From 09ede3acde939ff2580700132982188ba3ff5291 Mon Sep 17 00:00:00 2001
From: Julin S <famubu@rawtext.club>
Date: Mon, 26 Jun 2023 17:12:11 +0530
Subject: [PATCH] [haskell] brzozowski derivative

---
 haskell/brzozowksi.hs | 95 +++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 95 insertions(+)
 create mode 100644 haskell/brzozowksi.hs

diff --git a/haskell/brzozowksi.hs b/haskell/brzozowksi.hs
new file mode 100644
index 0000000..6d1e622
--- /dev/null
+++ b/haskell/brzozowksi.hs
@@ -0,0 +1,95 @@
+-- {-# LANGUAGE UnicodeSyntax #-}
+
+-- Brzozowski derivatives
+
+-- | Type of regexes
+data Re a
+  = Nil
+  | Eps
+  | Chr a
+  | Cat (Re a) (Re a)
+  | Alt (Re a) (Re a)
+  | Star (Re a)
+
+instance Show a => Show (Re a) where
+  show r =
+    case r of
+      Nil       -> "Nil"
+      Eps       -> "Eps"
+      Chr c     -> "C " ++ (show c)
+      Cat r1 r2 -> (show r1) ++ "; " ++ (show r2)
+      Alt r1 r2 -> (show r1) ++ "| " ++ (show r2)
+      Star r    -> (show r) ++ "* "
+
+-- | Check if ε can be derived from a regex
+εderiv :: Eq a => Re a -> Bool
+εderiv r =
+  case r of
+    Nil -> False
+    Eps -> True
+    Chr _ -> False
+    Cat r1 r2 -> (εderiv r1) && (εderiv r2)
+    Alt r1 r2 -> (εderiv r1) || (εderiv r2)
+    Star _ -> True
+
+-- | Find Brzozowski derivative of a regex with respect to a letter
+deriv :: Eq a => a -> Re a -> Re a
+deriv a r =
+  case r of
+    Nil       -> Nil
+    Eps       -> Nil
+    Chr c     ->
+      if c==a then Eps
+      else Nil
+    Cat r1 r2 ->
+      if εderiv r1 then deriv a r2
+      else Cat (deriv a r1) r2
+    Alt r1 r2 -> Alt (deriv a r1) (deriv a r2)
+    Star rr   -> Cat (deriv a rr) (Star rr)
+
+
+-- | See if a string matches a regex
+-- exact match only
+match :: Eq a => [a] -> Re a -> Bool
+match [] r =
+  if εderiv r then True
+  else False
+match (x:xs) r = 
+  let newr = deriv x r in
+  case newr of
+    Nil -> False
+    _   -> match xs newr
+-- λ> match "" (Star (Chr 'a'))
+-- True
+-- λ> match "aaaaa" (Star (Chr 'a'))
+-- True
+-- λ> match "aaaaab" (Star (Chr 'a'))
+-- False
+
+-- Couldn't figure out how to make unicode work
+(/\) = Cat
+(\/) = Alt
+-- (@) = Chr
+
+(|=) :: Eq a => [a] -> Re a -> Bool
+(|=) = match
+
+-- lower precedence for smaller numbers 
+-- infixr 7 @
+infixr 6 /\
+infixr 5 \/
+infixr 4 |=
+
+-- ↑0;(↑1│↑0∗);↑1
+-- egr1 = Cat (Chr 0) (Cat (Alt (Chr 1) (Chr 2)) (Chr 3))
+egr1 = (Chr 0) /\ ((Chr 1) \/ (Chr 2)) /\ (Chr 3)
+-- egr1 = (@ 0) /\ ((Chr 1) \/ (Chr 2)) /\ (Chr 3)
+-- λ> match [0,2,3] egr1
+-- True
+-- λ> match [0,1,3] egr1
+-- True
+-- λ> match [0,1,2,3] egr1
+-- False
+--
+-- λ> [0,2,3] |= egr1
+-- True