DOCSLIB.ORG

Parse Tree Fragmentation of Ungrammatical Sentences

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Parse Tree Fragmentation of Ungrammatical Sentences Proceedings of the Twenty-Fifth International Joint Conference on Artificial Intelligence (IJCAI-16) Parse Tree Fragmentation of Ungrammatical Sentences Homa B. Hashemi, Rebecca Hwa Intelligent Systems Program, Computer Science Department University of Pittsburgh [email protected], [email protected] Abstract resulting reliable structures may still provide some useful in- formation for down-stream NLP applications such as infor- Ungrammatical sentences present challenges for mation extraction (IE), machine translation (MT), and auto- statistical parsers because the well-formed trees matic evaluation of text (e.g., generated by MT or summariza- they produce may not be appropriate for these sen- tion systems or human second language learners); the omis- tences. We introduce a framework for reviewing sion of the problematic structures also helps to prevent mod- the parses of ungrammatical sentences and extract- els that learn from syntactic structures from degrading due to ing the coherent parts whose syntactic analyses incorrect syntactic analysis. make sense. We call this task parse tree fragmen- tation. In this paper, we propose a training method- ology for fragmenting parse trees without using a One approach for obtaining these partially completed task-specific annotated corpus. We also propose structures is to use shallow parsing [Abney, 1991; Sha and some fragmentation strategies and compare their Pereira, 2003; Sun et al., 2008] to identify recognizable performance on an extrinsic task – fluency judg- low-level constituents, but this excludes higher-level com- ments in two domains: English-as-a-Second Lan- plex structures. Instead, we propose to review the full parse guage (ESL) and machine translation (MT). Exper- tree generated by a state-of-the-art parser and identify the imental results show that the proposed fragmenta- parts of it that are plausible interpretations for the phrases tion strategies are competitive with existing meth- they cover. We call these isolated parts of the parse tree ods for making fluency judgments; they also sug- fragments, and the process of breaking up the tree, parse gest that the overall framework is a promising way tree fragmentation. Our approach differs from systems that to handle syntactically unusual sentences. produce partial parses (e.g., the Connexor parser) because we are not using a deterministic grammar building bottom 1 Introduction up; we are re-interpreting the parse tree post-hoc. Our task Syntactic parse trees are integral to many Natural Language also differs from disfluency detection in spoken utterances, Processing (NLP) applications. While state-of-the-art statisti- which focuses on removing extra fillers and repeated phrases cal parsers perform well on standard (newswire) benchmarks, [Honnibal and Johnson, 2014; Rasooli and Tetreault, 2013; their analyses for sentences from different domains are less Ferguson et al., 2015]; ungrammatical sentences written by reliable [Gildea, 2001; McClosky et al., 2010; Foster, 2010; non-native speakers or generated by machines have a wider Petrov et al., 2010; Foster et al., 2011]. Ungrammatical1 sen- range of error types, such as missing phrases and incorrect tences (or even awkward sentences that are technically gram- phrasal ordering. matical) can be seen as special kinds of out-of-domain sen- tences; in some cases, it is not even clear whether a complete In this paper, we present a framework for extracting parse parse should be given to the sentence. A statistical parser tree fragments from problematic sentences. We develop a trained on a standard treebank, however, often produces full, methodology for creating gold standard data for training and syntactically well-formed trees that are not appropriate for the evaluating parse tree fragmentation methods. We propose two sentences. fragmentation algorithms and compare them in an empirical Rather than throwing out parses with low-confidence study. Finally, we perform an extrinsic evaluation to deter- scores entirely or transforming the problematic sentences first mine the potential utility of tree fragmentation to a down- (which may not always be possible), we believe that a valu- stream application. In particular, we choose the task of sen- able middle ground is to identify well-formed syntactic struc- tential fluency judgment, in which a system automatically tures of those parts of the sentences that do make sense. The predicts how “natural” a sentence might sound to a native- 1In this context, a sentence is considered ungrammatical if all its speaker human. We consider two domains: MT outputs words are valid in the language, but it contains grammatical or usage and the writings of English-as-a-Second Language (ESL) stu- errors [Foster, 2007]. dents. 2796 S S NP VP ? ? NP VP NP PP VBZ S NP PP ? VBZ ? DT NNS IN NP opposes NP NP DT NNS IN NP ? ? opposes The members of DT NN DT PRP The members of DT NN DT PRP the vote any him the vote any him (a) Stanford parse tree (b) Coherent fragments Figure 1: (a) An ungrammatical sentence gets a well-formed but inappropriate parse tree. (b) A set of coherent tree fragments that might be extracted from the full parse tree. 2 A Framework for Parse Tree sentence. With only a sentence and an automatically gener- Fragmentation ated tree for it, we may mentally error-correct the sentence in different ways. If we are also given an acceptable paraphrase The goal of parse tree fragmentation is to take a sentence for the sentence, the fragmentation task becomes more cir- and its tree as input and extract from the tree a set of par- cumscribed because we now know the intended meaning. An tial trees that are well-formed and appropriate for the phrases example data source of this type is an MT evaluation cor- they cover. Before we explore methods for doing so, we need pus, which consists of machine-translated sentences and their to address some more fundamental problems: What kind of corresponding human-translated references. Furthermore, if partial trees are considered to be well-formed and appropri- we not only have access to a closely worded paraphrase but ate? How do we obtain enough examples of appropriate ways also an explanation for each change, the fragmentation deci- to fragment the trees? How should this task be evaluated? sions are purely deterministic (e.g., whenever a phrase is rec- ommended for deletion, the tree over it is fragmented). An 2.1 Ideal Fragmentation example data source of this type is an ESL learner’s corpus, One factor that dictates how fragmentation should be done is which consists of student sentences and their detailed correc- how the fragments will be used in a downstream application. tions. For example, a one-off slight grammar error (e.g., number agreement) probably will not greatly alter a parser output. For 2.2 Developing a Fragmentation Corpus the purpose of information extraction, this type of slight mis- Because the definition of an ideal fragmentation depends on matches should probably be ignored; for the purpose of train- multiple factors (e.g., the intended use and the context in ing future syntax-based computational models, on the other which the original sentences were generated), this task is not hand, more aggressive fragmentation may be necessary to fil- well-suited for a large-scale human annotation project. In- ter out unwanted syntactic relationships. stead, we propose to develop our fragmentation corpus by Even assuming a particular downstream application choice leveraging existing data sources previously mentioned (an (sentential fluency judgment in our case), the ideal fragmen- ESL learner’s corpus and an MT evaluation corpus). tation may not be obvious, especially when the errors inter- act with each other. Consider the following output from a An ESL learner’s machine translation system that contains three problem areas Pseudo Gold Fragmentation (PGold) corpus in which every sentence has been hand corrected by (underlined): an English teacher is ideal for our purpose. We identified The members of the vote opposes any him. sentences that are marked as containing word-level mistakes: Figure 1a shows the Stanford parser’s output for this sen- unnecessary, missing or replacing word errors. Given the po- tence. The first problem is the subject noun phrase even sitions and error types, a fluent sentence can be reconstructed though the embedded NP and PP subtrees are well-formed. and reliably parsed. The parse tree of the fluent sentence can The second problem is a number disagreement between the then be iteratively fragmented according to the error types subject and the verb. The third problem is an unusual bigram that occur in the original sentence (see Figure 2). The re- that causes the parser to group any and him into a sentential sulting sets of fragments approximate an explicitly manually clause to serve as the object of the main verb. created fragmentation corpus; however, since a parser may Which fragments should be salvaged from this parse tree? make mistakes even on a fluent sentence, we call these frag- Someone who thinks the sentence says: The members of the ments pseudo gold. voting body oppose any proposal by him might produce the fragment set shown in Figure 1b. On the other hand, if they REference Fragmentation (REF) Even if we do not have think it says: No parliament members voted against him, they detailed information about why certain parts of a sentence are might have opted to not keep the PP intact. problematic, we can construct an almost-as-good fragmenta- This example illustrates that fragmentation decisions are tion if we have access to a fluent paraphrase of the original. influenced by the amount of information we glean from the We call this a reference sentence, borrowing the terminology 2797 ? ? ? l1 l2 l1 l2 l3 (a) Unnecessary word (l3) error ? ? l1 l2 l1 l2 l3 Figure 3: Word N-gram features for the dotted edge.
Load more

Recommended publications
  • Syntax-Directed Translation, Parse Trees, Abstract Syntax Trees
    Syntax-Directed Translation Extending CFGs Grammar Annotation Parse Trees Abstract Syntax Trees (ASTs) Readings: Section 5.1, 5.2, 5.5, 5.6 Motivation: parser as a translator syntax-directed translation stream of ASTs, or tokens parser assembly code syntax + translation rules (typically hardcoded in the parser) 1 Mechanism of syntax-directed translation syntax-directed translation is done by extending the CFG a translation rule is defined for each production given X Æ d A B c the translation of X is defined in terms of translation of nonterminals A, B values of attributes of terminals d, c constants To translate an input string: 1. Build the parse tree. 2. Working bottom-up • Use the translation rules to compute the translation of each nonterminal in the tree Result: the translation of the string is the translation of the parse tree's root nonterminal Why bottom up? a nonterminal's value may depend on the value of the symbols on the right-hand side, so translate a non-terminal node only after children translations are available 2 Example 1: arith expr to its value Syntax-directed translation: the CFG translation rules E Æ E + T E1.trans = E2.trans + T.trans E Æ T E.trans = T.trans T Æ T * F T1.trans = T2.trans * F.trans T Æ F T.trans = F.trans F Æ int F.trans = int.value F Æ ( E ) F.trans = E.trans Example 1 (cont) E (18) Input: 2 * (4 + 5) T (18) T (2) * F (9) F (2) ( E (9) ) int (2) E (4) * T (5) Annotated Parse Tree T (4) F (5) F (4) int (5) int (4) 3 Example 2: Compute type of expr E -> E + E if ((E2.trans == INT) and (E3.trans == INT) then E1.trans = INT else E1.trans = ERROR E -> E and E if ((E2.trans == BOOL) and (E3.trans == BOOL) then E1.trans = BOOL else E1.trans = ERROR E -> E == E if ((E2.trans == E3.trans) and (E2.trans != ERROR)) then E1.trans = BOOL else E1.trans = ERROR E -> true E.trans = BOOL E -> false E.trans = BOOL E -> int E.trans = INT E -> ( E ) E1.trans = E2.trans Example 2 (cont) Input: (2 + 2) == 4 1.
    [Show full text]
  • Derivatives of Parsing Expression Grammars
    Derivatives of Parsing Expression Grammars Aaron Moss Cheriton School of Computer Science University of Waterloo Waterloo, Ontario, Canada [email protected] This paper introduces a new derivative parsing algorithm for recognition of parsing expression gram- mars. Derivative parsing is shown to have a polynomial worst-case time bound, an improvement on the exponential bound of the recursive descent algorithm. This work also introduces asymptotic analysis based on inputs with a constant bound on both grammar nesting depth and number of back- tracking choices; derivative and recursive descent parsing are shown to run in linear time and constant space on this useful class of inputs, with both the theoretical bounds and the reasonability of the in- put class validated empirically. This common-case constant memory usage of derivative parsing is an improvement on the linear space required by the packrat algorithm. 1 Introduction Parsing expression grammars (PEGs) are a parsing formalism introduced by Ford [6]. Any LR(k) lan- guage can be represented as a PEG [7], but there are some non-context-free languages that may also be represented as PEGs (e.g. anbncn [7]). Unlike context-free grammars (CFGs), PEGs are unambiguous, admitting no more than one parse tree for any grammar and input. PEGs are a formalization of recursive descent parsers allowing limited backtracking and infinite lookahead; a string in the language of a PEG can be recognized in exponential time and linear space using a recursive descent algorithm, or linear time and space using the memoized packrat algorithm [6]. PEGs are formally defined and these algo- rithms outlined in Section 3.
    [Show full text]
  • Parsing 1. Grammars and Parsing 2. Top-Down and Bottom-Up Parsing 3
    Syntax Parsing syntax: from the Greek syntaxis, meaning “setting out together or arrangement.” 1. Grammars and parsing Refers to the way words are arranged together. 2. Top-down and bottom-up parsing Why worry about syntax? 3. Chart parsers • The boy ate the frog. 4. Bottom-up chart parsing • The frog was eaten by the boy. 5. The Earley Algorithm • The frog that the boy ate died. • The boy whom the frog was eaten by died. Slide CS474–1 Slide CS474–2 Grammars and Parsing Need a grammar: a formal specification of the structures allowable in Syntactic Analysis the language. Key ideas: Need a parser: algorithm for assigning syntactic structure to an input • constituency: groups of words may behave as a single unit or phrase sentence. • grammatical relations: refer to the subject, object, indirect Sentence Parse Tree object, etc. Beavis ate the cat. S • subcategorization and dependencies: refer to certain kinds of relations between words and phrases, e.g. want can be followed by an NP VP infinitive, but find and work cannot. NAME V NP All can be modeled by various kinds of grammars that are based on ART N context-free grammars. Beavis ate the cat Slide CS474–3 Slide CS474–4 CFG example CFG’s are also called phrase-structure grammars. CFG’s Equivalent to Backus-Naur Form (BNF). A context free grammar consists of: 1. S → NP VP 5. NAME → Beavis 1. a set of non-terminal symbols N 2. VP → V NP 6. V → ate 2. a set of terminal symbols Σ (disjoint from N) 3.
    [Show full text]
  • Abstract Syntax Trees & Top-Down Parsing
    Abstract Syntax Trees & Top-Down Parsing Review of Parsing • Given a language L(G), a parser consumes a sequence of tokens s and produces a parse tree • Issues: – How do we recognize that s ∈ L(G) ? – A parse tree of s describes how s ∈ L(G) – Ambiguity: more than one parse tree (possible interpretation) for some string s – Error: no parse tree for some string s – How do we construct the parse tree? Compiler Design 1 (2011) 2 Abstract Syntax Trees • So far, a parser traces the derivation of a sequence of tokens • The rest of the compiler needs a structural representation of the program • Abstract syntax trees – Like parse trees but ignore some details – Abbreviated as AST Compiler Design 1 (2011) 3 Abstract Syntax Trees (Cont.) • Consider the grammar E → int | ( E ) | E + E • And the string 5 + (2 + 3) • After lexical analysis (a list of tokens) int5 ‘+’ ‘(‘ int2 ‘+’ int3 ‘)’ • During parsing we build a parse tree … Compiler Design 1 (2011) 4 Example of Parse Tree E • Traces the operation of the parser E + E • Captures the nesting structure • But too much info int5 ( E ) – Parentheses – Single-successor nodes + E E int 2 int3 Compiler Design 1 (2011) 5 Example of Abstract Syntax Tree PLUS PLUS 5 2 3 • Also captures the nesting structure • But abstracts from the concrete syntax a more compact and easier to use • An important data structure in a compiler Compiler Design 1 (2011) 6 Semantic Actions • This is what we’ll use to construct ASTs • Each grammar symbol may have attributes – An attribute is a property of a programming language construct
    [Show full text]
  • Compiler Construction
    UNIVERSITY OF CAMBRIDGE Compiler Construction An 18-lecture course Alan Mycroft Computer Laboratory, Cambridge University http://www.cl.cam.ac.uk/users/am/ Lent Term 2007 Compiler Construction 1 Lent Term 2007 Course Plan UNIVERSITY OF CAMBRIDGE Part A : intro/background Part B : a simple compiler for a simple language Part C : implementing harder things Compiler Construction 2 Lent Term 2007 A compiler UNIVERSITY OF CAMBRIDGE A compiler is a program which translates the source form of a program into a semantically equivalent target form. • Traditionally this was machine code or relocatable binary form, but nowadays the target form may be a virtual machine (e.g. JVM) or indeed another language such as C. • Can appear a very hard program to write. • How can one even start? • It’s just like juggling too many balls (picking instructions while determining whether this ‘+’ is part of ‘++’ or whether its right operand is just a variable or an expression ...). Compiler Construction 3 Lent Term 2007 How to even start? UNIVERSITY OF CAMBRIDGE “When finding it hard to juggle 4 balls at once, juggle them each in turn instead ...” character -token -parse -intermediate -target stream stream tree code code syn trans cg lex A multi-pass compiler does one ‘simple’ thing at once and passes its output to the next stage. These are pretty standard stages, and indeed language and (e.g. JVM) system design has co-evolved around them. Compiler Construction 4 Lent Term 2007 Compilers can be big and hard to understand UNIVERSITY OF CAMBRIDGE Compilers can be very large. In 2004 the Gnu Compiler Collection (GCC) was noted to “[consist] of about 2.1 million lines of code and has been in development for over 15 years”.
    [Show full text]
  • Advanced Parsing Techniques
    Advanced Parsing Techniques Announcements ● Written Set 1 graded. ● Hard copies available for pickup right now. ● Electronic submissions: feedback returned later today. Where We Are Where We Are Parsing so Far ● We've explored five deterministic parsing algorithms: ● LL(1) ● LR(0) ● SLR(1) ● LALR(1) ● LR(1) ● These algorithms all have their limitations. ● Can we parse arbitrary context-free grammars? Why Parse Arbitrary Grammars? ● They're easier to write. ● Can leave operator precedence and associativity out of the grammar. ● No worries about shift/reduce or FIRST/FOLLOW conflicts. ● If ambiguous, can filter out invalid trees at the end. ● Generate candidate parse trees, then eliminate them when not needed. ● Practical concern for some languages. ● We need to have C and C++ compilers! Questions for Today ● How do you go about parsing ambiguous grammars efficiently? ● How do you produce all possible parse trees? ● What else can we do with a general parser? The Earley Parser Motivation: The Limits of LR ● LR parsers use shift and reduce actions to reduce the input to the start symbol. ● LR parsers cannot deterministically handle shift/reduce or reduce/reduce conflicts. ● However, they can nondeterministically handle these conflicts by guessing which option to choose. ● What if we try all options and see if any of them work? The Earley Parser ● Maintain a collection of Earley items, which are LR(0) items annotated with a start position. ● The item A → α·ω @n means we are working on recognizing A → αω, have seen α, and the start position of the item was the nth token. ● Using techniques similar to LR parsing, try to scan across the input creating these items.
    [Show full text]
  • Lecture 3: Recursive Descent Limitations, Precedence Climbing
    Lecture 3: Recursive descent limitations, precedence climbing David Hovemeyer September 9, 2020 601.428/628 Compilers and Interpreters Today I Limitations of recursive descent I Precedence climbing I Abstract syntax trees I Supporting parenthesized expressions Before we begin... Assume a context-free struct Node *Parser::parse_A() { grammar has the struct Node *next_tok = lexer_peek(m_lexer); following productions on if (!next_tok) { the nonterminal A: error("Unexpected end of input"); } A → b C A → d E struct Node *a = node_build0(NODE_A); int tag = node_get_tag(next_tok); (A, C, E are if (tag == TOK_b) { nonterminals; b, d are node_add_kid(a, expect(TOK_b)); node_add_kid(a, parse_C()); terminals) } else if (tag == TOK_d) { What is the problem node_add_kid(a, expect(TOK_d)); node_add_kid(a, parse_E()); with the parse function } shown on the right? return a; } Limitations of recursive descent Recall: a better infix expression grammar Grammar (start symbol is A): A → i = A T → T*F A → E T → T/F E → E + T T → F E → E-T F → i E → T F → n Precedence levels: Nonterminal Precedence Meaning Operators Associativity A lowest Assignment = right E Expression + - left T Term * / left F highest Factor No Parsing infix expressions Can we write a recursive descent parser for infix expressions using this grammar? Parsing infix expressions Can we write a recursive descent parser for infix expressions using this grammar? No Left recursion Left-associative operators want to have left-recursive productions, but recursive descent parsers can’t handle left recursion
    [Show full text]
  • Top-Down Parsing & Bottom-Up Parsing I
    Top-Down Parsing and Introduction to Bottom-Up Parsing Lecture 7 Instructor: Fredrik Kjolstad Slide design by Prof. Alex Aiken, with modifications 1 Predictive Parsers • Like recursive-descent but parser can “predict” which production to use – By looking at the next few tokens – No backtracking • Predictive parsers accept LL(k) grammars – L means “left-to-right” scan of input – L means “leftmost derivation” – k means “predict based on k tokens of lookahead” – In practice, LL(1) is used 2 LL(1) vs. Recursive Descent • In recursive-descent, – At each step, many choices of production to use – Backtracking used to undo bad choices • In LL(1), – At each step, only one choice of production – That is • When a non-terminal A is leftmost in a derivation • And the next input symbol is t • There is a unique production A ® a to use – Or no production to use (an error state) • LL(1) is a recursive descent variant without backtracking 3 Predictive Parsing and Left Factoring • Recall the grammar E ® T + E | T T ® int | int * T | ( E ) • Hard to predict because – For T two productions start with int – For E it is not clear how to predict • We need to left-factor the grammar 4 Left-Factoring Example • Recall the grammar E ® T + E | T T ® int | int * T | ( E ) • Factor out common prefixes of productions E ® T X X ® + E | e T ® int Y | ( E ) Y ® * T | e 5 LL(1) Parsing Table Example • Left-factored grammar E ® T X X ® + E | e T ® ( E ) | int Y Y ® * T | e • The LL(1) parsing table: next input token int * + ( ) $ E T X T X X + E e e T int Y ( E ) Y * T e e e rhs of production to use 6 leftmost non-terminal E ® T X X ® + E | e T ® ( E ) | int Y Y ® * T | e LL(1) Parsing Table Example • Consider the [E, int] entry – “When current non-terminal is E and next input is int, use production E ® T X” – This can generate an int in the first position int * + ( ) $ E T X T X X + E e e T int Y ( E ) Y * T e e e 7 E ® T X X ® + E | e T ® ( E ) | int Y Y ® * T | e LL(1) Parsing Tables.
    [Show full text]
  • Parse Trees (=Derivation Tree) by Constructing a Derivation
    CFG: Parsing •Generative aspect of CFG: By now it should be clear how, from a CFG G, you can derive strings wÎL(G). CFG: Parsing •Analytical aspect: Given a CFG G and strings w, how do you decide if wÎL(G) and –if so– how do you determine the derivation tree or the sequence of production rules Recognition of strings in a that produce w? This is called the problem of parsing. language 1 2 CFG: Parsing CFG: Parsing • Parser A program that determines if a string w Î L(G) Parse trees (=Derivation Tree) by constructing a derivation. Equivalently, A parse tree is a graphical representation it searches the graph of G. of a derivation sequence of a sentential form. – Top-down parsers • Constructs the derivation tree from root to leaves. • Leftmost derivation. Tree nodes represent symbols of the – Bottom-up parsers grammar (nonterminals or terminals) and • Constructs the derivation tree from leaves to tree edges represent derivation steps. root. • Rightmost derivation in reverse. 3 4 CFG: Parsing CFG: Parsing Parse Tree: Example Parse Tree: Example 1 E ® E + E | E * E | ( E ) | - E | id Given the following grammar: Lets examine this derivation: E Þ -E Þ -(E) Þ -(E + E) Þ -(id + id) E ® E + E | E * E | ( E ) | - E | id E E E E E Is the string -(id + id) a sentence in this grammar? - E - E - E - E Yes because there is the following derivation: ( E ) ( E ) ( E ) E Þ -E Þ -(E) Þ -(E + E) Þ -(id + id) E + E E + E This is a top-down derivation because we start building the id id parse tree at the top parse tree 5 6 1 CFG: Parsing CFG: Parsing S ® SS | a | b Parse Tree: Example 2 Rightmost Parse Tree: Example 2 abÎ L( S) derivation S Þ SS Þ Sb Þ ab S S S S S S S S Derivation S S S S Derivation S S S S Trees S S Trees a a b S S b a b S S S Leftmost S derivation S Þ SS Þ aS Þ ab Rightmost Derivation a b S S in Reverse 7 8 CFG: Parsing CFG: Parsing Practical Parsers Example 3 Consider the CFG grammar G • Language/Grammar designed to enable deterministic (directed S ® A and backtrack-free) searches.
    [Show full text]
  • Technical Correspondence Techniques for Automatic Memoization with Applications to Context-Free Parsing
    Technical Correspondence Techniques for Automatic Memoization with Applications to Context-Free Parsing Peter Norvig* University of California It is shown that a process similar to Earley's algorithm can be generated by a simple top-down backtracking parser, when augmented by automatic memoization. The memoized parser has the same complexity as Earley's algorithm, but parses constituents in a different order. Techniques for deriving memo functions are described, with a complete implementation in Common Lisp, and an outline of a macro-based approach for other languages. 1. Memoization The term memoization was coined by Donald Michie (1968) to refer to the process by which a function is made to automatically remember the results of previous compu- tations. The idea has become more popular in recent years with the rise of functional languages; Field and Harrison (1988) devote a whole chapter to it. The basic idea is just to keep a table of previously computed input/result pairs. In Common Lisp one could write: 1 (defun memo (fn) "Return a memo-function of fn." (let ((table (make-hash-table))) #'(lambda (x) (multiple-value-bind (val found) (gethash x table) (if found val (setf (gethash x table) (funcall fn x))))))). (For those familiar with Lisp but not Common Lisp, gethash returns two values, the stored entry in the table, and a boolean flag indicating if there is in fact an entry. The special form multiple-value-bind binds these two values to the symbols val and found. The special form serf is used here to update the table entry for x.) In this simple implementation fn is required to take one argument and return one value, and arguments that are eql produce the same value.
    [Show full text]
  • Chart Parsing and Probabilistic Parsing
    Chapter 8 Chart Parsing and Probabilistic Parsing 8.1 Introduction Chapter 7 started with an introduction to constituent structure in English, showing how words in a sentence group together in predictable ways. We showed how to describe this structure using syntactic tree diagrams, and observed that it is sometimes desirable to assign more than one such tree to a given string. In this case, we said that the string was structurally ambiguous; and example was old men and women. Treebanks are language resources in which the syntactic structure of a corpus of sentences has been annotated, usually by hand. However, we would also like to be able to produce trees algorithmically. A context-free phrase structure grammar (CFG) is a formal model for describing whether a given string can be assigned a particular constituent structure. Given a set of syntactic categories, the CFG uses a set of productions to say how a phrase of some category A can be analyzed into a sequence of smaller parts ±1 ... ±n. But a grammar is a static description of a set of strings; it does not tell us what sequence of steps we need to take to build a constituent structure for a string. For this, we need to use a parsing algorithm. We presented two such algorithms: Top-Down Recursive Descent (7.5.1) and Bottom-Up Shift-Reduce (7.5.2). As we pointed out, both parsing approaches suffer from important shortcomings. The Recursive Descent parser cannot handle left-recursive productions (e.g., productions such as NP → NP PP), and blindly expands categories top-down without checking whether they are compatible with the input string.
    [Show full text]
  • Cs 473: Compiler Design
    Lecture 3 CS 473: COMPILER DESIGN 1 creating an abstract representation of program syntax PARSING 2 Today: Parsing Source Code (Character stream) if (b == 0) { a = 1; } Lexical Analysis Token stream: if ( b == 0 ) { a = 0 ; } Parsing Abstract Syntax Tree: If Analysis & Eq Assn None Transformation b 0 a 1 Backend Assembly Code l1: cmpq %eax, $0 jeq l2 jmp l3 l2: … 3 Parsing: Finding Syntactic Structure { if (b == 0) a = b; while (a != 1) { print_int(a); a = a – 1; } Block } Source input If While Bop … … Bop Block Expr … b == 0 a != 1 Call Abstract Syntax tree … 4 Syntactic Analysis (Parsing): Overview • Input: stream of tokens (generated by lexer) • Output: abstract syntax tree • Strategy: – Parse the token stream to build a tree showing how the pieces relate – Forget the “concrete” syntax, remember the “abstract” syntax • Why abstract? Consider these three different concrete inputs: a + b (a + ((b))) Bop ((a) + (b)) Same abstract syntax tree a + b • Will catch lots of malformed programs! Wrong number of operators, missing semicolons, unmatched parens; most “syntax errors” appear here – But no type errors, initialization, etc.: we still don’t know what anything means! 5 Specifying Language Syntax • First question: how to describe language syntax precisely and conveniently? • Last time: we described tokens using regular expressions – Easy to implement, efficient DFA representation – Why not use regular expressions on tokens to specify programming language syntax? • Limits of regular expressions: – DFAs have only finite # of states – So DFAs can’t “count” – For example, consider the language of all strings that contain balanced parentheses – easier than most programming languages, but not regular.
    [Show full text]