Computer Science 112 Fundamentals of Programming II Recursive Processing of Languages

Languages and Grammars A grammar specifies the rules for constructing well-formed sentences in a language Every language, including a programming language, has a grammar

Applications Grammar checkers in word processors Programming language compilers Natural language queries (Google, etc.)

Generate Sentences in English Given a vocabulary and grammar rules, one can generate some random and perhaps rather silly sentences Vocabulary - the set of words belonging to the parts of speech (nouns, verbs, articles, prepositions) Grammar - the set of rules for building phrases in a sentence (noun phrase, verb phrase, prepositional phrase)

The Structure of a Sentence sentence noun phrase verb phrase A sentence is a noun phrase followed by a verb phrase

The Structure of a Sentence sentence noun phrase verb phrase article noun A noun phrase is an article followed by a noun

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun the girl Pick actual words for those parts of speech at random

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase the girl A verb phrase is a verb followed by a noun phrase and a prepositional phrase

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase the girl hit Pick a verb at random

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase article noun the girl hit Expand a noun phrase again

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase article noun the girl hit the boy Pick an article and a noun at random

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase article noun preposition noun phrase the girl hit the boy A prepositional phrase is a preposition followed by a noun phrase

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase article noun preposition noun phrase the girl hit the boy with Pick a preposition at random

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase article noun preposition noun phrase article noun the girl hit the boy with Expand another noun phrase

The Structure of a Sentence Similar to the behavior of strings so far sentence noun phrase verb phrase article noun verb noun phrase prepositional phrase article noun preposition noun phrase article noun the girl hit the boy with a bat More random words from the parts of speech

Representing the Vocabulary nouns = ['bat', 'boy', 'girl', 'dog', 'cat', 'chair', 'fence', 'table', 'computer', 'cake', 'field'] verbs = ['hit', 'threw', 'pushed', 'ate', 'dragged', 'jumped'] prepositions = ['with', 'to', 'from', 'on', 'below', 'above', 'beside'] articles = ['a', 'the'] Use a list of words for each part of speech (lexical category)

Picking a Word at Random nouns = ['bat', 'boy', 'girl', 'dog', 'cat', 'chair', 'fence', 'table', 'computer', 'cake', 'field'] verbs = ['hit', 'threw', 'pushed', 'ate', 'dragged', 'jumped'] prepositions = ['with', 'to', 'from', 'on', 'below', 'above', 'beside'] articles = ['a', 'the'] import random print(random.choice(verbs)) # Prints a randomly chosen verb The random module includes functions to select numbers, sequence elements, etc., at random

Grammar Rules sentence = nounphrase verbphrase nounphrase = article noun verbphrase = verb nounphrase prepositionalphrase prepositonalphrase = preposition nounphrase A sentence is a noun phrase followed by a verb phrase Etc., etc.

Define a Function for Each Rule # sentence = nounphrase verbphrase def sentence(): return nounphrase() + ' ' + verbphrase() Each function builds and returns a string that is an instance of the phrase Separate phrases and words with a space

Define a Function for Each Rule # sentence = nounphrase verbphrase def sentence(): return nounphrase() + ' ' + verbphrase() # nounphrase = article noun def nounphrase(): return random.choice(articles) + ' ' + random.choice(nouns) When a part of speech is reached, select an instance at random from the relevant list of words

Call sentence() to Try It Out # sentence = nounphrase verbphrase def sentence(): return nounphrase() + ' ' + verbphrase() # nounphrase = article noun def nounphrase(): return random.choice(articles) + ' ' + random.choice(nouns) … for x in range(10): print(sentence()) # Display 10 sentences You can also generate examples of the other phrases by calling their functions

Kinds of Symbols in a Grammar Terminal symbols: words in the vocabulary of the language Non-terminal symbols: words that describe phrases or portions of sentences Metasymbols: used to construct rules

Metasymbols for a Grammar MetasymbolsUse "" Enclose literal items = Means "is defined as" [ ] Enclose optional items { } Enclose zero or more items ( ) Group together required choices | Indicates a choice

A Grammar of Arithmetic Expressions expression = term { addingOperator term } term = factor { multiplyOperator factor } factor = primary ["^" primary ] primary = number | "(" expression ")" number = digit { digit } digit = "0" | "1" | "2" | "3" | "4" | "5" | "6" | "7" | "8" | "9" addingOperator = "+" | "-" multiplyingOperator = "*" | "/" Example sentences: 3, 4 + 5, * 3, (5 + 2) * 3 ^ 4

Alternative Notation: Train Track term = factor { multiplyingOperator factor } factor * / primary = number | "(" expression ")" number () expression

Parsing A parser analyzes a source program to determine whether or not it is syntactically correct Parser Source language program Syntax error messages OK or not OK

Scanning A scanner picks out words in a source program and sends these to the parser Parser Source language program Syntax error messages Ok or not OK Scanner Lexical error messages Tokens

Scanner(aString)Creates a scanner on a source string get()Returns the current token (at the cursor) next()Advances the cursor to the next token The Scanner Interface

Tokens A Token object has two attributes: –type (indicating an operand or operator) –value (an int if it ’ s an operand, or the source string otherwise) Token types are –Token.EOE –Token.PLUS, Token.MINUS –Token.MUL, Token.DIV –Token.INT –Token.UNKNOWN

The Token Interface Token(source)Creates a token from a source string str(aToken)String representation isOperator()True if an operator, false otherwise getType()Returns the type getValue()Returns the value

Recursive Descent Parsing Each rule in the grammar translates to a Python parsing method def expression(self): self.term() token = self.scanner.get() while token.getType() in (Token.PLUS, Token.MINUS): self.scanner.next() self.term() token = self.scanner.get() expression = term { addingOperator term }

Recursive Descent Parsing Each method is responsible for a phrase in an expression def term(self): self.factor() token = self.scanner.get() while token.getType() in (Token.MUL, Token.DIV): self.scanner.next() self.factor() token = self.scanner.get() term = factor { multiplyingOperator factor }

Recursive Descent Parsing primary = number | "(" expression ")" def primary(self): token = self.scanner.get() if token.getType() == Token.INT: self.scanner.next() elif token.getType() == Token.L_PAR: self.scanner.next() self.expression() self.accept(self._scanner.get(), Token.R_PAR, "')' expected") self.scanner.next() else: self.fatalError(token, "bad primary")

For Monday Expression Trees