From 1deb18ef22f2bbbb3d8b061c8dacf0ca341aa189 Mon Sep 17 00:00:00 2001
From: Yuri Tatishchev <itatishch@gmail.com>
Date: Thu, 27 Feb 2025 22:43:33 -0800
Subject: [PATCH] NFA: implement transitions as dict instead of function

---
 src/glemt.gleam | 156 ++++++++++++++++++++++++++++++++++++++----------
 1 file changed, 126 insertions(+), 30 deletions(-)

diff --git a/src/glemt.gleam b/src/glemt.gleam
index 6a15f11..e1b0767 100644
--- a/src/glemt.gleam
+++ b/src/glemt.gleam
@@ -1,37 +1,110 @@
-import gleam/list
-import gleam/string
-import gleam/set.{type Set}
+import gleam/dict.{type Dict}
 import gleam/io
+import gleam/list
+import gleam/result
+import gleam/set.{type Set}
+import gleam/string
 
-//pub type State {
-//  State(Int)
-//}
+pub type State =
+  Int
 
-pub type State = Int
+pub type AlphabetChar =
+  String
 
-//pub type AlphabetChar {
-//  AlphabetChar(String)
-//}
+pub type NFATransitionKey =
+  #(State, AlphabetChar)
 
-pub type AlphabetChar = String
+pub type NFATransitionFunction =
+  Dict(NFATransitionKey, Set(State))
 
 pub type NFAError {
   NoTransition
 }
 
 pub type NFA {
-  NFA(states: Set(State), alphabet: Set(AlphabetChar), transition_func: fn(Set(State), AlphabetChar) -> Set(State), init_state: State, accepting_states: Set(State))
+  NFA(
+    states: Set(State),
+    alphabet: Set(AlphabetChar),
+    transitions: NFATransitionFunction,
+    init_state: State,
+    accepting_states: Set(State),
+  )
 }
 
-//pub type DFAViolation {
-//  NotAllTransitionsDefined(state: State, missing_chars: Set(AlphabetChar))
-//  MultiplePossibleTransitions(state: State, duplicate_chars: Set(AlphabetChar))
-//}
+pub type DFAViolation {
+  NotAllTransitionsDefined(state: State, missing_chars: Set(AlphabetChar))
+  MultiplePossibleTransitions(state: State, duplicate_chars: Set(AlphabetChar))
+}
+
+pub fn is_dfa(nfa: NFA) -> Result(Nil, List(DFAViolation)) {
+  let violations =
+    nfa.states
+    |> set.map(fn(state) {
+      let missing_transitions =
+        nfa.alphabet
+        |> set.filter(fn(char) {
+          nfa.transitions
+          |> dict.get(#(state, char))
+          |> result.unwrap(set.new())
+          |> set.is_empty
+        })
+
+      let multi_transitions =
+        nfa.transitions
+        |> dict.filter(fn(_key, val) { set.size(val) > 1 })
+        |> dict.keys
+        |> list.map(fn(transition_key) { transition_key.1 })
+        |> set.from_list
+
+      let missing_transitions = case set.size(missing_transitions) {
+        count if count > 0 -> [
+          NotAllTransitionsDefined(state, missing_transitions),
+        ]
+        _ -> []
+      }
+
+      let multi_transitions = case set.size(multi_transitions) {
+        count if count > 0 -> [
+          MultiplePossibleTransitions(state, multi_transitions),
+        ]
+        _ -> []
+      }
+
+      list.append(missing_transitions, multi_transitions)
+    })
+    |> set.to_list
+    |> list.flatten
+
+  case list.length(violations) {
+    count if count > 0 -> Error(violations)
+    _ -> Ok(Nil)
+  }
+}
+
+fn exec_transition(
+  transitions: Dict(#(State, AlphabetChar), Set(State)),
+  states: Set(State),
+  char: AlphabetChar,
+) -> Set(State) {
+  states
+  |> set.filter(fn(state) { dict.has_key(transitions, #(state, char)) })
+  |> set.fold(set.new(), fn(new_states, state) {
+    new_states
+    |> set.union(
+      transitions
+      |> dict.get(#(state, char))
+      |> result.unwrap(set.new()),
+    )
+  })
+}
 
 pub fn check_string(nfa: NFA, input: String) -> Bool {
-  let final_states = input
-  |> string.to_graphemes
-  |> list.fold(set.from_list([nfa.init_state]), nfa.transition_func)
+  let final_states =
+    input
+    |> string.to_graphemes
+    |> list.fold(set.from_list([nfa.init_state]), fn(states, char) {
+      exec_transition(nfa.transitions, states, char)
+    })
 
   !set.is_disjoint(nfa.accepting_states, final_states)
 }
@@ -39,27 +112,50 @@ pub fn check_string(nfa: NFA, input: String) -> Bool {
 pub fn even_a() -> NFA {
   let states = set.from_list([0, 1])
   let alphabet = set.from_list(["a"])
-  let transition_func = fn (states, char) {
-    states
-    |> set.fold(set.new(), fn(n_states, state) {
-      case state, char {
-        0, "a" -> set.insert(n_states, 1)
-        1, "a" -> set.insert(n_states, 0)
-        _, _ -> n_states
-      }
-    })
-  }
+  let transitions =
+    dict.from_list([
+      #(#(0, "a"), set.from_list([1])),
+      #(#(1, "a"), set.from_list([0])),
+    ])
   let init_state = 0
   let accepting_states = set.from_list([0])
-  NFA(states:, alphabet:, transition_func:, init_state:, accepting_states:)
+  NFA(states:, alphabet:, transitions:, init_state:, accepting_states:)
+}
+
+pub fn ends_with_b() -> NFA {
+  let states = set.from_list([0, 1, 2])
+  let alphabet = set.from_list(["a", "b"])
+  let transitions =
+    dict.from_list([
+      #(#(0, "a"), set.from_list([1])),
+      #(#(0, "b"), set.from_list([0, 2])),
+      #(#(1, "a"), set.from_list([1])),
+      #(#(1, "b"), set.from_list([2])),
+      // #(#(2, "a"), set.from_list([0])),
+      // #(#(2, "b"), set.from_list([1])),
+    ])
+  let init_state = 0
+  let accepting_states = set.from_list([0, 2])
+  NFA(states:, alphabet:, transitions:, init_state:, accepting_states:)
 }
 
 pub fn main() {
   io.println("Hello from glemt!")
 
   let automaton = even_a()
+  let _ = io.debug(is_dfa(automaton))
   io.debug(check_string(automaton, ""))
   io.debug(check_string(automaton, "a"))
   io.debug(check_string(automaton, "aa"))
   io.debug(check_string(automaton, "aaab"))
+
+  let automaton = ends_with_b()
+  io.debug(is_dfa(automaton))
+  io.debug(check_string(automaton, ""))
+  io.debug(check_string(automaton, "a"))
+  io.debug(check_string(automaton, "aa"))
+  io.debug(check_string(automaton, "aaaaaa"))
+  io.debug(check_string(automaton, "aaabaaa"))
+  io.debug(check_string(automaton, "bbbbbaab"))
+  io.debug(check_string(automaton, "abaabaaab"))
 }