72 lines
No EOL
2 KiB
FSharp
72 lines
No EOL
2 KiB
FSharp
module DFA
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open System
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open Shields.GraphViz
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///
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/// A deterministic finite automaton
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///
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type DFA = {
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/// All possible characters
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sigma: Char list
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/// All possible states
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states: String list
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/// All possible transitions
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delta: String -> Char -> String
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/// The state this DFA begins in
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beginState: String
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/// The states in which this DFA accepts
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/// the word
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acceptingStates: String list
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}
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(*
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let createGraph (dfa:DFA) =
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let mutable graph = Graph.Directed.Add(EdgeStatement.For("a", "b"))
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graph
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*)
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/// Returns true if the DFA is valid, false otherwise
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let validateDFA (dfa:DFA) =
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let allAcceptingStatesAreStates =
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dfa.acceptingStates
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|> List.map (fun x -> List.contains x dfa.states)
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|> List.filter not
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|> List.length
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|> (<) 1
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let deltaIsComplete =
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// Gets the cartesian product of states * sigma
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dfa.states
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|> List.collect (fun x -> dfa.sigma |> List.map (fun y -> (x, y)))
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// Processes all tuples through delta
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|> List.map (fun x -> dfa.delta (fst x) (snd x))
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// Checks if there is any result from delta which is not
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// a valid state
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|> List.filter (fun x -> not (List.contains x dfa.states))
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|> List.length
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|> (<) 1
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List.contains dfa.beginState dfa.states ||
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allAcceptingStatesAreStates ||
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deltaIsComplete
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/// Returns the state the DFA is in after
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/// reading this character
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let processChar (dfa: DFA) (state: String) (char: Char) =
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dfa.delta state char
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/// Returns the state the DFA is in after
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/// reading this character array
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let rec processCharArray (dfa: DFA) (state: String) (charArr: Char list) =
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match charArr with
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| [] -> state
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| head :: tail -> processCharArray dfa (processChar dfa state head) tail
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/// Returns whether the DFA accepts this word
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let acceptsWord (dfa: DFA) (word: String) =
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dfa.acceptingStates
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|> List.contains (processCharArray dfa dfa.beginState (Seq.toList word)) |