Adds the NFA example by Bollig et al

src/Examples/ContrivedNFAs.hs

@@ -1,16 +1,18 @@
 {-# LANGUAGE DeriveGeneric #-}
+{-# LANGUAGE TupleSections #-}
 module Examples.ContrivedNFAs where
 
 import           NLambda
 
 -- Explicit Prelude, as NLambda has quite some clashes
-import           Prelude      (Eq, Ord, Show, ($))
+import           Prelude      (Eq, Ord, Show, ($), Int, (+), (-))
 import qualified Prelude      ()
 
 import           GHC.Generics (Generic)
 
 -- Language = u a v a w for any words u,v,w and atom a
 -- The complement of 'all distinct atoms'
+-- Not determinizable
 data NFA1 = Initial1 | Guessed1 Atom | Final1
   deriving (Show, Eq, Ord, Generic)
 instance BareNominalType NFA1
@@ -32,3 +34,26 @@ exampleNFA1 = automaton
     (singleton Initial1)
     -- final states
     (singleton Final1)
+
+
+-- The typical example of a smal NFA: the n-last symbol was something nice
+-- We will use the first symbol as distinguished atom
+-- The DFA (in sets) will have something like 2^n states
+-- whereas the NFA will be linear in n.
+-- So this one *is* determinizable.
+-- Also used in the Bollig et al paper.
+data NFA2 = Initial2 | Distinguished Atom | Count Int
+  deriving (Show, Eq, Ord, Generic)
+instance BareNominalType NFA2
+exampleNFA2 n = automaton
+    (singleton Initial2
+        `union` map Distinguished atoms
+        `union` fromList [Count i | i <- [0 .. n]])
+    atoms
+    (map (\a -> (Initial2, a, Distinguished a)) atoms
+        `union` pairsWith (\a b -> (Distinguished a, b, Distinguished a)) atoms atoms
+        `union` map (\a -> (Distinguished a, a, Count 0)) atoms
+        `union` sum (fromList [map (Count i, , Count (i+1)) atoms | i <- [0 .. n-1]]))
+    (singleton Initial2)
+    (singleton (Count n))
+