CSC5125 Program Verification

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CSC5125 Program Verification

• Denotational Semantics An introduction

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What is denotational semantics?

• A formal method for defining the semantics of
  programming languages. It is of interest to the
  language designer, compiler writer and
  programmer. Allison
• A technique for describing the meaning of
  programs in terms of mathematical functions on
  programs and program components. Programs are
  translated into functions about which properties
  can be proved using the standard mathematical
  theory of functions, and especially domain
  theory. -- http//wombat.doc.ic.ac.uk/foldoc/fold
  oc.cgi?denotationalsemantics

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Operational vs. denotational

• Operational semantics imagines the program
  running on an abstract machine. Denoatational
  semantics recognizes the subtle distinction
  between a function as a probably infinite set of
  ordered pairs and an algorithm as a finite
  description of the function. -- Allison

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Denotational semantics

• Each part of a program (often called a phrase) is
  given a denotation, P
• Example -- Binary and natural numbers

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Evaluating semantic descriptions

• Compositionality
• The meaning of every composite phrase can be
  expressed in terms of the meaning of its
  immediate subphrases
• Example wrt binary numbers
• Example wrt while for imperative languages

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Evaluating semantic descriptions

• Full abstraction
• If E and E are expressions with different
  meanings, then there is a context S such that
  S(E) gives a different value than S(E)
• Completeness
• Soundness

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Mathematics

• Mostly from discrete math