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Lecture 14, Lecture 15 - Coggle Diagram

- - - - Imports, Sees, Promotes
      - Refines
      - Sets and their Properties
      - Concrete Variables and their Invariant
      - Concrete Constants
    - - Skip
      - Sequence
      - Alternation
      - Case
      - Loops
      - Blocks
      - Variable Blocks
      - Operation calls of Imported machines
      - Read-only Operation calls of Imported machines
    - - Identifier or Literal Constant
      - Access to an element of an array
      - Bool(condition)
        
        Predicates
        
        not
        
        &
        
        or
        
        Comparison
        
        op(y), +,-,*,/ cannot be used in a condition
    - - Scalar Types
      - NAT
      - INT
      - Bool
      - Defined or enumerated Sets
        
        Values
        
        Subsets
        
        MY_SET = 0..10
        
        Scalar Value
        
        cc = 10
        
        Array
        
        MY_SETS*{0}
      - Arrays
      - Concrete Variables: Scalars and Arrays
      - Concrete Constants: Scalars, Arrays adn Subsets
- - - - The commands before the loop establish the loop invariant
      - the body of the loop establishes the loop invariant
      - The invariant is true and the loop guard is false, we can guarantee the post-condition of the loop
  - - - loop invariant and its guard guarantee that the variant is a Natural Expression
      - Provided that the invariant and its guard are true, the body of the loop decreases the value