type PStack = Stack (Int, LNode String)
type PMap = Map Int (Int, LNode String)
data CommandIO = IO { args :: Int
, results :: Int }
argMap :: String -> CommandIO
argMap "absTerm" = IO 2 1
argMap "absThm" = IO 2 1
argMap "appTerm" = IO 2 1
argMap "appThm" = IO 2 1
argMap "assume" = IO 1 1
argMap "axiom" = IO 2 1
argMap "betaConv" = IO 1 1
argMap "cons" = IO 2 1
argMap "const" = IO 1 1
argMap "constTerm" = IO 2 1
argMap "deductAntisym" = IO 2 1
argMap "defineConst" = IO 2 2
argMap "defineTypeOp" = IO 5 5
argMap "eqMp" = IO 2 1
argMap "nil" = IO 0 1
argMap "opType" = IO 2 1
argMap "refl" = IO 1 1
argMap "subst" = IO 2 1
argMap "thm" = IO 3 0
argMap "typeOp" = IO 1 1
argMap "var" = IO 2 1
argMap "varTerm" = IO 1 1
argMap "varType" = IO 1 1
argMap x | (isName x) = IO 0 1
process :: String -> CommandIO -> PGraph -> PStack -> (PGraph, PStack)
process str io graph stack =
let argList = map (\x -> fromJust (stack `at` x)) [0..((args io) - 1)]
nextNum = head (Graph.newNodes 1 graph)
node = (nextNum, str)
edgeList = map (\x -> (nextNum, (fst . snd . snd $ x), (fst x, fst . snd $ x))) (zip [1..(args io)] argList)
graph' = (Graph.insEdges edgeList) . (Graph.insNode node) $ graph
nodeList = map (\x -> (x, node)) [1..(results io)]
stack' = foldr (<:>) (Stack.pop (args io) stack) nodeList
in (graph', stack')
parse :: (PGraph,PStack,PMap) -> String -> (PGraph,PStack,PMap)
parse gs@(graph,stack,dictionary) str =
case str of
"def" -> let num = fst . fromJust $ stack `at` 0
node = fromJust $ stack `at` 1
dictionary' = Map.insert num node dictionary
stack' = Stack.pop 1 stack
in (graph, stack', dictionary')
"ref" -> let num = fst . fromJust $ stack `at` 0
node = fromJust (Map.lookup num dictionary)
stack' = node <:> (Stack.pop 1 stack)
in (graph, stack', dictionary)
"remove" -> let num = fst . fromJust $ stack `at` 0
node = fromJust (Map.lookup num dictionary)
stack' = node <:> (Stack.pop 1 stack)
dictionary' = Map.delete num dictionary
in (graph, stack', dictionary')
"pop" -> (graph, (Stack.pop 1 stack), dictionary)
'#':rest -> gs
n | (isNumber n) -> let node = (read n, (0,""))
stack' = node <:> stack
in (graph, stack', dictionary)
x -> let (graph', stack') = process x (argMap x) graph stack
in (graph', stack', dictionary)
checkDupe :: PGraph -> PGraph
checkDupe graph =
let f = (\g n ->
let list = filter (\x -> (x /= n) && (nodeEquals g n x)) (Graph.nodes g)
in if (list == []) then g else merge g n (head list))
merge =
(\g n r ->
let edgesFixed = map (\(a,b,c) -> (a,r,c)) (Graph.inn g n)
in (Graph.insEdges edgesFixed) . (Graph.delNode n) $ g)
in foldl' f graph (Graph.nodes graph)
nodeEquals :: Gr String (Int,Int) -> Node -> Node -> Bool
nodeEquals graph one two =
let edgesOne = sortBy sortFunc (Graph.out graph one)
edgesTwo = sortBy sortFunc (Graph.out graph two)
sortFunc = (\(_,_,x) (_,_,y) -> compare x y)
paired = zip (map (\(_,x,_) -> x) edgesOne) (map (\(_,x,_) -> x) edgesTwo)
in (Graph.gelem one graph) &&
(Graph.gelem two graph) &&
(Graph.lab graph one == Graph.lab graph two) &&
(length edgesOne == length edgesTwo) &&
(all (\x -> nodeEquals graph (fst x) (snd x)) paired)
resolveNodeClash :: Gr String (Int,Int) -> Gr String (Int,Int) -> (Gr String (Int,Int), Map Int Int)
resolveNodeClash ref graph =
let dict = Map.fromList (zip (Graph.nodes graph) (Graph.newNodes (Graph.noNodes graph) ref))
nodeList = map (\(x,y) -> (fromJust (Map.lookup x dict), y)) (Graph.labNodes graph)
edgeList = map (\(x,y,z) -> (fromJust (Map.lookup x dict),
fromJust (Map.lookup y dict), z)) (Graph.labEdges graph)
in (Graph.mkGraph nodeList edgeList, dict)
doGraphGen :: [String] -> PGraph
doGraphGen list =
let graph = Graph.empty
stack = Stack.empty
dictionary = Map.empty
result = foldl' parse (graph,stack,dictionary) list
in case result of (g,s,d) -> checkDupe g
|
