BNF to EBNF conversion - discrete-mathematics

Question

I've trying to convert a given BNF list to EBNF and im completely clueless how. Can anyone help?
The BNF is:
<Sentence> :== <NounPhrase><VerbPhrase>
<NounPhrase> :== <Noun>
<NounPhrase> :== <Article><Noun>
<NounPhrase> :== <Article><AdjectiveList><Noun>
<NounPhrase> :== <AdjectiveList><Noun>
<AdjectiveList> :== <Adjective>
<AdjectiveList> :== <Adjective><AdjectiveList>
<VerbPhrase> :== <Verb>
<VerbPhrase> :== <Verb><Adverb>
<Noun> :== frog | grass | goblin
<Article> :== a | the | that
<Adjective> :== purple | green | tiny
<Verb> :== grows | dreams | eats
<Adverb> :== quickly | slowly | badly
Extended BNF grammar uses the following conventions:
A superscript ? after a symbol means it is optional and can appear once or not at all.
A superscript + after a symbol means it must appear at least once but can appear more than once.
A superscript * after a symbol means it can appear not at all, once, or may times.
Paired parentheses can be used to group together symbols for purposes of the: ?, +, * operators.
The angle brackets are typically dropped from non-terminal symbols and a different font is used to distinguish terminals from non-terminals.
This is what I've came up with so far, but I'm not sure it's right.
Sentence :== (<NounPhrase><VerbPhrase>) +
NounPhrase :== <Noun> + (<Article>< AdjectiveList>)?
AdjectiveList :== <Adjective> *
VerbPhrase :== <Verb> + <Adverb>?
Noun :== (frog | grass | goblin)*
Article :== (a | the | that)*
Adjective :== (purple | green | tiny)*
Verb :== (grows | dreams | eats)*
Adverb :== (quickly | slowly | badly)*

Answer 1

The original BNF is:
<Sentence> :== <NounPhrase><VerbPhrase>
<NounPhrase> :== <Noun>
<NounPhrase> :== <Article><Noun>
<NounPhrase> :== <Article><AdjectiveList><Noun>
<NounPhrase> :== <AdjectiveList><Noun>
<AdjectiveList> :== <Adjective>
<AdjectiveList> :== <Adjective><AdjectiveList>
<VerbPhrase> :== <Verb>
<VerbPhrase> :== <Verb><Adverb>
<Noun> :== frog | grass | goblin
<Article> :== a | the | that
<Adjective> :== purple | green | tiny
<Verb> :== grows | dreams | eats
<Adverb> :== quickly | slowly | badly
The first attempt at conversion to the dialect of EBNF required is:
Sentence :== (<NounPhrase><VerbPhrase>) +
NounPhrase :== <Noun> + (<Article>< AdjectiveList>)?
AdjectiveList :== <Adjective> *
VerbPhrase :== <Verb> + <Adverb>?
Noun :== (frog | grass | goblin)*
Article :== (a | the | that)*
Adjective :== (purple | green | tiny)*
Verb :== (grows | dreams | eats)*
Adverb :== (quickly | slowly | badly)*
What you've come up with isn't correct:
You've not dropped the angle brackets.
In the original, a sentence is a noun phrase followed by a verb phrase; in your rewrite, it is a sequence of one or more 'noun phrase followed by verb phrase'.
In the original, a noun phrase ends with a noun; in your rewrite, it can be followed by a list of zero or one combinations of an article and an adjective list (but not preceded by either an article or an adjective list).
In the original, an adjective list is a sequence of one or more adjectives; in your rewrite, is a list of zero or more adjectives.
In the original, a verb phrase is a single verb, optionally followed by an adverb; in your rewrite, it is one or more verbs followed by zero or more adverbs.
In the original, each of noun, article, adjective, verb and adverb is exactly one of three alternative values; in your rewrite, each is a list of zero or more or the corresponding three alternative values.
I'm a little confused as to which brackets to drop. I don't know what the difference is between terminal and non terminal and how to differentiate them in the above. Would removing the superscript "+" and parenthesis correct it?
Terminal symbols are things that represent themselves. In this context, the words such as 'frog', 'the', 'green', 'dreams' and 'badly' are terminals.
Non-terminal symbols are defined in terms of other symbols, either other non-terminals or in terms of terminals. Things such as <Sentence> and <Noun> are non-terminals.
Angle brackets are the < and > symbols (versus round brackets or parentheses (), square brackets [], or curly brackets or braces {}).
Removing the parentheses and + (and angle brackets) from Sentence :== (<NounPhrase><VerbPhrase>) + would improve it. In standard BNF, the :== symbol is normally ::= and in standard EBNF is replaced by just =, and concatenation is indicated explicitly with a comma:
Sentence = Noun Phrase, Verb Phrase
In standard EBNF, terminals are enclosed in double quotes or single quotes (rather than with a font change). And the 'superscript' isn't necessary, either — the ?, + and * simply appear after the unit that repeats. (Note that standard EBNF uses [ … ] around optional matter and { … } around repeated (zero or more) items, and { … }- around repeated (one or more) items).
NounPhrase = Article ? AdjectiveList ? Noun
Noun = "frog" | "grass" | "goblin"