56 lines
1.7 KiB
FSharp
56 lines
1.7 KiB
FSharp
module NFA
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open System
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/// A non-deterministic finite automaton
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type NFA = {
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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 list
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/// The state this NFA begins in
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beginState: String
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/// The states in which this NFA accepts
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/// the word
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acceptingStates: String list
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}
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/// Returns a list of possible states after this charater
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/// was read
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let processChar (nfa: NFA) state (char: Char) =
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nfa.delta state char
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/// Returns a list of possible states after this character
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/// list was read
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let rec processCharArray (nfa: NFA) (states: String list) (charArr: Char list) : String list =
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match charArr with
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| [] -> states
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| head :: tail ->
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processCharArray
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nfa
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(
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// Look at all states
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states
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// Where are we going to from each state
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// if we read this character
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|> List.map (fun x -> processChar nfa x head)
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// Which entries are not empty
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|> List.filter (List.isEmpty >> not)
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// If there are no states left,
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// return an empty list
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|> (fun x ->
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if not (List.isEmpty x) then
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List.reduce List.append x
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else [])
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)
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tail
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/// Returns whether this NFA accepts this word
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let acceptsWord nfa word =
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match processCharArray nfa [nfa.beginState] (Seq.toList word) with
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| [] -> false
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| x -> x
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|> List.map (fun x -> List.contains x nfa.acceptingStates)
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|> List.exists id
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