From 09f7d54f7fa691987ba93655394eb0e211435066 Mon Sep 17 00:00:00 2001
From: Franciszek Malinka <franciszek.malinka@gmail.com>
Date: Mon, 14 Mar 2022 20:51:04 +0100
Subject: finite automaton to regex converter WIP

---
 regex.ml | 82 ++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++++
 1 file changed, 82 insertions(+)
 create mode 100644 regex.ml

diff --git a/regex.ml b/regex.ml
new file mode 100644
index 0000000..e0b7b35
--- /dev/null
+++ b/regex.ml
@@ -0,0 +1,82 @@
+include List
+
+type letter = string
+type alphabet = letter list
+type state = int
+type transition = state * letter * state
+type trans_func = transition list
+
+type regex =
+  | Empty
+  | Epsilon
+  | Letter of letter
+  | Plus of regex * regex
+  | Concat of regex * regex
+  | Star of regex
+
+(* <E, Q, q0, d, F> *)
+type automaton = Automaton of alphabet * (state list) * state * trans_func * (state list)
+
+let rec big_plus letters = 
+  match letters with
+  | [] -> Empty
+  | "" :: [] -> Epsilon
+  | l :: [] -> Letter l
+  | "" :: tl -> Plus (Epsilon,  big_plus tl)
+  | l :: tl -> Plus ((Letter l), (big_plus tl))
+
+let basic_regexes states delta =
+  let get_letters_aux s1 s2 = 
+    List.map 
+      (fun (w,l,v) -> l) 
+      (List.filter (fun (w,l,v) -> w = s1 && v = s2) delta)
+  in let get_letters s1 s2 =
+    let res = (get_letters_aux s1 s2) in
+    if s1 = s2 then "" :: res else res
+  in let gen_basic state =  
+    List.map big_plus (List.map (get_letters state) states)
+  in List.map gen_basic states
+ 
+let s = [0;1;2;3;4];;
+let delta = [ (0, "a", 0); (0, "b", 1); 
+              (1, "a", 2); (1, "b", 1); 
+              (2, "a", 0); (2, "b", 3);
+              (3, "a", 4); (3, "b", 1);
+              (4, "a", 4); (4, "b", 4)]
+
+let rec iter_list = function
+  | 0 -> [0]
+  | n -> n :: iter_list (n - 1)
+
+let rec iter n = List.rev (iter_list (n-1))
+
+let increment_phis states_num regexes k = 
+  let ijth i j = (List.nth (List.nth regexes i) j) in 
+  let increment_regex i j =
+    let rij = (ijth i j) in
+    let rik = (ijth i k) in
+    let rkk = (ijth k k) in
+    let rkj = (ijth k j) in
+    Plus (rij, Concat (rik, Concat (Star rkk, rkj))) in
+  let incr_for_i i = List.map (fun j -> increment_regex i j) (iter states_num) in
+  List.map incr_for_i (iter states_num)
+
+let get_results states_num delta = 
+  let states = iter states_num in
+  let regexes = basic_regexes states delta in
+  let rec update_regexes regexes k =
+    if k = states_num then regexes else
+      update_regexes (increment_phis states_num regexes k) (k+1) in
+  update_regexes regexes 1
+
+let rec string_of_regex regex = 
+  match regex with
+    | Empty -> "∅"
+    | Epsilon -> "ε"
+    | Letter l -> l
+    | Plus (phi1, phi2) -> "(" ^ (string_of_regex phi1) ^ ") + (" ^ (string_of_regex phi2) ^ ")"
+    | Concat (phi1, phi2) ->  (string_of_regex phi1) ^ (string_of_regex phi2)
+    | Star phi -> "(" ^ (string_of_regex phi) ^ ")*"
+
+let pp_print_regex fmtr f =
+  Format.pp_print_string fmtr (string_of_regex f)
\ No newline at end of file
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