Syntax and Semantics

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Chapter 3

• Syntax and Semantics

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Issues of a programming language

• The language description must be concise yet
  understandable
• The language description must be understood by a
  diverse group of people
• The language itself must define both structure
  and meaning of various constructs such as
  expressions, statements and program units
• Language users must be able to write programs by
  referring to the languages reference manual

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Properties of programming languages

• Syntax the form of the languages expressions,
  statements and program units.
• Semantics the meaning of the languages
  expressions, statements and program units.

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• Given a language L that uses the alphabet, ?, of
  character, what are the ways to define a
  programming language?

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Ways to define programming languages (1)

• Language recognizers
• Use a recognition device, R, to
• Read strings of characters from ? and determine
  whether the string is in the language, L, or not
• Separate correct sentences from incorrect
  sentences
• - Language recognizers performs the syntax
  analysis of a compiler

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Ways to define programming languages (2)

• Language generators
• Use to generate sentences of a language
• Use generators to determne the correct syntax of
  a statement by comparing it with the structure
  provided by a generator.

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• Terms associated with programming languages
• Sentences statement or strings of a language
• Lexemes lowest level of static units which
  includes identifiers, literals, operators and
  keywords
• Tokens category of lexemes

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index 2 count 17

• Lexemes
• index
• count
• 2
• 17

• Tokens
• identifier
• identifier
• int_literal
• int_literal
• equal_sign
• mult_op
• plus_op
• semicolon

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• What is grammar?
• grammar is a formal method to describe syntax
• Two classes of grammar used in programming
  languages (Chomsky)
• Regular grammar used to describe tokens
• Context-Free used to describe the programming
  language itself as a whole

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What is BNF?

• Acronym for Backus-Naur form
• Used initially to describe ALGOL 58, it is a
  formal notation for specifying programming
  language syntax
• Developed by John Backus in 1959 and later
  amended by Peter Naur in 1960
• Nearly identical to Chomskys context-free
  grammar.
• A metalanguage for programming languages

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• A metalanguage is a language used to describe
  another language.
• An example of a metalanguage is BNF

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BNF Basics

• It is a metalanguage used to describe another
  language.
• It is a collection of rules or productions of the
  form
• LHS -gt RHS
• where LHS (left-hand side) is the rule being
  defined
• RHS (right-hand side) is the definition
  of the rule and consists of tokens, lexemes or
  references to other rules.
• A rule is made up of terminal (T) and nonterminal
  (NT) symbols
• Example of a rule ltassigngt ? ltvargt
  ltexpressiongt

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BNF Basics (cont.)

• Nonterminal symbols can be further defined by two
  or more distinct rules of the language whereas
  terminal symbols can only be defined by lexemes
  and tokens of the language.
• From the previous example, assign, var and
  expression are nonterminal symbols and is a
  terminal symbol

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BNF Basics (cont.)

• BNF is used to describe lists of similar
  constructs, ordering which different constructs
  must appear, nested structure, operator
  precedence, and operator associativity.
• BNF is a generative device for defining
  languages. This means that sentences of the
  programming language defined by BNF are generated
  through the application of the grammars rules.

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• Ex. Grammar 1
• ltprogramgt ? begin ltstmt_listgt end
• ltstmt_listgt ? ltstmtgt ltstmtgtltstmt_listgt
• ltstmtgt ? ltvargt ltexprgt
• ltexprgt ? ltvargt ltvargt ltvargt - ltvargt ltvargt
• ltvargt ? a b c

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Anatomy of Grammar 1

• ltprogramgt ? begin ltstmt_listgt end
• START T NT T
• ltstmt_listgt ? ltstmtgt ltstmtgtltstmt_listgt
• NT T NT NT T
  NT
• ltstmtgt ? ltvargt ltexprgt
• NT NT T NT
• ltexprgt ? ltvargt ltvargt ltvargt - ltvargt ltvargt
• NT NT T NT NT T
  NT NT
• ltvargt ? a b c
• NT T T T

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• A program that uses ex. grammar 1
• begin
• a bc
• b c
• end
• How do you derive the program above using
  grammar one from the previous chart?

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Grammar and Parse Trees

• Grammars naturally describes the hierarchical
  syntactic structures, i.e., parse trees, of
  sentences
• Ex. grammar 2 for an assignment statement
• ltassigngt ? ltidgt ltexprgt
• ltidgt ? abc
• ltexprgt ? ltidgt ltexprgt
• ltidgt ltexprgt
• ( ltexprgt )
• ltidgt

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Grammar and Parse Trees

• ltassigngt ? ltidgt ltexprgt
• ltidgt ? abc
• ltexprgt ? ltidgt ltexprgt
• ltidgt ltexprgt
• ( ltexprgt )
• ltidgt
• Use the grammar 2 to parse the statements
• A B A C
• A B A C
• What can you say about operator precedence?

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Ambiguous vs. Unambiguous Grammar

• Ambiguous grammar a grammar that generates a
  sentence for which there are two or more distinct
  parse trees.
• Unambiguous grammar a grammar for which a
  sentence generated can be represented by only one
  parse tree.

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Ambiguous Grammar

• Ex. grammar 3 for an assignment statement
• ltassigngt ? ltidgt ltexprgt
• ltidgt ? abc
• ltexprgt ? ltexprgt ltexprgt
• ltexprgt ltexprgt
• ( ltexprgt )
• ltidgt
• Example statement A B C A
• Based on the above example why is the grammar
  ambiguous?

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Grammar 4 correct version of Grammars 2 and 3

• ltassigngt ? ltidgt ltexprgt
• ltidgt ? A B C
• ltexprgt ? ltexprgt lttermgt lttermgt
• lttermgt ? lttermgt ltfactorgt ltfactorgt
• ltfactorgt ? (ltexprgt) ltidgt
• Example statement A B C A
• Is the operator precedence still enforced with
  grammar 4 with this statement?

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Recursivity

• Left recursive
• grammar rule is left recursive if it has its LHS
  appearing at the RHS,
• Left recursive rule specifies left associativity
• Right Recursive
• grammar rule is right recursive if it has its LHS
  appearing at the right end of RHS
• right recursive rules specify right associativity

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Right associative operator exponent operator

• ltfactorgt ? ltexprgt lt factorgt ltexprgt
• ltexprgt ? (ltexprgt) id
• Example statement abc
• What does the parse tree look like?
• Is operator precedence enforced?

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Grammar Requirements

• It must be unambiguous
• It must enforce operator precedence
• It must enforce operator associativity

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Extended BNF (EBNF)

• Extensions to BNF to improve readability and
  writability
• Extensions include
• to mean optional
• to mean none or infinite repetitions
• n with n as the maximum number of
  repetitions
• to mean one or more repetitions
• ( ) to mean multiple choice

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Notational Symbols in BNF, EBNF

• lt gt used for nonterminals (BNF, EBNF)
• ? rule assignment (BNF, EBNF)
• selection (BNF, EBNF)
• optional (EBNF)
• repetition (EBNF)
• ( ) used with for selection (EBNF)

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Attribute Grammar informal definition

• An attribute grammar is an extension to a
  context-free grammar to allow for the description
  of more structure in a programming language than
  is possible with BNF. It allows for the
  description of static semantics such as
  variable-type compatibility

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Static Semantics

• language syntax rules that cannot be defined by
  BNF. Typically, these are related to variable
  type constraints. Static semantics rules are
  resolved at compile time, not execution time.

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Examples of static semantics

• A floating point values cannot be assigned to an
  integer-type variable.
• For some languages such as Ada, if the end
  statement of a subprogram is followed by a name,
  the name must match the name of the subprogram.

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Attribute Grammar formal definition

• An attribute grammar is context-free grammar with
  the following additional features
• Associated with each grammar symbol are sets of
  inherited and synthesized attributes.
• Synthesized attributes are used to pass semantic
  information up the parse tree from the nodes
  children
• inherited attributes are semantic information
  passed down the parse tree from the nodes parent
  and siblings.
• Associated with each grammar rule is a set of
  attribute computation function and predicate
  function (optional) over the attributes of the
  symbols in the rule.

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Other definitions

• Fully attributed parse tree
• if all the attribute values of a parse tree have
  been computed.
• Intrinsic attributes
• synthesized attributes of leaf nodes whose values
  are determined outside the parse tree. An
  example would be the attributes of an identifier
  taken from the symbol table.

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Example 5 Attribute Grammar

• ltassigngt ? ltvargt ltexprgt
• ltexprgt.expected_type ? ltvargt.actual_type
• ltexprgt ? ltvargt2 ltvargt3
• ltexprgt.actual_type ? if (ltvargt2.actual_type
  int) and (ltvargt3.actual_type int)
• then int
• else real
• end if
• ltexprgt.actual_type ltexprgt.expected_type
• ltexprgt ? ltvargt
• ltexprgt.actual_type ? ltvargt.actual_type
• ltexprgt.actual_type ltexprgt.expected_type
• ltvargt ? A B C
• ltvargt.actual_type ? look-up(ltvargt.string)

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Steps to building a fully attributed parse tree

• Step 1 From the given grammar, derive the parse
  tree using the grammars production rules as
  discussed previously.
• Step 2 Get the intrinsic attributes of the leaf
  nodes.

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Steps to building a fully attributed parse tree
(cont.)

• Step 3 Calculate the attributes of the
  intermediate nodes, starting with the leaf node
  and using the attribute computation functions,
  possibly the predicate function and the intrinsic
  attribute values of the leaf nodes.

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Sample Parse Tree of Grammar 4

• Use the attribute grammar 4 and the steps
  outlined above to create a fully attributed parse
  tree of the expression
• A A B

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Dynamic Semantics

• A description of what expressions, statements,
  and program units actually do when executed.
• Three methods to define a languages dynamic
  semantics
• Operational Semantics
• Axiomatic Semantics
• Denotational Semantics

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Operational Semantics

• defines the meaning of a program written in some
  language by the changes that occur in the state
  of the computer that runs the program.
• As each statement is executed, examine the
  contents of the registers and memory cells
• Needs a low-level virtual computer

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Operational Semantics (cont.)

• Advantages
• Provides an effective means of describing
  semantics as long as the description is simple
  and informal.
• Intuitive and easy to implement.

• Disadvantages
• Depends on algorithms, not mathematics therefore
  the semantic descriptions are inexact.
• Can lead to circular definitions.
• Limited to simple language constructs.

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Axiomatic Semantics

• defines the meaning of a program by proving that
  it executed correctly through the use of
  assertions before and after each statement.
• An assertion is a logical expression that defines
  the constraints in the statements variables.
• Precondition - assertion before the statement
• Postcondition - assertion after the statement
  executes.
• The weakest precondition is the least restrictive
  precondition that will guarantee the validity of
  the postcondition.

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Axiomatic Semantics (2)

• Advantages
• Powerful tool for research into program
  correctness proofs.
• Provides excellent framework with which to reason
  about programs both before and after development.

• Disadvantages
• Limited in describing the meaning of programming
  languages.
• Requires that an axiom or inference rule be
  defined for each statement type in the language.
  Note that this has been proven to be a difficult
  task.

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Denotational Semantics

• defines the meaning of a program by mapping each
  language entity with which the program is written
  to a mathematical object.
• The idea is that mathematical objects can be
  rigorously defined using classical mathematics.
  If a language entity can be mapped using some
  function to a mathematical object, it follows
  that the language entity mapped to this object is
  also defined.

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Denotational Semantics (2)

• Advantages
• Provides a framework for thinking about
  programming in a highly rigorous way.
• Can be used as an aide in language design.
• Limited use in automatic generation of compilers.
• Provides an excellent method of concisely
  describing a language

• Disadvantages
• Too complex to be useful to language users.
• Difficult to create mathematical objects and
  mapping functions.