Parser

• To: mathgroup at yoda.physics.unc.edu
• Subject: Parser
• From: cfw2 at po.cwru.edu (Charles F. Wells)
• Date: Tue, 29 Jun 93 10:34:27 -0400

```Some interest has been shown in parsers in Mathematica.  The
following notebook contains a command AcceptQ that takes a
context free grammar and a string as arguments and determines
whether the string is generated by the grammar.  As a side
effect it prints successively a list of strings that derive to
the given string in n steps.  It stops and accepts when it finds
the start symbol in that list.  If it comes up with the empty
list, it rejects.  The algorithm is a backward exhaustive
search, so is exponential in the length of the input and the
size of the grammar.  It would be difficult to adapt it
to give a derivation tree.  A forward breadth first search would
be easier to adapt for that purpose.

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(*^

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Context-Free Grammars
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Preliminary and incomplete version
27 January 1993
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Implementation
:[font = input; nowordwrap; ]
FindPlaces[grammar_List,s_String] :=
StringPosition[s,Part[#,2]]& /@ grammar
(*FindPlaces[grammar,string] produces a list of pairs {m,n}
where the right side of a production in grammar occurs
as a substring of string from position m to position n.
The lists of pairs are grouped by production: the kth
list of pairs correspond to the occurrences of the right
side of production k of grammar.*)
:[font = input; nowordwrap; ]
BDL[placeslist_List,r_String,s_String] :=
If[Length[placeslist]>0,
StringInsert[StringDrop[s,#],r,Part[#,1]]&
/@ placeslist,
{}
]
(*placeslist should consist of a list of pairs (m,n) of positive
integers.  BDL[placeslist,r,s] produces a list of strings,
each of which is the result of replacing characters m through
n of s with the string r for one of the pairs (m,n) of
placeslist.*)
:[font = input; nowordwrap; ]
BackDerive[grammar_List,s_String] :=
Module[{places = StringPosition[s,Part[#,2]]& /@ grammar},
(BDL[FindPlaces[grammar,s][[#]],grammar[[#]][[1]],s]& /@
Table[k,{k,Length[grammar]}])]
:[font = input; nowordwrap; ]
BackDerive[grammar_List,x_List] :=
BackDerive[grammar,#]& /@ x
:[font = input; nowordwrap; ]
SimpleBackDerive[grammar_List,x_List] :=
Union[Flatten[BackDerive[grammar,x]]]
:[font = input; nowordwrap; ]
EmptyQ[x_List] := Length[x]==0
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AcceptQ[grammar_List,s_String,maxit_Integer:30] :=
Module[{tries=List[s],k=0},
(While[(!MemberQ[tries,"S"] && !EmptyQ[tries] && k++<maxit),
(tries=SimpleBackDerive[grammar,tries];
Print[k," ",tries])
];
MemberQ[tries,"S"])
]
:[font = section; inactive; startGroup; Cclosed; ]
Examples
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Execute the following definitions, giving you a grammar g1
and some strings.  Then execute the commands.
:[font = input; nowordwrap; ]
g1 := {{"S","SS"},
{"S","aSb"},
{"S","bSa"},
{"S","cC"},
{"C","cC"},
{"C","c"}}
:[font = input; nowordwrap; ]
st = "abSabbaSbSacCab"
:[font = input; nowordwrap; ]
st2="aSbbcCa"
:[font = input; nowordwrap; ]
FindPlaces[g1,"aSSS"] (*Example*)
:[font = input; nowordwrap; ]
BDL[{{1,2},{2,5}},"xy","abcde"]
:[font = input; nowordwrap; ]
SimpleBackDerive[g1,{"ab","acCb","aSbb","SS"}]
:[font = input; nowordwrap; ]
AcceptQ[g1,st]
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AcceptQ[g1,st2]
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Acknowledgments
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This work was supported by the Consolidated Natural Gas Corporation
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Charles Wells
Department of Mathematics
Case Western Reserve University
University Circle
Cleveland, OH 44106-7058
:[font = text; inactive; ]
Phone 216 368 2893 or 216 774 1926
:[font = text; inactive; endGroup; ]
Email cfw2 at po.cwru.edu
^*)

--------------------------------
cut here

--

Charles Wells
Department of Mathematics
Case Western Reserve University

```

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