CS 21: Structure of Prog' Languages

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CS 21 Structure of Prog. Languages

• Jay R.C. Fernandez, M.S.
• Instructor

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Describing Syntax and Semantics
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Syntax Semantics

• What we need concise yet understandable
  description of a programming language
• implementers must understand
• how the statements are formed
• what they mean

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Syntax Semantics

• need for a language reference manual
• Syntax form of its expressions, statements and
  program units
• Semantics meaning of those expressions and
  program units

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Syntax Semantics

• Formal Methods of Describing Syntax
• Grammars
• Syntax Diagrams
• Parse Trees
• metalanguage language used to describe another
  language

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Describing Syntax

• Grammar
• constituted by a set of tokens, terminals,
  non-terminals, productions, and the goal symbol
• describe the hierarchical syntactic structure of
  the sentence of language
• BNF (Backus-Naur Form) one way of writing
  grammars

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Describing Syntax

• Backus-Naur Form (BNF)
• method of describing syntax
• originally presented by John Backus (to describe
  ALGOL 58)and later modified by Peter Naur
• similar to Chomskys Context-free Diagrams (1950)

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Describing Syntax

• Parts of a Grammar
• a set of tokens
• a set of non-terminal symbols
• a set of rules called productions
• a goal symbol

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Describing Syntax

• Grammar
• lexemes small syntactic units (lexical
  specifications)
• e.g. identifiers, constants, operators, and
  special words
• language statements string of lexemes
• token a category of lexemes

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Describing Syntax

• Grammar Symbols
• Goal Symbol
• one of the set of non-terminal symbols
• also referred to as the start symbol
• Terminal Symbols
• symbols that are atomic / non-divisible
• can be combined to form valid constructs in the
  language

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Describing Syntax

• Grammar Symbols
• Non-Terminal Symbols
• symbols used to represent intermediate
  definitions within the language
• defined by productions
• syntactic classes or categories

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Describing Syntax

• Grammar Productions
• BNF uses abstraction for syntactic structures
• ltassigngt ? ltvargtltexpressiongt

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Describing Syntax

• Grammar Productions
• LHS abstraction being defined
• RHS tokens, lexemes, references to other
  abstractions

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Describing Syntax

• Grammar Productions
• a definition of a non-terminal symbol
• has the form
• x ? y
• where x is a non-terminal symbol and y is a
  sequence of symbols (non-terminal or terminal)

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Describing Syntax

• Grammar Derivation
• sentences of the language are generated through
  repeated application of the rules, beginning with
  a start symbol

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Describing Syntax

• Grammar Production Example
• ltif_stmtgt ? if ltlogic_exprgt then
• ltstatement_listgt
• else
• ltstatement_listgt

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Describing Syntax

• Rules to form Grammar
• every non-terminal symbol must appear to the left
  of the ? at least one production
• the goal symbol must not appear to the right of
  the ? of any production

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Describing Syntax

• Rules to form Grammar
• a rule is recursive if its LHS appears in its RHS
• ltid_listgt ? ltidentifiergt

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Describing Syntax

• Given Grammar Productions
• ltprogramgt ? begin ltstmt_listgt end
• ltstmt_listgt ? ltstmtgt ltstmtgt ltstmt_listgt
• ltstmtgt ? ltvargt ltexpressiongt
• ltvargt ? A B C
• ltexpressiongt ? ltvargt ltvargt

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Describing Syntax

• Sample Derivation
• ltprogramgt ? begin ltstmt_listgt end
• begin ltstmtgt end
• begin ltvargt ltexpressiongt end
• begin ltvargt ltvargt ltvargt end
• begin A B C end

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Describing Syntax

• When does derivation stop?
• by exhaustingly choosing all combinations of
  choices, the entire language can generate

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Describing Syntax

• Syntax Diagrams
• a.k.a. Syntax Graphs / Syntax Charts
• represented by a directed graph
• a separate graph is used for each syntactic unit
• Rectangles Non-terminal Symbols
• Circles Terminal Symbols

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Describing Syntax

• Syntax Diagrams

Calculator

ltexprgt
ltexprgt
ltvalgt
ltoprgt
ltexprgt
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Describing Syntax

• Syntax Diagrams

ltvalgt
ltunsgngt
.
ltunsgngt
ltsgngt
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Describing Syntax

• Syntax Diagrams

ltunsgngt
ltdigitgt
ltunsgngt
ltsigngt

-
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Describing Syntax

• Syntax Diagrams

ltdigitgt
0
1
2
3
4
5
..
9
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Describing Syntax

• Syntax Diagrams

ltoprgt

-

/
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Describing Syntax

• Parse Trees
• parse trees hierarchical structure
• node non-terminal symbol
• leaves terminal symbol

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ltprogramgt
begin
end
ltstmt_listgt
ltstmtgt
ltvargt
ltexprgt

ltvargt
ltvargt

A
B
C
Derivation of begin A B C end
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Describing Syntax

• Why do we need to describe syntax?
• to express our ideas to a form understandable by
  the computer
• be acquainted with rules
• transformation/translation
• comparison with other languages

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Describing Semantics

• Informal Description
• Attribute Grammars
• Operational Semantics
• Axiomatic Semantics
• Denotational Semantics

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Describing Semantics

• Informal Description
• uses informal neutral language descriptions
• construed from English language description
• example when an integer and a double are added,
  the result is a double

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Describing Semantics

• Attribute Grammars
• the CFG (Context Free Grammar) for the language
  is augmented with a set of attributes and rules
  for computing those attributes
• describe the syntax and static semantics
• Static Semantics that part of its semantics
  which can be determined without executing its code

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Describing Semantics

• Attribute Grammar
• grammars with sets of attribute values associated
  with a grammar symbol
• attribute computation functions -- how attribute
  values are computed
• predicate functions -- state some of the syntax
  and semantic rules

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Describing Semantics

• Example of Attribute Grammar
• expr ? term
• expr ? expr term
• 1 2 3
• some attributes of symbols aret typev
  values scope

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Describing Semantics

• to compute the v attribute of the attribute
  grammar might be the following rule
• (1.t 3.t)
• switch (1.t)
• case INTEGER .t INTEGER
• .v 1.v.INTEGER
  3.v.INTEGER
• break
• case DOUBLE ...

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Describing Semantics

• Operational Semantics
• the semantics of a program language is described
  by executing its statements on a machine, either
  real or simulated
• the changes that occur in the machines state
  when it executes a given statement define the
  meaning of that statement

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Describing Semantics

• Example of Operational Semantics

Operational Semantics expr1 loop if expr2 0
goto out expr3 goto loop out
C Statement for (expr1 expr2 expr3)
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Describing Semantics

• Axiomatic Semantics
• prove the correctness of programs
• assertions preconditions and post-conditions
• only for very simple statements

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Describing Semantics

• Example of Axiomatic Semantics
• P S Q
• where P is the Precondition
• S is the statement to be defined
• Q is the Postcondition
• xgt5 sum 2 x 1 sum gt11

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Describing Semantics

• Denotational Semantics
• describe the language by execution
• define a mathematical object for each entity
• define a function that maps instances of the
  entity to the instances of mathematical objects

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Describing Semantics

• Example of Denotational Semantics
• ltnumgt ltnumgtltdigitgt ltdigitgt
• ltdigitgt 0 1 2 3 4 5 6 7 8 9
• V(0) 0
• V(1) 1
• V(9) 9
• V(ltnumgtltdigitgt) V(ltnumgt)10 V(ltdigitgt)

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Describing Semantics

• Why do we need to describe semantics?
• understanding programs
• transformation/translation
• proving correctness
• comparison with other languages