Renamed a bunch of stuff

app/ExampleAutomata.hs

@@ -0,0 +1,101 @@
+{-# language DeriveGeneric #-}
+{-# language DerivingVia #-}
+{-# language FlexibleContexts #-}
+{-# language RecordWildCards #-}
+{-# language UndecidableInstances #-}
+{-# OPTIONS_GHC -Wno-missing-signatures #-}
+
+module ExampleAutomata
+  ( module ExampleAutomata
+  , module Automata
+  ) where
+
+import Nominal hiding (product)
+import Automata
+import IO
+import OrbitList
+import qualified EquivariantMap as Map
+import qualified EquivariantSet as Set
+
+import Data.Foldable (fold)
+import qualified GHC.Generics as GHC
+import Prelude as P hiding (map, product, words, filter, foldr)
+
+-- All example automata follow below
+
+-- words of length <= m
+words m = fold $ go (m+1) (singleOrbit []) where
+  go 0 _   = []
+  go k acc = acc : go (k-1) (productWith (:) rationals acc)
+
+fromKeys f = Map.fromSet f . Set.fromOrbitList
+
+
+data DoubleWord = Store [Atom] | Check [Atom] | Accept | Reject
+  deriving (Eq, Ord, GHC.Generic)
+  deriving Nominal via Generic DoubleWord
+
+instance ToStr DoubleWord where
+  toStr (Store w) = "S " ++ toStr w
+  toStr (Check w) = "C " ++ toStr w
+  toStr Accept    = "A"
+  toStr Reject    = "R"
+
+doubleWordAut 0 = Automaton {..} where
+  states = fromList [Accept, Reject]
+  initialState = Accept
+  acceptance = fromKeys (Accept ==) states
+  transition = fromKeys (const Reject) $ product states rationals
+doubleWordAut n = Automaton {..} where
+  states = fromList [Accept, Reject] <> map Store (words (n-1)) <> map Check (productWith (:) rationals (words (n-1)))
+  initialState = Store []
+  acceptance = fromKeys (Accept ==) states
+  trans Accept _ = Reject
+  trans Reject _ = Reject
+  trans (Store l) a
+    | length l + 1 < n = Store (a:l)
+    | otherwise        = Check (reverse (a:l))
+  trans (Check (a:as)) b
+    | a == b    = if (P.null as) then Accept else Check as
+    | otherwise = Reject
+  transition = fromKeys (uncurry trans) $ product states rationals
+
+
+-- alphetbet for the Fifo queue example
+data Fifo = Put Atom | Get Atom
+  deriving (Eq, Ord, Show, GHC.Generic)
+  deriving Nominal via Generic Fifo
+
+instance ToStr Fifo where
+  toStr (Put a) = "Put " ++ toStr a
+  toStr (Get a) = "Get " ++ toStr a
+
+instance FromStr Fifo where
+  fromStr ('P':'u':'t':' ':a) = let (x, r) = fromStr a in (Put x, r)
+  fromStr ('G':'e':'t':' ':a) = let (x, r) = fromStr a in (Get x, r)
+  fromStr _ = error "Cannot parse Fifo"
+
+data FifoS = FifoS [Atom] [Atom]
+  deriving (Eq, Ord, GHC.Generic)
+  deriving Nominal via Generic FifoS
+
+instance ToStr FifoS where
+  toStr (FifoS l1 l2) = "F " ++ toStr l1 ++ " - " ++ toStr l2
+
+fifoAlph = map Put rationals <> map Get rationals
+
+fifoAut n = Automaton {..} where
+  states0 = filter (\(FifoS l1 l2) -> length l1 + length l2 <= n) $ productWith (\l1 l2 -> FifoS l1 l2) (words n) (words n)
+  states = fromList [Nothing] <> map Just states0
+  initialState = Just (FifoS [] [])
+  acceptance = fromKeys (Nothing /=) states
+  trans Nothing _ = Nothing
+  trans (Just (FifoS l1 l2)) (Put a)
+    | length l1 + length l2 >= n = Nothing
+    | otherwise                  = Just (FifoS (a:l1) l2)
+  trans (Just (FifoS [] [])) (Get _) = Nothing
+  trans (Just (FifoS l1 [])) (Get b) = trans (Just (FifoS [] (reverse l1))) (Get b)
+  trans (Just (FifoS l1 (a:l2))) (Get b)
+    | a == b    = Just (FifoS l1 l2)
+    | otherwise = Nothing
+  transition = fromKeys (uncurry trans) $ product states fifoAlph

app/FoSolver.hs

@@ -1,7 +1,5 @@
 {-# LANGUAGE PatternSynonyms #-}
 
-module Main where
-
 import OrbitList hiding (head)
 import Support (Rat)
 

app/IO.hs

@@ -1,45 +1,16 @@
-{-# language DeriveGeneric #-}
-{-# language DerivingVia #-}
-{-# language FlexibleContexts #-}
 {-# language RecordWildCards #-}
-{-# language UndecidableInstances #-}
-module OnsAutomata where
+
+module IO where
 
 import Data.Char (isSpace)
 import Data.Ratio
 import Data.List (intersperse)
 
 import Nominal
+import Automata
 import Support (Rat(..), Support(..))
-import OrbitList as L (OrbitList, toList)
-import EquivariantMap as M (EquivariantMap, toList, (!))
-
-import Prelude hiding (print, Word)
-import qualified GHC.Generics as GHC
-
-
-type Word a = [a]
-
--- states, initial state, acceptance, transition
-data Automaton q a = Automaton
-  { states :: OrbitList q
-  , initialState :: q
-  , acceptance :: EquivariantMap q Bool
-  , transition :: EquivariantMap (q, a) q
-  }
-
-accepts :: (Nominal q, Ord (Orbit q), Nominal a, Ord (Orbit a))
-        => Automaton q a -> Word a -> Bool
-accepts aut l = go (initialState aut) l
-  where
-    go s []    = acceptance aut ! s
-    go s (a:w) = go (transition aut ! (s, a)) w
-
-
--- alphetbet for the Fifo queue example
-data Fifo = Put Rat | Get Rat
-  deriving (Eq, Ord, Show, GHC.Generic)
-  deriving Nominal via Generic Fifo
+import OrbitList as L (toList)
+import EquivariantMap as M (toList)
 
 
 -- I do not want to give weird Show instances for basic types, so I create my
@@ -57,10 +28,6 @@ instance ToStr Rat where
 instance ToStr Support where
   toStr (Support s) = "{" ++ toStr s ++ "}"
 
-instance ToStr Fifo where
-  toStr (Put a) = "Put " ++ toStr a
-  toStr (Get a) = "Get " ++ toStr a
-
 instance ToStr Bool where toStr b = show b
 instance ToStr Int where toStr i = show i
 instance ToStr a => ToStr [a] where
@@ -88,8 +55,3 @@ instance FromStr a => FromStr [a] where
     where
       (a, str2) = fromStr str
       (l, emptyStr)    = fromStr (dropWhile isSpace str2)
-
-instance FromStr Fifo where
-  fromStr ('P':'u':'t':' ':a) = let (x, r) = fromStr a in (Put x, r)
-  fromStr ('G':'e':'t':' ':a) = let (x, r) = fromStr a in (Get x, r)
-  fromStr _ = error "Cannot parse Fifo"

app/LStar.hs

@@ -3,11 +3,9 @@
 {-# LANGUAGE RecordWildCards #-}
 {-# OPTIONS_GHC -Wno-partial-type-signatures #-}
 
-module Main where
-
-import OnsAutomata
-import OnsQuotient
-
+import ExampleAutomata
+import IO
+import Quotient
 import OrbitList
 import EquivariantMap (EquivariantMap(..), lookup, (!))
 import qualified EquivariantMap as Map

app/Minimise.hs

@@ -6,17 +6,14 @@
 {-# language UndecidableInstances #-}
 {-# OPTIONS_GHC -Wno-partial-type-signatures #-}
 
-import Nominal hiding (product)
-import Support (Rat(..), Support)
-import OnsAutomata
-import OnsQuotient
+import ExampleAutomata
+import IO
+import Quotient
 import OrbitList
 import EquivariantMap ((!))
 import qualified EquivariantMap as Map
 import qualified EquivariantSet as Set
 
-import Data.Foldable (fold)
-import qualified GHC.Generics as GHC
 import Prelude as P hiding (map, product, words, filter, foldr)
 
 
@@ -78,69 +75,3 @@ main :: IO ()
 main = do
   putStrLn . toStr $ (minimiseB (doubleWordAut 4) rationals)
   -- putStrLn . toStr $ (minimiseB (fifoAut 4) fifoAlph)
-
-
--- All example automata follow below
-
--- words of length <= m
-words m = fold $ go (m+1) (singleOrbit []) where
-  go 0 acc = []
-  go k acc = acc : go (k-1) (productWith (:) rationals acc)
-
-fromKeys f = Map.fromSet f . Set.fromOrbitList
-
-
-data DoubleWord = Store [Rat] | Check [Rat] | Accept | Reject
-  deriving (Eq, Ord, GHC.Generic)
-  deriving Nominal via Generic DoubleWord
-
-instance ToStr DoubleWord where
-  toStr (Store w) = "S " ++ toStr w
-  toStr (Check w) = "C " ++ toStr w
-  toStr Accept    = "A"
-  toStr Reject    = "R"
-
-doubleWordAut 0 = Automaton {..} where
-  states = fromList [Accept, Reject]
-  initialState = Accept
-  acceptance = fromKeys (Accept ==) states
-  transition = fromKeys (const Reject) $ product states rationals
-doubleWordAut n = Automaton {..} where
-  states = fromList [Accept, Reject] <> map Store (words (n-1)) <> map Check (productWith (:) rationals (words (n-1)))
-  initialState = Store []
-  acceptance = fromKeys (Accept ==) states
-  trans Accept _ = Reject
-  trans Reject _ = Reject
-  trans (Store l) a
-    | length l + 1 < n = Store (a:l)
-    | otherwise        = Check (reverse (a:l))
-  trans (Check (a:as)) b
-    | a == b    = if (P.null as) then Accept else Check as
-    | otherwise = Reject
-  transition = fromKeys (uncurry trans) $ product states rationals
-
-
-data FifoS = FifoS [Rat] [Rat]
-  deriving (Eq, Ord, GHC.Generic)
-  deriving Nominal via Generic FifoS
-
-instance ToStr FifoS where
-  toStr (FifoS l1 l2) = "F " ++ toStr l1 ++ " - " ++ toStr l2
-
-fifoAlph = map Put rationals <> map Get rationals
-
-fifoAut n = Automaton {..} where
-  states0 = filter (\(FifoS l1 l2) -> length l1 + length l2 <= n) $ productWith (\l1 l2 -> FifoS l1 l2) (words n) (words n)
-  states = fromList [Nothing] <> map Just states0
-  initialState = Just (FifoS [] [])
-  acceptance = fromKeys (Nothing /=) states
-  trans Nothing _ = Nothing
-  trans (Just (FifoS l1 l2)) (Put a)
-    | length l1 + length l2 >= n = Nothing
-    | otherwise                  = Just (FifoS (a:l1) l2)
-  trans (Just (FifoS [] [])) (Get _) = Nothing
-  trans (Just (FifoS l1 [])) (Get b) = trans (Just (FifoS [] (reverse l1))) (Get b)
-  trans (Just (FifoS l1 (a:l2))) (Get b)
-    | a == b    = Just (FifoS l1 l2)
-    | otherwise = Nothing
-  transition = fromKeys (uncurry trans) $ product states fifoAlph

ons-hs.cabal

@@ -15,12 +15,14 @@ cabal-version:       >=1.10
 
 library
   hs-source-dirs:      src
-  exposed-modules:     EquivariantMap
+  exposed-modules:     Automata
+                     , EquivariantMap
                      , EquivariantSet
                      , Nominal
                      , Nominal.Class
                      , Nominal.Products
                      , OrbitList
+                     , Quotient
                      , Support
                      , Support.Rat
                      , Support.OrdList
@@ -33,7 +35,7 @@ library
 
 executable ons-hs-solver
   hs-source-dirs:      app
-  main-is:             Main.hs
+  main-is:             FoSolver.hs
   build-depends:       base
                      , ons-hs
   ghc-options:         -threaded -rtsopts -with-rtsopts=-N -O2
@@ -45,8 +47,8 @@ executable ons-hs-lstar
   build-depends:       base
                      , mtl
                      , ons-hs
-  other-modules:       OnsAutomata
-                     , OnsQuotient
+  other-modules:       ExampleAutomata
+                     , IO
   ghc-options:         -threaded -rtsopts -with-rtsopts=-N -O2
   default-language:    Haskell2010
 
@@ -56,8 +58,8 @@ executable ons-hs-minimise
   build-depends:       base
                      , mtl
                      , ons-hs
-  other-modules:       OnsAutomata
-                     , OnsQuotient
+  other-modules:       ExampleAutomata
+                     , IO
   ghc-options:         -threaded -rtsopts -with-rtsopts=-N -O2
   default-language:    Haskell2010
 

src/Automata.hs

@@ -0,0 +1,27 @@
+{-# language FlexibleContexts #-}
+
+module Automata where
+
+import Nominal (Nominal(..))
+import OrbitList (OrbitList)
+import EquivariantMap (EquivariantMap, (!))
+
+import Prelude hiding (Word)
+
+
+type Word a = [a]
+
+-- states, initial state, acceptance, transition
+data Automaton q a = Automaton
+  { states :: OrbitList q
+  , initialState :: q
+  , acceptance :: EquivariantMap q Bool
+  , transition :: EquivariantMap (q, a) q
+  }
+
+accepts :: (Nominal q, Ord (Orbit q), Nominal a, Ord (Orbit a))
+        => Automaton q a -> Word a -> Bool
+accepts aut l = go (initialState aut) l
+  where
+    go s []    = acceptance aut ! s
+    go s (a:w) = go (transition aut ! (s, a)) w

src/Nominal.hs

@@ -9,8 +9,9 @@ import Data.Proxy
 
 import Nominal.Products
 import Nominal.Class
-import Support (def)
+import Support (Rat, def)
 
+type Atom = Rat
 
 -- We can get 'default' values, if we don't care about the support.
 getElementE :: forall a. Nominal a => Orbit a -> a

src/Quotient.hs

@@ -1,26 +1,34 @@
 {-# language FlexibleContexts #-}
-module OnsQuotient where
+module Quotient where
 
 import Nominal (Nominal(..))
 import Support (Support, intersect)
 import OrbitList
-import EquivariantMap (EquivariantMap(..))
+import EquivariantMap (EquivariantMap)
 import qualified EquivariantMap as Map
-import EquivariantSet (EquivariantSet(..))
+import EquivariantSet (EquivariantSet)
 import qualified EquivariantSet as Set
 
 import Prelude (Bool, Int, Ord, (.), (<>), (+), ($), fst, snd, fmap, uncurry)
 
+
+{- Computes the quotient of some set (given as OrbitList) and equivalence
+   relations. Returns the quotientmap and the set of images. The non-trivial
+   part is computing the least support, this is done by iteratively
+   intersecting supports. -}
+
 type QuotientType = (Int, Support)
 type QuotientMap a = EquivariantMap a QuotientType
 
 -- Computes a quotient map given an equivalence relation
-quotient :: (Nominal a, Ord (Orbit a)) => EquivariantSet (a, a) -> OrbitList a -> (QuotientMap a, OrbitList QuotientType)
+quotient :: (Nominal a, Ord (Orbit a))
+         => EquivariantSet (a, a) -> OrbitList a -> (QuotientMap a, OrbitList QuotientType)
 quotient equiv = post . quotientf 0 (\a b -> (a, b) `Set.member` equiv)
   where post (a, b, _) = (a, map fst b)
 
 -- f should be equivariant and an equivalence relation
-quotientf :: (Nominal a, Ord (Orbit a)) => Int -> (a -> a -> Bool) -> OrbitList a -> (QuotientMap a, OrbitList (QuotientType, EquivariantSet a), Int)
+quotientf :: (Nominal a, Ord (Orbit a))
+          => Int -> (a -> a -> Bool) -> OrbitList a -> (QuotientMap a, OrbitList (QuotientType, EquivariantSet a), Int)
 quotientf k f ls = go k Map.empty empty (toList ls)
   where
     go n phi acc []     = (phi, acc, n)