CafeOBJ Algebraic Specification

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CafeOBJ Algebraic Specification

• Formal Methods se304/cs407

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Programming Languages

• When you compile your program 1 of two
  things happens
• It compiles successfully (the compiler says yes,
  that is syntactically correct)
• It does not compile (the compiler says no,
  that is not syntactically correct)
• Why does the compiler never say maybe

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Programming Languages

• Why does the compiler never say maybe
• Because compilers are precise
• The language is precisely laid out using special
  notation
• No ambiguities

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Programming Languages

• Imagine
• Compiler A says no
• Compiler B says yes
• Rarely happens (unless theres a bug)
• Why?
• Programming languages are consistent
• Wasnt always the case
• ANSI C

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Programming languages as specifications

• Programming languages are specifications
• Sets out what the system does
• precisely,
• unambiguously,
• consitently
• Not very good specifications

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Programming languages are not good specifications

• Hard to relate
• What system does
• With what system should do
• Too much detail
• Makes design mistakes difficult to spot
• Too difficult to read
• Often dont make assumptions explicit
• Implementation dependent

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Algebraic Specification

• What is it?
• Descriptions of what a system does
• In maths
• Implementation independent

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Algebraic Specification

• What is it for?
• Formal description of systems
• Automatic checking for
• Ambiguity
• Incompleteness
• Inconsistency
• One of the classes of Formal Methods
• More on different types of FM tomorrow

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CafeOBJ

• What is CafeOBJ?
• Among other things
• An algebraic specification language
• A subset is executable

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CafeOBJ

• The point
• to state axioms that can be used to draw logical
  conclusions (about the system)
• The axioms are made up of
• sorts (types)
• operators on those sorts (, f(a, b), )

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Maths

• Algebra
• Operator is based on mathematical concept of
  function
• Unambiguous, static mapping
• Not an algorithm
• Symmetrical
• (Non symmetrical transitions after the break)

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Mathematical functions

• Domain
• Set from which arguments can come
• Codomain
• Set from which results can come

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Mathematical functions

• Arity
• Number and sort of arguments
• No arity constant
• Coarity
• Sort of result
• Rank
• Pair of arity and coarity

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Mathematical functions

• Infix
• a b
• Prefix
• -a
• Postfix
• b!
• Standard
• f(a, b, c)

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CafeOBJ - modules

• Concepts you are trying to specify are outlined
  in modules
• Divided into 3 sections
• Imports
• Signature definitions
• Axioms

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Modules - syntax

• module module_name
• imports
• module_element
• signature
• module_element
• axioms
• module_element

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Modules

• Imports
• Very like the concept of extends in Java
• Allows us to reuse other modules
• Signature definitions
• Like method declarations (not definitions)
• Describe operations without implementation details

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Modules

• Axioms
• The basis for a logical argument
• Assumptions which
• Are reasonable
• By logical steps
• Allow us to draw a conclusion
• Allow us to reason about our modules

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Todays lab

• An introduction to CafeOBJ
• j\cafeobj\cafeobj.exe
• http//www.ldl.jaist.ac.jp/cafeobj/

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Experiment