53 lines
2 KiB
Markdown
53 lines
2 KiB
Markdown
# rextra
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At the moment, rextra can display DFAs and NFAs using Graphviz,
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convert between NFAs and DFAs, and minimize DFAs.
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The representation of DFAs and NFAs assumes an infinite alphabet:
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* DFA states always contain a default transition (marked with `*` in
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the visualisations), which is taken if the current token doesn't
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appear in any of the other transitions.
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* NFA transitions either apply to a set of tokens, or to all tokens
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*except* a specified set. In the visualisation, the character `Σ`
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denotes the alphabet of tokens.
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## Example NFA-to-DFA conversion
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This example ghci session converts the NFA shown on the
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[wikipedia article about the powerset construction](https://en.wikipedia.org/wiki/Powerset_construction)
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into a DFA, using the aforementioned powerset construction.
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The conversion assumes that tokens other than `0` and `1` may appear
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in the input. Because of this, the resulting DFA looks different from
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the one on wikipedia.
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``` haskell
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>>> Just a = nfa [ (1,[(only "0",2)],[3]), (2,[(only "1",2),(only "1",4)],[]), (3,[(only "0",4)],[2]), (4,[(only "0",3)],[]) ] (1::Int) [3,4]
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>>> saveDotAsPng "nfa.png" $ nfaToDot a
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```
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``` haskell
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>>> saveDotAsPng "dfa.png" $ dfaToDot $ nfaToDfa a
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```
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## Example DFA minimization
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This example ghci session minimizes the DFA shown on the
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[wikipedia article about DFA minimization](https://en.wikipedia.org/wiki/DFA_minimization).
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Transitions for the token `1` are specified explicitly (where
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necessary), while transitions for the token `0` are represented by the
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default transition marked with `*`.
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``` haskell
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>>> Just a = dfa [ ("a",[('1',"c")],"b"), ("b",[('1',"d")],"a"), ("c",[('1',"f")],"e"), ("d",[('1',"f")],"e"), ("e",[('1',"f")],"e"), ("f",[],"f") ] "a" ["c","d","e"]
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>>> saveDotAsPng "dfa.png" $ dfaToDot a
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```
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``` haskell
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>>> saveDotAsPng "dfa_minimized.png" $ dfaToDot $ minimizeDfa a
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```
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