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Lexikon

context clash

When a ref="module.php?name=Lexikon&file=search&eid=1&query=parser">parser cannot tell which alternative ref="module.php?name=Lexikon&file=search&eid=1&query=production">production of a ref="module.php?name=Lexikon&file=search&eid=1&query=syntax">syntax applies by looking at the next input ref="module.php?name=Lexikon&file=search&eid=1&query=token">token ("lexeme"). E.g. given syntax C -> A | b c A -> d | b e If you' re parsing non-terminal C and the next token is ' b' , you don' t know whether it' s the first or second alternative of C since they both can start with b. To discover whether a grammar has a context clash: For each non-terminal, N, with multiple alternatives, look at the first symbol of each alternative' s right-hand side, call it s. If s is the empty string, then find the set FOLLOWER(N) otherwise find the set FIRST*(s). If any of the sets for N' s alternatives intersect then there will be a context clash when parsing N. If the next input symbol is one of those in the intersection of two sets then you won' t know which of the alternatives applies. FIRST(s) is the set of symbols with which s can start, including s itself. If s is a non-terminal then FIRST(s) also includes the first symbol of each alternative right-hand side of s. The ' *' in FIRST*(s) means the "ref="module.php?name=Lexikon&file=search&eid=1&query=transitive closure">transitive closure" of FIRST which means keep applying FIRST to each element of the result until the result doesn' t change. I.e. start with just the set R = ref="module.php?name=Lexikon&file=search&eid=1&query=s">s, then for each non-terminal x in R, add FIRST(x) to R. Keep doing this until nothing new is added. (We are really only interested in the terminals in FIRST*(s) but some definitions include the non-terminals). FOLLOWER(N) is the set of symbols which can come after N in a sentence. Find each occurrence of N on the right-hand side of a rule, e.g. M -> ... | ... N ... | ... If there is a symbol s immediately following N then add FIRST*(s) to the result (again, we' re only interested in the terminal symbols in FIRST*(s)) if there is no symbol after N in the alternative then add FOLLOWER(M) to the result (i.e. if N can be the last symbol in an M then anything that can follow M can also follow N). If a grammar can generate the same sentence in multiple different ways (with different parse tress) then it is ambiguous. An ambiguity must start with a context clash (but not all context clashes imply ambiguity). The context clash occurs when trying to parse the first token of the phrase with multiple parses - you will not be able to tell which alternative to take. To see if a context clash is also a case of ambiguity you would need to follow the alternatives involved in each context clash to see if they can generate the same complete sequence of tokens. (1995-04-05)

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Free On-line Dictionary of Computing

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