Motivation for Language Specification

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Motivation for Language Specification
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Languages
Natural Languages
Artificial Languages
(descriptive)
Logic Languages
Programming Languages
(prescriptive)
Aspects
Syntax
Semantics
Pragmatics
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Motivation for Specifying Semantics of
Programming Languages

• The language of mathematics is precise,
  well-understood, and standard.
• In contrast, the PL notations are diverse and
  similar looking syntax have been given different
  meaning. So it is important to specify
  unambiguously what a system of notation stands
  for.

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• Semantics seeks profound definitions rather than
  difficult theorems.
• Software Design
• Use Divide and Conquer Team effort.
• Language Design
• Unify and study interactions among language
  features. Individual effort common.
• Pascal, Modula-2, Oberon - Niklaus Wirth
• C - Dennis Ritchie
• C - Bjarne Stroustrup
• Java - James Gosling
• C - Anders Hejlsberg

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Formal Proofs

• Proofs
• Hand-waving
• x x x x x
• d/dx ( x x x) d/dx (x x)
• x 2 x
• 1 2
  
• 
  
• 
  QED!

x times
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(contd)

• Rigorous
• Informal
• 1 3 (2i - 1) i i
• Formal Using Mathematical Induction

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5
3
...
5
5
5
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(contd)

• Formal proofs are those formulated in the syntax
  of a particular logic using its axioms and rules
  of inference.
• E.g., Rigorous but informal proofs in Abstract
  Algebra can be converted into formal proofs in
  first-order logic.
• FORMAL
• Reduce to symbol manipulation.

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Problems with Informal Specifications

• Some Historically Significant Examples of
  Ambiguity/Incompleteness

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Algol Example

• Algol-60 report is ambiguous since it does not
  specify a fixed-order of evaluation for
  sub-expressions, or rule out the possibility of
  side-effects in programs.
• If function f has side-effect on variable x then
  it is possible to have
• x f(x) / x f(x)
• f(x) f(x) / 2 f(x)
• f(x) / f(x) / 1
• Loss of Referential Transparency

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Non-portability gotcha.c

• main()
• int i 5
• printf(d d d \n,
• i, i/i, i)
• Intuitively??
• 5 0 6

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Possible Outcomes

• SPARC cc/gcc gotcha.c -ldl a.out
• 6 1 6
• Alpha, MIPS cc/gcc gotcha.c a.out
• 5 1 6
• SUN-3 cc gotcha.c a.out
• 6 1 5

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Pascal Example

• Type Equivalence
• type T array 1..10 of integer
• var A,B array 1..10 of integer
• C array 1..10 of integer
• D T E T
• Structural Equivalence A,B,C,D,E
• Name Chain Equivalence A,B,C,D,E
• Name Equivalence A,B,C,D,E

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Example

• Are the following statements equivalent?
• while ltcondgt do ltstatementgt
• vs
• 25 if ltcondgt then
• begin ltstatementgt
• goto 25
• end

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• include ltstdio.hgt
• main()
• int i, j, k1 2, k2 2
• do i 2
• while ( i gt 0 )
• printf("\t i d \n", i--)
• while (k1--) printf("\n")
• do j 2
• TAG
• if ( j gt 0 )
• printf("\t j d \n", j--)
• goto TAG
• while (k2--)

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• include ltstdio.hgt
• main()
• int i, j, k1 2, k2 2
• do i 2
• while ( i gt 0 )
• printf("\t i d \n", i--)
• break
• while (k1--) printf("\n")
• do j 2
• TAG
• if ( j gt 0 )
• printf("\t j d \n", j--)
• break
• goto TAG
• while (k2--)

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Approaches to Formal Semantics

• Operational How a program executes?
• Specifies abstract interpreter to carry-out
  the meaning of the programs.
• Denotational What a program computes?
• Maps a program to a mathematical function from
  its inputs to its outputs.
• Axiomatic For reasoning about programs
• Specifies properties of language constructs
  through pre-post conditions.
• Abstraction level OS lt DS lt AS

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Interpreter vs Compiler

• Interpreter evaluates the meaning of a program.
• Compiler transforms a program in one language
  into an equivalent program in another language.
  That is, it preserves meaning.
• Semantics of a language is independent of its
  machine implementation.

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Why is formal semantics not widely used?

• It is relatively complex and not yet cost
  effective for everyday (and everybodys) use.
• Semantics is general. In particular, it must
  consider all possible situations (including the
  boundary cases).
• However, most programmers want to know
• What is the output for the particular inputs?

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Who needs semantics?

• Those who write (meta-)programs that must work
  for all programs.
• Designers of
• program transformation tools.
• compilers and interpreters.
• program analyzers.
• software engineering tools.
• critical software.