CafeOBJ Algebraic Specification

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CafeOBJ Algebraic Specification

• Formal Methods se304/cs407

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This lecture

• Review CafeOBJ
• The point
• The constructs
• The syntax
• Example
• List

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CafeOBJ version 1.4.5

• Does not have the same bug
• Well look at it in the lab
• Lets recap

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The point

• Specification
• Maths
• Precise
• Unambiguous
• Consistent
• What, not how

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Specification

• A specification is a precise, unambiguous and
  complete statement of the requirements of a
  system (or program or process), written in such a
  way that it can be used to predict how the system
  will behave.

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In algebraic specification

• State axioms built of
• Sorts
• Operators
• Variables
• Combine them to
• Draw conclusions

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CafeOBJ

• Modules
• Imports
• Reuse modules written by other people
• Signature
• Declare sorts and operations
• Like a method signature
• Axioms
• Statements of truth from which to build arguments

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CafeOBJ syntax

• Comments
• , -- normal comments
• gt, --gt print to the screen
• Note no spaces
• Module
• module module_name
• module_element

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CafeOBJ syntax

• Imports
• imports
• protecting(module_name)

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CafeOBJ syntax

• Signature declaration, not definition
• signature

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CafeOBJ syntax

• Signature declaration, not definition
• Sorts
• list_of_sorts
• Subsorts, eg
• Int lt Rat

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CafeOBJ Syntax

• Signature declaration, not definition
• Operators
• op symbol list_of_sorts -gt sort
• Underscores represent argument position
• op if_then_else_fi Bool Nat Nat -gt Nat
• if N lt M then N else M fi

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CafeOBJ syntax

• Axioms
• axioms

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CafeOBJ syntax

• Axioms
• Variables (must be declared before used)
• var variable_name variable_sort
• Equations (note spaces)
• eq term term .
• Conditional equations
• ceq term term if boolean_term .

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Axioms

• Tomorrow
• Well take a close look at term rewriting, and
  using axioms

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Example List

• Well develop it on the board
• Lab will be similar but more complex

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http//home.planet.nl/faase009/HaCAR_CDR.html