diff --git a/LICENSE b/LICENSE
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+++ b/LICENSE
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+                    GNU GENERAL PUBLIC LICENSE
+                       Version 3, 29 June 2007
+
+ Copyright (C) 2007 Free Software Foundation, Inc. <http://fsf.org/>
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+WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS
+THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY
+GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE
+USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF
+DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD
+PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS),
+EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF
+SUCH DAMAGES.
+
+  17. Interpretation of Sections 15 and 16.
+
+  If the disclaimer of warranty and limitation of liability provided
+above cannot be given local legal effect according to their terms,
+reviewing courts shall apply local law that most closely approximates
+an absolute waiver of all civil liability in connection with the
+Program, unless a warranty or assumption of liability accompanies a
+copy of the Program in return for a fee.
+
+                     END OF TERMS AND CONDITIONS
+
+            How to Apply These Terms to Your New Programs
+
+  If you develop a new program, and you want it to be of the greatest
+possible use to the public, the best way to achieve this is to make it
+free software which everyone can redistribute and change under these terms.
+
+  To do so, attach the following notices to the program.  It is safest
+to attach them to the start of each source file to most effectively
+state the exclusion of warranty; and each file should have at least
+the "copyright" line and a pointer to where the full notice is found.
+
+    {one line to give the program's name and a brief idea of what it does.}
+    Copyright (C) {year}  {name of author}
+
+    This program is free software: you can redistribute it and/or modify
+    it under the terms of the GNU General Public License as published by
+    the Free Software Foundation, either version 3 of the License, or
+    (at your option) any later version.
+
+    This program is distributed in the hope that it will be useful,
+    but WITHOUT ANY WARRANTY; without even the implied warranty of
+    MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
+    GNU General Public License for more details.
+
+    You should have received a copy of the GNU General Public License
+    along with this program.  If not, see <http://www.gnu.org/licenses/>.
+
+Also add information on how to contact you by electronic and paper mail.
+
+  If the program does terminal interaction, make it output a short
+notice like this when it starts in an interactive mode:
+
+    {project}  Copyright (C) {year}  {fullname}
+    This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'.
+    This is free software, and you are welcome to redistribute it
+    under certain conditions; type `show c' for details.
+
+The hypothetical commands `show w' and `show c' should show the appropriate
+parts of the General Public License.  Of course, your program's commands
+might be different; for a GUI interface, you would use an "about box".
+
+  You should also get your employer (if you work as a programmer) or school,
+if any, to sign a "copyright disclaimer" for the program, if necessary.
+For more information on this, and how to apply and follow the GNU GPL, see
+<http://www.gnu.org/licenses/>.
+
+  The GNU General Public License does not permit incorporating your program
+into proprietary programs.  If your program is a subroutine library, you
+may consider it more useful to permit linking proprietary applications with
+the library.  If this is what you want to do, use the GNU Lesser General
+Public License instead of this License.  But first, please read
+<http://www.gnu.org/philosophy/why-not-lgpl.html>.
diff --git a/README.md b/README.md
new file mode 100644
--- /dev/null
+++ b/README.md
@@ -0,0 +1,17 @@
+# Turing Machine Model
+An implementation of Turing Machine and Automaton for language theory
+
+## Models
+### Finite Automaton
+
+Finite State machine, with no memory.
+Exist:
+
+1. Recognizer
+2. Generator
+3. Transducer
+
+### Stack Automaton
+Stack memory machine with states
+
+### Turing Machine
diff --git a/Setup.hs b/Setup.hs
new file mode 100644
--- /dev/null
+++ b/Setup.hs
@@ -0,0 +1,2 @@
+import Distribution.Simple
+main = defaultMain
diff --git a/src/Data/Delta.hs b/src/Data/Delta.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Delta.hs
@@ -0,0 +1,43 @@
+{-# OPTIONS_GHC -fno-warn-tabs #-}
+{-# OPTIONS_HADDOCK show-extensions #-}
+{-# LANGUAGE TypeOperators #-}
+{-|
+Module      : Delta
+Description : Implementacion de un mapeo
+Copyright   : (c) Jorge Santiago Alvarez Cuadros, 2016
+License     : GPL-3
+Maintainer  : sanjorgek@ciencias.unam.mx
+Stability   : experimental
+Portability : portable
+
+Map implementation, represent a partial function
+-}
+module Data.Delta
+(
+	-- * Delta
+	-- ** Deterministic
+	-- *** Constructor
+	(:->:)(..)
+	-- *** Functions
+	,nextD
+	-- ** Not deterministic
+	-- *** Constructor
+	,(:>-:)(..)
+	-- * Transductor
+	-- ** Constructor
+	,(:*>:)(..)
+) where
+import Data.State
+import Control.Applicative
+import Data.Monoid
+import Data.Foldable
+import qualified Data.Map.Lazy as Map
+
+type (:->:) a p1 p2 = Map.Map (State a, p1) (State a, p2)
+
+nextD :: (Ord p1, Ord a) => (:->:) a p1 p2 -> (State a, p1) -> State a
+nextD dt k = if Map.member k dt then fst (dt Map.! k) else QE 
+
+type (:>-:) a p1 p2 = Map.Map (State a, p1) ([State a], p2)
+
+type (:*>:) a p o = Map.Map (State a, p) o
diff --git a/src/Data/Sigma.hs b/src/Data/Sigma.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/Sigma.hs
@@ -0,0 +1,48 @@
+{-# OPTIONS_HADDOCK show-extensions #-}
+{-# OPTIONS_GHC -fno-warn-tabs #-}
+{-# LANGUAGE TypeSynonymInstances #-}
+{-|
+Module      : Sigma
+Description : Alphabet and symbols
+Copyright   : (c) Jorge Santiago Alvarez Cuadros, 2016
+License     : GPL-3
+Maintainer  : sanjorgek@ciencias.unam.mx
+Stability   : experimental
+Portability : portable
+
+Alphabet and symbols of languaje
+-}
+module Data.Sigma 
+(
+	Symbol(..)
+	,blank
+	,z0
+	,Wd(..)
+) where
+import Data.Monoid
+import Data.Char
+
+{-|
+Symbols are character, and with Unicode CharSet we have a big amount of them.
+-}
+type Symbol = Char
+
+{-|
+Symbol type are forced to be a monoid
+-}
+instance Monoid Symbol where
+	mempty = blank
+	mappend x y = chr (mod ((ord x)+(ord y)) (ord maxBound))
+
+-- |Blank symbol
+blank::Symbol
+blank = '\164'
+
+-- |Initial symbol for stack
+z0::Symbol
+z0 = '\248'
+
+{-|
+List symbol alias, Word are defined in Prelude
+-}
+type Wd = [Symbol]
diff --git a/src/Data/State.hs b/src/Data/State.hs
new file mode 100644
--- /dev/null
+++ b/src/Data/State.hs
@@ -0,0 +1,92 @@
+{-# OPTIONS_GHC -fno-warn-tabs #-}
+{-# OPTIONS_HADDOCK show-extensions #-}
+{-|
+Module      : State
+Description : Simple state data
+Copyright   : (c) Jorge Santiago Alvarez Cuadros, 2016
+License     : GPL-3
+Maintainer  : sanjorgek@ciencias.unam.mx
+Stability   : experimental
+Portability : portable
+
+Simple State function, have an isomorphism with Maybe but order are diferent
+-}
+module Data.State 
+(
+	-- * Data and type
+	State(..)
+	,Final(..)
+	,terminal
+	-- * Functions
+	,isError
+) where
+import Control.Applicative
+import Control.Monad
+
+{-|
+Macine states are only a label, maybe a letter
+-}
+data State a = 
+	-- |State constructor
+	Q a 
+	-- |Error state
+	| QE deriving(Show, Eq, Ord)
+
+-- |Same as Maybe
+instance Functor State where
+	fmap _ QE = QE
+	fmap f (Q q) = Q $ f q 
+
+-- |Same as Maybe
+instance Applicative State where
+	pure = Q
+	QE <*> _ = QE
+	(Q f) <*> q = fmap f q
+
+-- |Same as Maybe
+instance Monad State where
+	return = pure
+	QE >>= _ = QE
+	(Q q) >>= f = f q
+
+-- |Same as Maybe
+instance (Enum a) => Enum (State a) where
+	toEnum n = if n<0 then QE else Q (toEnum n)
+	fromEnum QE = -1
+	fromEnum (Q a) = fromEnum a
+
+-- |In this differ with Maybe because this show a upper bounded order
+instance (Bounded a)=> Bounded (State a) where
+	minBound = Q minBound
+	maxBound = QE 
+
+instance Monoid a => Monoid (State a) where
+	mempty = QE
+	QE `mappend` m = m
+	m `mappend` QE = m
+	(Q a) `mappend` (Q b) = Q (a `mappend` b)
+
+instance Foldable State where
+    foldr _ z QE = z
+    foldr f z (Q x) = f x z
+    foldl _ z QE = z
+    foldl f z (Q x) = f z x
+
+{-|
+Final state represent a set of states which elements put end to computation
+-}
+type Final a = [State a]
+
+{-|
+Tells if a state is final
+-}
+terminal :: (Eq a) => Final a -> State a -> Bool
+terminal qs q = elem q qs
+
+-- |Verifica si el estado es de error, comparandolo con la definicion de 
+-- estado de error
+{-|
+Tells if a state is a error state
+-}
+isError::(Eq a) => State a -> Bool
+isError q = q==QE
diff --git a/src/Math/Model/Automaton/Finite.hs b/src/Math/Model/Automaton/Finite.hs
new file mode 100644
--- /dev/null
+++ b/src/Math/Model/Automaton/Finite.hs
@@ -0,0 +1,168 @@
+{-# OPTIONS_GHC -fno-warn-tabs #-}
+{-# OPTIONS_HADDOCK show-extensions #-}
+{-# LANGUAGE TypeOperators #-}
+{-|
+Module      : Finite Automaton
+Description : Finite Automaton
+Copyright   : (c) Jorge Santiago Alvarez Cuadros, 2016
+License     : GPL-3
+Maintainer  : sanjorgek@ciencias.unam.mx
+Stability   : experimental
+Portability : portable
+
+Finite Automaton is a stateful machine where all transition means that machine 
+reads a symbol
+-}
+module Math.Model.Automaton.Finite
+(
+	-- * Deterministic
+	-- ** Function 
+	-- *** Recognizer
+	Delta(..)
+	,liftD
+	-- ** Transducer
+	,Lambda1(..)
+	,liftL1
+	,Lambda2(..)
+	,liftL2
+	-- ** Constructor
+	,FiniteA(..)
+	,Transductor(..)
+	-- ** Function
+	,checkString
+	,translate
+	-- * Not deterministic
+	-- ** Function
+	,DeltaN(..)
+	,liftDN
+	-- ** Constructor
+	,FiniteAN(..)
+	,checkStringN
+) where
+import Data.State
+import Data.Sigma
+import Data.Delta
+import Data.List
+import Data.Monoid
+import Control.Monad
+import qualified Data.Map.Lazy as Map
+import qualified Data.Foldable as Fold
+
+{-|
+Transition function hava a State and a Symbol by domain to decide next state in 
+machine
+-}
+type Delta a = (:->:) a Symbol ()
+
+{-|
+Lift a list of 3-tuples in a Delta
+
+>>>let delta = liftD [(0,'0',0),(0,'1',1),(1,'0',1),(1,'1',0)]
+-}
+liftD::(Ord a) => [(a,Symbol,a)] -> Delta a
+liftD ds = let
+		(xs,ys,zs) = unzip3 ds
+		f = map return 
+		xys = zip (f xs) ys
+		qzs = zip (f zs) (repeat ())
+	in Map.fromList (zip xys qzs)
+
+type Lambda1 a = (:*>:) a () Symbol
+
+liftL1::(Ord a) => [(a, Symbol)] -> Lambda1 a
+liftL1 ds = let
+		(xs, ys) = unzip ds
+		f = map return
+		nds = zip (zip (f xs) (repeat ())) ys
+	in Map.fromList nds
+
+type Lambda2 a = (:*>:) a Symbol Symbol
+
+liftL2::(Ord a) => [(a, Symbol, Symbol)] -> Lambda2 a
+liftL2 ds = let
+		(xs, ys, zs) = unzip3 ds
+		f = map return
+		nds = zip (zip (f xs) ys) zs
+	in Map.fromList nds
+ 
+{-|
+Finite deterministic Automaton
+-}
+data FiniteA a = 
+	-- |>>>let autFin = F delta [Q 0] (Q 0)
+	F (Delta a) (Final a) (State a) deriving(Show, Eq)
+
+{-|
+Executes a automaton over a word
+
+>>>checkString autFin "1010010101101010"
+True
+>>>checkString autFin "1010010101101010001010101010"
+False
+-}
+checkString::(Ord a) => FiniteA a -> Wd -> Bool
+checkString (F d qF s) ws = let
+		q = checkString' d s ws
+		f y = ((not.isError) y)&&(terminal qF y)
+	in f q
+	where
+		checkString' _ q [] = q
+		checkString' dt q (x:xs) = checkString' dt (nextD dt (q,x)) xs
+
+data Transductor a = 
+	Moore (Delta a) (Lambda1 a) (Final a) (State a) 
+	|Mealy (Delta a) (Lambda2 a) (Final a) (State a) deriving(Show, Eq)
+
+translate::(Ord a) => Transductor a -> Wd -> Wd
+translate (Moore d l qF s) ws = let
+		(q, w) = translate d l s ws []
+	in w
+	where
+		translate _ _ QE xs ys = (QE, "Error: \nCadena:"++xs++"\nResp parcial: "++ys)
+		translate _ _ q [] xs = (q, xs)
+		translate dt lm q (y:ys) xs = translate dt lm (nextD dt (q,y)) ys (xs++[lm Map.! (q, ())])
+translate (Mealy d l qF s) ws = let
+		(q, w) = translate d l s ws []
+	in ws
+	where 
+		translate _ _ QE xs ys = (QE, "Error: \nCadena:"++xs++"\nResp parcial: "++ys)
+		translate _ _ q [] xs = (q, xs)
+		translate dt lm q (x:xs) ys = translate dt lm (nextD dt (q, x)) xs (ys++[lm Map.! (q,x)])
+
+
+type DeltaN a = (:>-:) a Symbol ()
+
+{-|
+Lift a list of 3-tuples in a non deterministic delta
+
+>>>let deltaN = liftDN [(0,'0',[0]),(0,'1',[1]),(1,'0',[1]),(1,'1',[0])]
+-}
+liftDN::(Ord a) => [(a,Symbol,[a])] -> DeltaN a
+liftDN ds = let
+		(xs,ys,zs) = unzip3 ds
+		f = map return
+		xys = zip (f xs) ys
+		qzs = zip (map f zs) (repeat ())
+	in Map.fromList (zip xys qzs)
+
+{-|
+Finite non deterministic Automaton
+-}
+data FiniteAN a = 
+	-- |>>>let autFinN = FN deltaN (terminal [Q 0]) (Q 0)
+	FN (DeltaN a) (Final a) (State a) deriving(Show,Eq)
+
+{-|
+Executes a non-deterministic automaton over a word, maybe overload your pc 
+-}
+checkStringN::(Ord a) => FiniteAN a -> Wd -> Bool
+checkStringN (FN dn qF s) ws = let
+		qs = checkStringN' dn [s] ws
+		f y = ((not.isError) y)&&(terminal qF y)
+		g y = or (map f y)
+	in g qs
+	where
+		check dt k = if Map.member k dt then dt Map.! k else ([QE], ())
+		mDelta dt lq a = (nub.concat.(map fst)) (map (\q -> check dt (q,a)) lq)
+		checkStringN' _ qs [] = qs
+		checkStringN' dn qs (x:xs) = checkStringN' dn (mDelta dn qs x) xs
diff --git a/src/Math/Model/Automaton/Stack.hs b/src/Math/Model/Automaton/Stack.hs
new file mode 100644
--- /dev/null
+++ b/src/Math/Model/Automaton/Stack.hs
@@ -0,0 +1,72 @@
+{-# OPTIONS_GHC -fno-warn-tabs #-}
+{-# OPTIONS_HADDOCK show-extensions #-}
+{-# LANGUAGE TypeOperators #-}
+{-|
+Module      : StackA
+Description : Stack Automaton
+Copyright   : (c) Jorge Santiago Alvarez Cuadros, 2016
+License     : GPL-3
+Maintainer  : sanjorgek@ciencias.unam.mx
+Stability   : experimental
+Portability : portable
+
+Stack Automaton
+-}
+module Math.Model.Automaton.Stack
+(
+	Delta(..)
+	,liftD
+	,StackA(..)
+	,checkString
+) where
+import Data.List
+import Data.Monoid
+import qualified Data.Map.Lazy as Map
+import qualified Data.Foldable as Fold
+import Data.Delta
+import Data.State
+import Data.Sigma
+
+{-|
+Delta for stack machine, takes a state, a symbol in string input and a symbol in
+stack head and returns next state and update stack
+-}
+type Delta a = (:->:) a (Symbol, Symbol) [Symbol]
+
+{-|
+Takes a list of tuples and lift a Delta
+
+>>>let delta = liftD [(0,'1','A',1,[AA]),(0,'0',blank,0,[A])]
+-}
+liftD::(Ord a) => [(a, Symbol, Symbol, a, [Symbol])]-> Delta a
+liftD xs = let
+		(as,bs,cs,ds,es) = unzip5 xs
+		f = map (Q)
+		p = zip bs cs
+		k = zip (f as) p
+		r = zip (f ds) es
+	in Map.fromList (zip k r)
+
+-- |Stack machine only needs a delta and a init state
+data StackA a = S (Delta a) (State a)
+
+{-|
+Executes a stack machine over a word
+
+>>>checkString autStack 'aaabbbcccccc'
+True
+-}
+checkString::(Ord a) => StackA a -> Wd -> Bool
+checkString (S d s) ws = let
+		q = checkString' d s [z0] ws
+		f = not.isError
+	in f q
+	where
+		check dt s = if Map.member s dt then dt Map.! s else (QE,[])
+		checkString' _ QE _ _ = QE
+		checkString' _ q [] [] = q
+		checkString' _ _ (_:_) [] = QE
+		checkString' _ q [] (_:_) = QE
+		checkString' dt q (x:xs) (y:ys) = let 
+				(qn, st) = check dt (q, (y, x))
+			in checkString' dt qn (st++xs) ys
diff --git a/src/Math/Model/Turing.hs b/src/Math/Model/Turing.hs
new file mode 100644
--- /dev/null
+++ b/src/Math/Model/Turing.hs
@@ -0,0 +1,94 @@
+{-# OPTIONS_GHC -fno-warn-tabs #-}
+{-# OPTIONS_HADDOCK show-extensions #-}
+{-# LANGUAGE MultiParamTypeClasses #-}
+{-# LANGUAGE GADTSyntax #-}
+{-# LANGUAGE ExistentialQuantification #-}
+{-|
+Module      : Turing
+Description : Abstraccion de las maquinas de turing
+Copyright   : (c) Jorge Santiago Alvarez Cuadros, 2016
+License     : GPL-3
+Maintainer  : sanjorgek@ciencias.unam.mx
+Stability   : experimental
+Portability : portable
+
+Turing machine abstaction
+-}
+module Math.Model.Turing where
+import Data.Delta
+import Data.State
+import Data.Sigma
+import Data.List
+import Data.Monoid
+import Control.Applicative
+import qualified Data.Map.Lazy as Map
+import qualified Data.Foldable as Fold
+
+class Ways a where
+	oposite::a -> a
+
+data LRS = 
+	-- |Movimiento a la izquierda
+	L
+	-- |No movimiento
+	| S
+	-- |Movimiento a la derecha
+	| R deriving(Show, Eq, Ord, Bounded)
+
+instance Ways LRS where
+	oposite L = R
+	oposite R = L
+	oposite S = S
+
+data FW = 
+	Dw
+	|Lf
+	|Rt
+	|Up deriving(Show, Eq, Bounded)
+
+instance Ways FW where
+	oposite Up = Dw
+	oposite Dw = Up
+	oposite Lf = Rt
+	oposite Rt = Lf
+
+type Delta a b c= (:->:) a b (b,c)
+
+type MDelta a b c = (:->:) a [b] ([b],[c])
+
+liftD::(Ord a, Ord b) => [(a,b,a,b,c)]->Delta a b c
+liftD ls = let
+		(as,bs,cs,ds,es) = unzip5 ls
+		f = map return
+		xs = zip (f as) bs
+		ys = zip (f cs) (zip ds es)
+	in Map.fromList (zip xs ys)
+
+liftMD::(Ord a, Ord b) => [(a,[b],a,[b],[c])]->MDelta a b c
+liftMD ls = let
+		(as,bs,cs,ds,es) = unzip5 ls
+		f = map return
+		xs = zip (f as) bs
+		ys = zip (f cs) (zip ds es)
+	in Map.fromList (zip xs ys)
+
+class (Applicative t) => Tapeable t a where
+	getHead::t a -> a
+	liftTape::(Monoid (t a)) => [a] -> t a
+
+data MultiTape t a = MT [t a] deriving(Show, Eq)
+
+getMHead::(Tapeable t a) => MultiTape t a -> [a]
+getMHead (MT ts) = [getHead t | t<-ts]
+
+liftMTape:: (Tapeable t a, Monoid (t a)) => [a] -> MultiTape t a
+liftMTape ws = MT [liftTape ws]
+
+class (Tapeable t b, Ways w) => TuringM t b w where
+	moveHead::(Monoid b) => w -> t b -> t b
+
+data Model a b c where
+	TS::(Ways c) => Delta a b c->State a->Final a->Model a b c
+
+data MultiModel a b c where
+	MTS::(Ways c) => MDelta a b c->State a->[Final a]->MultiModel a b c
diff --git a/turingMachine.cabal b/turingMachine.cabal
new file mode 100644
--- /dev/null
+++ b/turingMachine.cabal
@@ -0,0 +1,44 @@
+-- Initial turingMachine.cabal generated by cabal init.  For further 
+-- documentation, see http://haskell.org/cabal/users-guide/
+
+name:                turingMachine
+-- PVP summary:      +-+------- breaking API changes
+--                   | | +----- non-breaking API additions
+--                   | | | +--- code changes with no API change
+version:             0.1.1.2
+synopsis:            An implementation of Turing Machine and Automaton
+description:         An implementation of Turing Machine and Automaton for 
+                     language theory
+homepage:            https://github.com/sanjorgek/turingMachine
+license:             GPL-3
+license-file:        LICENSE
+author:              Jorge Santiago Alvarez Cuadros
+maintainer:          sanjorgek@ciencias.unam.mx
+bug-reports:         https://github.com/sanjorgek/turingMachine/issues
+copyright:           (c) Jorge Santiago Alvarez Cuadros
+category:            Math
+build-type:          Simple
+extra-source-files:  README.md
+cabal-version:       >=1.10
+
+source-repository head
+  type:                git
+  location:            git@github.com:sanjorgek/turingMachine.git
+
+library
+  exposed-modules:     Data.Delta
+                       , Data.Sigma
+                       , Data.State
+                       , Math.Model.Automaton.Finite
+                       , Math.Model.Automaton.Stack
+                       , Math.Model.Turing
+  -- other-modules:       
+  other-extensions:    TypeSynonymInstances
+                       , TypeOperators
+                       , MultiParamTypeClasses
+                       , GADTSyntax
+                       , ExistentialQuantification
+  build-depends:       base >=4.8 && <4.9
+                       , containers >= 0.5.6.2
+  hs-source-dirs:      src
+  default-language:    Haskell2010
