Add DFA constructor function

Also cleanes up the naming scheme, just like the last commit.

src/Rextra/Dfa.hs

@@ -1,5 +1,12 @@
-module Rextra.Dfa where
--- TODO don't export internals
+module Rextra.Dfa
+  ( Dfa
+  , dfa
+  , dfa'
+  , stateMap
+  , entryState
+  , transition
+  , State(..)
+  ) where
 
 import qualified Data.Map.Strict as Map
 import qualified Data.Set as Set
@@ -11,22 +18,36 @@ data State s t = State
   }
 
 data Dfa s t = Dfa
-  { dfaStates     :: Map.Map s (State s t)
-  , dfaEntryState :: s
+  { stateMap   :: Map.Map s (State s t)
+  , entryState :: s
   }
 
 {-
- - Constructing and modifying a DFA
+ - Constructing a DFA
  -}
 
--- TODO
+integrityCheck :: (Ord s) => Dfa s t -> Bool
+integrityCheck dfa =
+  let states = Map.elems $ stateMap dfa
+      transitionStates = concatMap (Map.elems . transitions) states
+      defaultTransitionStates = map defaultTransition states
+      referencedStates = Set.fromList $ concat [[entryState dfa], transitionStates, defaultTransitionStates]
+  in  referencedStates `Set.isSubsetOf` Map.keysSet (stateMap dfa)
+
+dfa :: (Ord s) => Map.Map s (State s t) -> s -> Maybe (Dfa s t)
+dfa stateMap entryState =
+  let myDfa = Dfa{stateMap=stateMap, entryState=entryState}
+  in  if integrityCheck myDfa then Just myDfa else Nothing
+
+dfa' :: (Ord s) => [(s, State s t)] -> s -> Maybe (Dfa s t)
+dfa' states entryState = dfa (Map.fromList states) entryState
 
 {-
  - "Executing" a DFA
  -}
 
 getState :: (Ord s) => Dfa s t -> s -> State s t
-getState dfa s = dfaStates dfa Map.! s
+getState dfa s = stateMap dfa Map.! s
 
 transition :: (Ord s, Ord t) => Dfa s t -> s -> t -> s
 transition dfa s t =