-- Hoogle documentation, generated by Haddock
-- See Hoogle, http://www.haskell.org/hoogle/


-- | grammars for TSP and SHP
--   
--   Grammars and default implementations for the shortest Hamiltonian path
--   and Travelling Salesman problems.
@package ShortestPathProblems
@version 0.0.0.1

module ShortestPath.SHP.Grammar.MinDist
data SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd
SigMinDist :: (s_adna -> t_k_0__adnc -> s_adna) -> (s_adna -> s_adna) -> (() -> s_adna) -> (t_s_0__adnd -> s_adna) -> (Stream m_adn9 s_adna -> m_adn9 r_adnb) -> SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd
[edge] :: SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd -> (s_adna -> t_k_0__adnc -> s_adna)
[fini] :: SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd -> (s_adna -> s_adna)
[mpty] :: SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd -> (() -> s_adna)
[node] :: SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd -> (t_s_0__adnd -> s_adna)
[h] :: SigMinDist m_adn9 s_adna r_adnb t_k_0__adnc t_s_0__adnd -> (Stream m_adn9 s_adna -> m_adn9 r_adnb)
gMinDist :: ((~#) * * (Fun (Arg (Stack (TW t1 (i1 -> i1 -> t6 t4))) -> t5)) (t5 -> t5), (~#) * * (Fun (Arg (Stack x) -> t5)) (t2 -> t5), (~#) * * (Fun (Arg ((:!:) (Stack (TW t1 (i1 -> i1 -> t6 t4))) b) -> t5)) (t5 -> t3 -> t5), Apply (Arg (Stack (TW t1 (i1 -> i1 -> t6 t4))) -> t5), Apply (Arg (Stack x) -> t5), Apply (Arg ((:!:) (Stack (TW t1 (i1 -> i1 -> t6 t4))) b) -> t5), Element ((:!:) (Stack (TW t1 (i1 -> i1 -> t6 t4))) b) i1, Element (Stack (TW t1 (i1 -> i1 -> t6 t4))) i, Element (Stack x) i1, MkStream t6 ((:!:) S Epsilon) i1, MkStream t6 ((:!:) (Stack (TW t1 (i1 -> i1 -> t6 t4))) b) i1, MkStream t6 (Stack (TW t1 (i1 -> i1 -> t6 t4))) i, MkStream t6 (Stack x) i1, RuleContext i, RuleContext i1, Build (TW t1 (i1 -> i1 -> t6 t4)), Build x) => SigMinDist t6 t5 t4 t3 t2 -> t1 -> t -> b -> x -> (:.) ((:.) Z (TW t1 (i1 -> i1 -> t6 t4))) (TW t (i -> i -> t6 t4))
instance (GHC.Base.Monad mL0, GHC.Base.Monad mR0, GHC.Classes.Eq xL0, mL0 ~ mR0, xL0 ~ rL0) => ADP.Fusion.Core.TH.Backtrack.ProductBacktracking (ShortestPath.SHP.Grammar.MinDist.SigMinDist mL0 xL0 rL0 t_k_0_0 t_s_0_0) (ShortestPath.SHP.Grammar.MinDist.SigMinDist mR0 xR0 rR0 t_k_0_0 t_s_0_0)
instance (GHC.Base.Monad mL0, GHC.Base.Monad mR0, GHC.Classes.Eq xL0, GHC.Classes.Ord xL0, GHC.Classes.Ord xR0, mL0 ~ mR0) => ADP.Fusion.Core.TH.Backtrack.ProductCombining (ShortestPath.SHP.Grammar.MinDist.SigMinDist mL0 xL0 rL0 t_k_0_0 t_s_0_0) (ShortestPath.SHP.Grammar.MinDist.SigMinDist mR0 xR0 rR0 t_k_0_0 t_s_0_0)

module ShortestPath.SHP.Grammar.EdgeProbIO
data SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA
SigEdgeProb :: (s_ahfx -> t_k_0__ahfz -> s_ahfx) -> (s_ahfx -> t_k_0__ahfz -> s_ahfx -> s_ahfx) -> (() -> s_ahfx) -> (s_ahfx -> t_s_0__ahfA -> s_ahfx) -> (Stream m_ahfw s_ahfx -> m_ahfw r_ahfy) -> SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA
[edge] :: SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA -> (s_ahfx -> t_k_0__ahfz -> s_ahfx)
[fini] :: SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA -> (s_ahfx -> t_k_0__ahfz -> s_ahfx -> s_ahfx)
[mpty] :: SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA -> (() -> s_ahfx)
[node] :: SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA -> (s_ahfx -> t_s_0__ahfA -> s_ahfx)
[h] :: SigEdgeProb m_ahfw s_ahfx r_ahfy t_k_0__ahfz t_s_0__ahfA -> (Stream m_ahfw s_ahfx -> m_ahfw r_ahfy)
gEdgeProb :: ((~#) * * (Fun (Arg ((:!:) ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) (TW t1 (i -> i -> t7 t5))) -> t6)) (t6 -> t4 -> t6 -> t6), (~#) * * (Fun (Arg ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) -> t6)) (t6 -> t3 -> t6), (~#) * * (Fun (Arg ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) -> t6)) (t6 -> t4 -> t6), (~#) * * (Fun (Arg ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) -> t6)) (t6 -> t3 -> t6), (~#) * * (Fun (Arg ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b1) -> t6)) (t6 -> t4 -> t6), Apply (Arg ((:!:) ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) (TW t1 (i -> i -> t7 t5))) -> t6), Apply (Arg ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) -> t6), Apply (Arg ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) -> t6), Apply (Arg ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) -> t6), Apply (Arg ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b1) -> t6), Element ((:!:) ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) (TW t1 (i -> i -> t7 t5))) i2, Element ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) i1, Element ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) i1, Element ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) i, Element ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b1) i, MkStream t7 ((:!:) S Epsilon) i1, MkStream t7 ((:!:) S Epsilon) i, MkStream t7 ((:!:) ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) (TW t1 (i -> i -> t7 t5))) i2, MkStream t7 ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) i1, MkStream t7 ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b1) i1, MkStream t7 ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) i, MkStream t7 ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b1) i, RuleContext i2, RuleContext i1, RuleContext i, Build (TW t2 (i1 -> i1 -> t7 t5)), Build (TW t1 (i -> i -> t7 t5))) => SigEdgeProb t7 t6 t5 t4 t3 -> t2 -> t1 -> t -> b1 -> b -> (:.) ((:.) ((:.) Z (TW t2 (i1 -> i1 -> t7 t5))) (TW t1 (i -> i -> t7 t5))) (TW t (i2 -> i2 -> t7 t5))
instance (GHC.Base.Monad mL0, GHC.Base.Monad mR0, GHC.Classes.Eq xL0, mL0 ~ mR0, xL0 ~ rL0) => ADP.Fusion.Core.TH.Backtrack.ProductBacktracking (ShortestPath.SHP.Grammar.EdgeProbIO.SigEdgeProb mL0 xL0 rL0 t_k_0_0 t_s_0_0) (ShortestPath.SHP.Grammar.EdgeProbIO.SigEdgeProb mR0 xR0 rR0 t_k_0_0 t_s_0_0)
instance (GHC.Base.Monad mL0, GHC.Base.Monad mR0, GHC.Classes.Eq xL0, GHC.Classes.Ord xL0, GHC.Classes.Ord xR0, mL0 ~ mR0) => ADP.Fusion.Core.TH.Backtrack.ProductCombining (ShortestPath.SHP.Grammar.EdgeProbIO.SigEdgeProb mL0 xL0 rL0 t_k_0_0 t_s_0_0) (ShortestPath.SHP.Grammar.EdgeProbIO.SigEdgeProb mR0 xR0 rR0 t_k_0_0 t_s_0_0)

module ShortestPath.SHP.Grammar.EdgeProb
data SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo
SigEdgeProb :: (s_ajzl -> t_k_0__ajzn -> s_ajzl) -> (s_ajzl -> t_k_0__ajzn -> s_ajzl -> s_ajzl) -> (() -> s_ajzl) -> (t_s_0__ajzo -> s_ajzl) -> (Stream m_ajzk s_ajzl -> m_ajzk r_ajzm) -> SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo
[edge] :: SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo -> (s_ajzl -> t_k_0__ajzn -> s_ajzl)
[fini] :: SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo -> (s_ajzl -> t_k_0__ajzn -> s_ajzl -> s_ajzl)
[mpty] :: SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo -> (() -> s_ajzl)
[node] :: SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo -> (t_s_0__ajzo -> s_ajzl)
[h] :: SigEdgeProb m_ajzk s_ajzl r_ajzm t_k_0__ajzn t_s_0__ajzo -> (Stream m_ajzk s_ajzl -> m_ajzk r_ajzm)
gEdgeProb :: ((~#) * * (Fun (Arg ((:!:) ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) (TW t2 (i1 -> i1 -> t7 t5))) -> t6)) (t6 -> t4 -> t6 -> t6), (~#) * * (Fun (Arg ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) -> t6)) (t6 -> t4 -> t6), (~#) * * (Fun (Arg (Stack x) -> t6)) (t3 -> t6), (~#) * * (Fun (Arg ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) -> t6)) (t6 -> t4 -> t6), Apply (Arg ((:!:) ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) (TW t2 (i1 -> i1 -> t7 t5))) -> t6), Apply (Arg ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) -> t6), Apply (Arg (Stack x) -> t6), Apply (Arg ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) -> t6), Element ((:!:) ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) (TW t2 (i1 -> i1 -> t7 t5))) i2, Element ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) i1, Element ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) i, Element (Stack x) i1, Element (Stack x) i, MkStream t7 ((:!:) S Epsilon) i1, MkStream t7 ((:!:) S Epsilon) i, MkStream t7 ((:!:) ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) (TW t2 (i1 -> i1 -> t7 t5))) i2, MkStream t7 ((:!:) (Stack (TW t2 (i1 -> i1 -> t7 t5))) b) i1, MkStream t7 ((:!:) (Stack (TW t1 (i -> i -> t7 t5))) b) i, MkStream t7 (Stack x) i1, MkStream t7 (Stack x) i, RuleContext i2, RuleContext i1, RuleContext i, Build (TW t2 (i1 -> i1 -> t7 t5)), Build (TW t1 (i -> i -> t7 t5)), Build x) => SigEdgeProb t7 t6 t5 t4 t3 -> t2 -> t1 -> t -> b -> x -> (:.) ((:.) ((:.) Z (TW t2 (i1 -> i1 -> t7 t5))) (TW t1 (i -> i -> t7 t5))) (TW t (i2 -> i2 -> t7 t5))
instance (GHC.Base.Monad mL0, GHC.Base.Monad mR0, GHC.Classes.Eq xL0, mL0 ~ mR0, xL0 ~ rL0) => ADP.Fusion.Core.TH.Backtrack.ProductBacktracking (ShortestPath.SHP.Grammar.EdgeProb.SigEdgeProb mL0 xL0 rL0 t_k_0_0 t_s_0_0) (ShortestPath.SHP.Grammar.EdgeProb.SigEdgeProb mR0 xR0 rR0 t_k_0_0 t_s_0_0)
instance (GHC.Base.Monad mL0, GHC.Base.Monad mR0, GHC.Classes.Eq xL0, GHC.Classes.Ord xL0, GHC.Classes.Ord xR0, mL0 ~ mR0) => ADP.Fusion.Core.TH.Backtrack.ProductCombining (ShortestPath.SHP.Grammar.EdgeProb.SigEdgeProb mL0 xL0 rL0 t_k_0_0 t_s_0_0) (ShortestPath.SHP.Grammar.EdgeProb.SigEdgeProb mR0 xR0 rR0 t_k_0_0 t_s_0_0)


-- | Calculate minimum-distance Hamiltonian Shortest Paths and
--   probabilities for starting nodes.
--   
--   NOTE: We explicitly model starting nodes. For symmetrical distance
--   matrices, this reports begin/end probabilities. For asymmetrical
--   distance matrices, a second instances with <tt>Last</tt> instead of
--   <tt>First</tt> boundary should be created to calculate begin/end
--   probabilities separately.
module ShortestPath.SHP.Edge.MinDist

-- | Minimal distance algebra
--   
--   TODO The two Ints are the indices of the nodes and could be replaced?
aMinDist :: Monad m => ScoreMatrix Double -> SigMinDist m Double Double (From :. To) (Int :. To)

-- | Maximum edge probability following the probabilities generated from
--   the <tt>EdgeProb</tt> grammar.
aMaxEdgeProb :: Monad m => ScoreMatrix (Log Double) -> SigMinDist m (Log Double) (Log Double) (From :. To) (Int :. To)
data PathBT
BTnode :: !(Int :. To) -> PathBT
BTedge :: !(From :. To) -> PathBT

-- | This should give the correct order of nodes independent of the
--   underlying <tt>Set1 First</tt> or <tt>Set1 Last</tt> because the
--   <tt>(From:.To)</tt> system is agnostic over these.
aPathBT :: Monad m => ScoreMatrix t -> SigMinDist m [PathBT] [[PathBT]] (From :. To) (Int :. To)

-- | This should give the correct order of nodes independent of the
--   underlying <tt>Set1 First</tt> or <tt>Set1 Last</tt> because the
--   <tt>(From:.To)</tt> system is agnostic over these.
aPretty :: Monad m => ScoreMatrix t -> SigMinDist m Text [Text] (From :. To) (Int :. To)

-- | Before using <tt>aInside</tt> the <tt>ScoreMatrix</tt> needs to be
--   scaled appropriately! Due to performance reasons we don't want to do
--   this within <tt>aInside</tt>.
aInside :: Monad m => ScoreMatrix (Log Double) -> SigMinDist m (Log Double) (Log Double) (From :. To) (Int :. To)
type TS1 x = TwITbl Id Unboxed EmptyOk (BS1 First I) x
type U x = TwITbl Id Unboxed EmptyOk (Unit I) x
type PF x = TwITbl Id Unboxed EmptyOk (Boundary First I) x
type TS1L x = TwITbl Id Unboxed EmptyOk (BS1 Last I) x
type UL x = TwITbl Id Unboxed EmptyOk (Unit I) x
type PFL x = TwITbl Id Unboxed EmptyOk (Boundary Last I) x
type BT1 x b = TwITblBt Unboxed EmptyOk (BS1 First I) x Id Id b
type BTU x b = TwITblBt Unboxed EmptyOk (Unit I) x Id Id b
type BT1L x b = TwITblBt Unboxed EmptyOk (BS1 Last I) x Id Id b
type BTUL x b = TwITblBt Unboxed EmptyOk (Unit I) x Id Id b

-- | Run the minimal distance algebra.
--   
--   This produces one-boundary sets. Meaning that for each boundary we get
--   the total distance within the set.
forwardMinDist1 :: ScoreMatrix Double -> (Z :. TS1 Double) :. U Double
backtrackMinDist1 :: ScoreMatrix Double -> (Z :. TS1 Double) :. U Double -> [Text]
pathbtMinDist :: ScoreMatrix Double -> (Z :. TS1 Double) :. U Double -> [[PathBT]]

-- | Given the <tt>Set1</tt> produced in <tt>forwardMinDist1</tt> we can
--   now extract the co-optimal paths using the <tt>Set1 -&gt; ()</tt>
--   index change.
--   
--   TODO do we want this one explicitly or make life easy and just extract
--   from all <tt>forwardMinDist1</tt> paths?
runCoOptDist :: ScoreMatrix Double -> (Double, [Text])

-- | Return the minimal distance and provide a list of co-optimal
--   backtraces.
runMinDist :: ScoreMatrix Double -> (Double, [[PathBT]])

-- | Extract the individual partition scores.
boundaryPartFun :: Double -> ScoreMatrix Double -> [(Boundary First I, Log Double)]

-- | Run the maximal edge probability grammar.
forwardMaxEdgeProbFirst :: ScoreMatrix (Log Double) -> (Z :. TS1 (Log Double)) :. U (Log Double)
forwardMaxEdgeProbLast :: ScoreMatrix (Log Double) -> (Z :. TS1L (Log Double)) :. UL (Log Double)
pathbtMaxEdgeProbFirst :: ScoreMatrix (Log Double) -> (Z :. TS1 (Log Double)) :. U (Log Double) -> [[PathBT]]
pathbtMaxEdgeProbLast :: ScoreMatrix (Log Double) -> (Z :. TS1L (Log Double)) :. UL (Log Double) -> [[PathBT]]

-- | Given the <tt>Set1</tt> produced in <tt>forwardMinDist1</tt> we can
--   now extract the co-optimal paths using the <tt>Set1 -&gt; ()</tt>
--   index change.
--   
--   TODO do we want this one explicitly or make life easy and just extract
--   from all <tt>forwardMinDist1</tt> paths?
runMaxEdgeProbFirst :: ScoreMatrix (Log Double) -> (Log Double, [[PathBT]])
runMaxEdgeProbLast :: ScoreMatrix (Log Double) -> (Log Double, [(Boundary Last I, Log Double)], [[PathBT]])
test :: Double -> FilePath -> IO ()
instance GHC.Show.Show ShortestPath.SHP.Edge.MinDist.PathBT