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on the left-corner of production rules.\n* Head-Corner Parser: a chart parser for parsing with top-down predictions \nbased on the head of production rules.\n\nAll four parsers are created and called in the same way and return the same \ntype of result, that is a chart with recognised items. Both context-free \ngrammars and unification grammars can be used. In the next section it will be\nexplained how grammars and parsers are used in general. After that each \nparser will be discussed in more detail.\n\n\n# Installation\nThis module can be installed using npm as follows:\n```\nnpm install chart-parsers\n```\n\n# Usage\nAll four parser are used in the same way: load a grammar, create a parser and\n parse sentences.\n```\nvar GrammarParser = require('GrammarParser');\nvar ParserFactory = require('ParserFactory');\nvar parserFactory = new ParserFactory();\n\nvar tagged_sentence = [['I', 'NP'], ['saw', 'V'], ['the', 'DET'], ['man', 'N'], \n ['with', 'P'], ['the', 'DET'], ['telescope', 'N']];\nvar grammar_text = \"S -> NP *VP*\\nNP -> DET *N*\\nNP -> *NP* PP\\nPP -> P *NP*\\nVP -> *V* NP\\nVP -> *VP* PP\";\n\n// Parse the grammar\nvar grammar = GrammarParser.parse(grammar_text);\n// Create a parser; other parsing algorithms are 'Earley', 'LeftCorner', 'HeadCorner'\nvar parser = parserFactory.createParser({\n grammar: grammar, \n type: 'CYK', \n unification: false, \n listOfCategories: true\n});\n// parse the sentence\nvar chart = parser.parse(tagged_sentence);\n```\nThe resulting chart is an array of length N+1, and each entry contains items of the form [rule, dot, from, children] where:\n* rule is the production rule; it has two members: lhs for the left-hand-side of the rule, and rhs for the right-hand-side of the rule.\n* dot is the position in the right hand side of the rule up to which it has been recognised. \n* from is the origin position pointing at the position in the sentence at which recognition of this rule began.\n* children are the completed items that are used to recognise the current item\n\nBased on the children of the completed items the parse(s) of a sentence can \nbe reconstructed.\n\n\n# Context-Free Grammars\nThe grammar module reads context-free grammars from file, and offers some methods that are practical for parsing.\n\nThe syntax of production rules is as follows (in EBNF):\n```\ngrammar = { comment | production_rule }\nproduction_rule = nonterminal, [ white_space ], \"->\", [ white_space ], [nonterminal_seq] , [\"*\" nonterminal \"*\" nonterminal_seq ]\nnonterminal_seq = nonterminal, { whitespace, nonterminal }\nnonterminal = non_whitespace_char, { non_whitespace_char }\ncomment = \"//\", { any_character }\n```\nNote the possibility of identifying one nonterminal as the head of the production rule. This information is used by the head-corner parser for predicting new partial parses.\nTerminals are not allowed in the grammar, because we assume these to be \nrecognised by a lexer and tagged with (lexical) categories (or feature \nstructures). In the grammar these lexical categories are seen as preterminals.\nThe grammar parser also allows adding constraints to the production rules. Contraints may have two possible forms:\n```\n = type\n = \n```\nwhere type is a type defined by a type lattice. See below for an explanation \nof type lattices.\n\n\n# CYK Chart Parser\nThe CYK algorithm works with context-free grammars in Chomsky Normal Form (CNF). Production rules are of the form:\n```\nA -> B C\nA -> a\n```\nwhere A, B and C are nonterminals and a is a terminal.\n\n##Algorithm\nThe CYK algorithm is as follows:\n```\nfunction CYK-PARSE(sentence, grammar)\n let the input be a sentence consisting of n characters: a1 ... an.\n This grammar contains the subset Rs which is the set of start symbols.\n\n chart = INITIALISE-CHART(sentence, grammar)\n for each i = 2 to n do // Length of span\n for each j = 1 to n-i+1 do // Start of span\n for each k = 1 to i-1 do // Partition of span\n for each production A -> B C do\n if chart[j,k,B] and chart[j+k,i-k,C] then \n chart[j,i,A] = true\n end\n end\n end\n end\n end\n return chart\nend\n\nfunction INITIALISE-CHART(sentence, grammar)\n let chart[n,n,r] be an array of booleans \n where n is the length of the sentence and\n r the number of nonterminal symbols. \n Initialize all elements of chart to false.\n for i = 1 to n do\n for each unit production A -> ai\n chart[i,1,A] = true\n end\n end\n return chart\nend\n```\n(Adapted from: Wikipedia, http://en.wikipedia.org/wiki/CYK_algorithm)\n\nBelow is a simple toy grammar that is in CNF:\n```\nS -> NP VP\nNP -> DET N\nNP -> NP PP\nPP -> P NP\nVP -> V NP\nVP -> VP PP\nDET -> the\nNP -> I\nN -> man\nN -> telescope\nP -> with\nV -> saw\nN -> cat\nN -> dog\nN -> pig\nN -> hill\nN -> park\nN -> roof\nP -> from\nP -> on\nP -> in\n```\nThe language generated by this grammar contains a.o. \"I saw the man with the telescope\". Clearly, this grammar contains the lexicon as well. In our parser the lexicon is separated from the grammar. The parser expects a tokenized and tagged sentence as input. In this way we feed the output of a tagger into the parser.\n\n# Earley Chart Parser\nThe Earley Chart Parser can parse all context-free languages and uses arbitrary context-free grammars.\n\n##Algorithm\nThe algorithm in pseudo code:\n```\nfunction EARLEY-PARSE(words, grammar)\n ENQUEUE((γ → •S, 0), chart[0])\n for i ← from 0 to LENGTH(words) do\n for each state in chart[i] do\n if INCOMPLETE?(state) then\n PREDICTOR(state, i, grammar)\n else\n COMPLETER(state, i)\n end\n end\n end\n return chart\nend\n \nprocedure PREDICTOR((A → α•B, i), j, grammar)\n for each (B → γ) in GRAMMAR-RULES-FOR(B, grammar) do\n ADD-TO-SET((B → •γ, j), chart[j])\n end\nend\n \nprocedure COMPLETER((B → γ•, j), k)\n for each (A → α•Bβ, i) in chart[j] do\n ADD-TO-SET((A → αB•β, i), chart[k])\n end\nend\n```\n(Adapted from: Wikipedia, http://en.wikipedia.org/wiki/Earley_parser)\n\n# Left-Corner Chart Parser\nThe left-corner algorithm is parses the sentence from left to right just like the Earley algorithm. The only difference is in the prediction of new items. The left-corner relation is used to optimise predictions top down. Therefore, the left-corner algorithm is called an bottom-up with top-down filtering.\nThe left-corner relation is based on the left-corner of production rules. Consider the following production rule\n```\nS -> NP VP\n```\nNP is called the left-corner of S, written as S >_lc NP. The transitive reflexive closure, written as >_lc*, is used for filtering.\n\n## Algorithm\n```\nfunction LEFT-CORNER-PARSE(sentence)\n chart = INITIALISE-CHART(sentence)\n agenda = INITIALISE-AGENDA(sentence)\n for i = 0 to n do\n for items [A → α•β, i] do\n LC-PREDICTOR(item, chart, grammar)\n COMPLETER(item, chart, grammar)\n end\n end\n return chart\nend\n```\nThe deduction rules that is applied by LC-PREDICTOR is:\n```\nD_lc = {[X → γ•, k, j], [A → α.Cβ,i,k] |- [B → X.δ, k, j] | B → Xδ, C >_lc* B}\n```\n\n# Head-Corner Chart Parser\nThe algorithm of head corner parsing is based on the idea that the right-hand side of a production rule contains a head, a word or constituent that determines the syntactic type of the complete phrase. To make the algorithm work in each production rule the right hand-side must a symbol that is decorated as head, like this:\n ```\nNP -> DET *N*\n```\nThis means that N is head-corner of NP, or NP >_hc N. The parser uses these the head-corner relation to predict new partial parses. In fact, it uses the reflexive transitive closure of the head-corner relation to create new goal items and head-corner items. The closure is written as >_hc*\n\n## Algorithm\nHead-corner parsing involves a complex administrative bookkeeping. It uses a chart and an agenda. As long as items are available on the agenda, it takes an item from the agenda and tries to combine it with items on the chart. New items are added to the agenda. Algorithm in pseudo-code:\n```\nfunction HEAD-CORNER-PARSE(sentence)\n chart = INITIALISE-CHART(sentence)\n agenda = INITIALISE-AGENDA(sentence)\n while not IS-EMPTY(agenda) do\n current = GET-ITEM-FROM-AGENDA(agenda)\n if not IS-ON-CHART(current) then\n ADD-TO-CHART(chart, current)\n COMBINE-WITH-CHART(chart, current)\n end\n end\n return chart\nend\n```\nThe following types of items are used:\n* CYK items are of the form [A, i, j] which means that nonterminal A can produce the sentence from position i to position j.\n* Goal items are of the form [l, r, A] which means that the nonterminal is expected to be recognised somewhere between position l and r.\n* Head-corner items are of the form [S -> NP VP, i, j, l, r] where the right hand side of the production rule has been recognised from position i to j, and the recognised part of the production can generate the sentence from position l to r.\n\nGiven a sentence a1, a2, .. , an, the following set is used to initialise the agenda; it adds goal items to the agenda for the start symbol.\n```\nD_init_agenda = {[i, j, S]|0 <= i <= j <= n}\n```\nThe following set is used to initialise the chart; for each word of the sentence appropriate CYK items are added to the chart.\n```\nD_init_chart = {[A, i, i+1]| A -> a_i, 0 <= i <= n}\n```\nThese deduction rules are used for creating new items in the combine step:\n```\n(1) D_HC = {[i, j, A], [X, i, j] |- [B -> α•X•β, i, j] | A >_hc* B}\n(2) D_HC_epsilon = {[j, j, A] |- [B -> ••, j, j] | A >_hc* B}\n(3) D_left_predict = {[l, r, A], [B -> αC•β•γ, k, r] |- [i, j, C] | A >_hc* B, l <= i <= j <= k}\n(4) D_right_predict = {[l, r, A], [B -> α•β•Cγ, l, i] |- [j, k, C] | A >_hc* B, i <= j <= k <= r}\n(5) D_pre_complete = {[A -> •β•, i, j] |- [A, i, j]}\n(6) D_left_complete = {[i, k, A], [X, i, j], [B -> αX•β•γ, j, k] |- [B -> α•Xβ•γ, i, k] | A >_hc* B}\n(7) D_right_complete = {[i, k, A], [B -> α•β•Xγ, i, j], [X, j, k] |- [B -> α•βX•γ, i, k] | A >_hc* B}\n```\nDeduction rules (1) and (2) introduce head-corner items from goal items. Rules (3) and (4) introduce goal items from partially recognised head-corner items. Rule (5) creates CYK items for head-corner items that are completely recognised. Rules (6) and (7) recognise parts of head-corner items based on CYK items. \n\n## Usage\nThe head-corner parser is created and applied as usual; there is one \ndifference: the production rules of the grammar must be decorated with heads \nas follows:\n```\nS -> NP *VP*\nNP -> DET *N*\nNP -> *NP* PP\nPP -> P *NP*\nVP -> *V* NP\nVP -> *VP* PP\n```\n\n# Specification of a type lattice\nA type lattice is specified as follows:\n```\nType type1 ()\nType type2 ()\nType type3 (type1 type2)\nType type4 (type1)\nType type5 (type 4)\n```\nEach type specification if started with keyword Type followed by the type \nname and the super types between braces. If no super types are supplied, \nBOTTOM (the most general type) is assumed to be the sole super type.\n\nOnce a type lattice has been created the least upper bound of two types can be \ndetermined:\n```\nvar LUB = type1.LUB(type2, type_lattice);\n```\nChecking if one type subsumes another type is done as follows:\n```\nif (type1.subsumes(type2, type_lattice)) {\n console.log(type1.prettyPrint() + ' subsumes ' + type2.prettyPrint());\n}\n```\nA type may be appropriate for a feature with a value type. These appropriate\n features are specified in the form of a feature structure:\n```\nType type1 ()\nType type2 ()\nType type3 (type1 type2) ->\n[type3\n FEATURE1: type1\n FEATURE2: [type2\n FEATURE3: type1\n ]\n]\n```\nWhen a new type with a feature structure is defined:\n* The feature structure of the type is unified with the feature structures of\n its super types.\n* The types used in the feature structure are unified with the respective \nfeature structures belonging to these types.\n\nAs a result the feature structure inherits all appropriate features and types\n from super types and used types.\n \nBuilt-in types are (types are case sensitive):\n* BOTTOM: least specific type\n* TOP: most specific type \n* LIST: a list of coreferences and/or feature structures\n* CONCATLIST: concatenation of lists referred to\n* STRING: a lexical string\n* RULE: type used for the feature structures of production rules\n* CONSTITUENT: type used for the feature structures of a \nRHS nonterminal \n\n# Typed feature structures\nFeature structures are specified using a specification language that largely \nfollows PATRII. The LexiconParser reads lexicons that assign feature structures \nto words. Multiple alternative feature structures may be assigned to the same\nword by specifying multiple entries of the word. Each node of a feature \nstructure has a type assigned that is specified in a type lattice.\n```\n[home] ->\n[sign\n CATEGORY: noun\n AGREEMENT: [agreement\n NUMBER: singular\n GENDER: neutrum\n ]\n]\n```\nIn this example the root node of the feature structure is of type sign and \ncategory is of type noun.\n\nFeature structures can be unified as follows:\n```\nvar result = fs1.unify(fs2, typeLattice);\n```\n\nFeatures may have several different values:\n**Type**: feature: type\n```\nPERSON: first\n```\n**Feature structure**: f1: [t1 f2: t2]\n```\nAGREEMENT: [agreement\n PERSON: first\n GENDER: masculin\n ]\n```\nA **coreference** to a feature structures: FEATURE: [1]\n```\nAGREEMENT: [1][agreement\n PERSON: first\n GENDER: masculin\n ]\nSAME: [1]\n```\nA **list** of coreferences to other feature structures: <[1], [2], ..\n.>; A list may contain embedded feature structures.\n```\nNP: [1]: [...]\nPP: [2]: [...]\nCAT: [cat\n COMPS: <[1], [2], [BOTTOM f: type]>\n ]\n```\nA **concatenated list** of coreferences: [1] + \n[2]\n```\nCAT: [cat\n SUBJ: [1]: <>\n SPR: [2]: <>\n COMPS: [3]: \n ARG-STR: <[1] + [2] + [3]>\n ]\n```\n\n# References\n* An Introduction to Unification-Based Approaches to Grammar, Stuart M. \nShieber, 2003, URL: https://dash.harvard.edu/handle/1/11576719\n* Head-Driven Phrase Structure Grammar, Pollard, Carl, and Ivan A. Sag. 1994. \n Chicago: University of Chicago Press and Stanford: CSLI Publications. \n Chapters 1, 3 and 4 are online available: http://hpsg.stanford.edu/LSA07/\n* Introduction to Head-driven Phrase Structure Grammar, Steve Harlow, 2009, \nURL: http://www-users.york.ac.uk/~sjh1/hpsgcourse.pdf\n","maintainers":[{"name":"hugo-ter-doest","email":"hwl.ter.doest@gmail.com"}],"time":{"modified":"2022-06-13T05:53:59.071Z","created":"2015-01-24T21:18:21.676Z","0.0.2":"2015-01-24T21:18:21.676Z","0.0.3":"2015-01-24T21:21:30.637Z","0.0.4":"2015-01-24T21:35:28.502Z","0.0.5":"2015-01-24T21:40:26.581Z","0.0.6":"2015-01-24T21:41:28.229Z","0.0.7":"2015-01-24T21:47:12.125Z","0.0.8":"2015-01-25T19:46:23.609Z","0.0.9":"2015-01-25T20:13:20.325Z","0.0.10":"2015-01-25T20:21:55.737Z","0.0.11":"2015-01-26T21:27:42.061Z","0.0.12":"2015-01-28T20:17:14.003Z","0.0.13":"2015-01-28T20:29:52.728Z","0.0.14":"2015-01-28T20:50:32.190Z","0.0.15":"2015-01-28T21:26:16.285Z","0.0.16":"2015-01-29T17:48:02.618Z","0.0.17":"2015-01-30T22:06:59.539Z","0.0.18":"2015-01-31T22:42:17.962Z","0.0.19":"2015-02-01T14:12:32.656Z","0.0.20":"2015-02-01T21:56:27.062Z","0.0.21":"2015-02-01T22:17:55.748Z","0.0.22":"2015-02-01T22:30:49.355Z","0.0.23":"2015-02-03T18:31:21.075Z","0.0.24":"2015-03-03T19:57:11.653Z","0.0.25":"2015-05-16T15:18:19.966Z","0.0.26":"2015-05-17T19:31:03.713Z","0.0.27":"2015-05-18T21:40:02.643Z","0.0.28":"2015-06-24T20:45:04.614Z","0.0.29":"2016-09-17T19:17:05.408Z","0.0.30":"2019-01-14T20:32:39.892Z"},"readmeFilename":"README.md","keywords":["natural language processing","parsing","chart parsing","chart parser","parser","unification-based grammar","feature structure","typed feature structure","type lattice","type hierarchy"],"author":{"name":"Hugo W.L. ter Doest","email":"hwl.ter.doest@gmail.com"},"homepage":"https://github.com/Hugo-ter-Doest/chart-parsers#readme","repository":{"type":"git","url":"git://github.com/Hugo-ter-Doest/chart-parsers.git"},"bugs":{"url":"https://github.com/Hugo-ter-Doest/chart-parsers/issues"},"license":"GPL-3.0"}