Example of Step by Step Evaluation

• predefined variables:
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• expression to be evaluated:
  

  

• expression rewritten replacing , a fixed point of , by :
  

  

• expression rewritten using rule 12:
  

  

• expression rewritten substituting the 1st occurrence of ::
  

  

• performing -reduction by substituting variable in the body of the lambda abstraction by the argument :
  

  

• performing -reduction by substituting variable in the body of the lambda abstraction by the argument :
  

  

• evaluating the `IF'-expression by selecting the `no'-branch and evaluating the subtraction:
  

  

• expression rewritten substituting by using rule 12:
  

  

• expression rewritten substituting the first occurrence of the variable by its value:
  

  

• performing -reduction substituting `fac' in the body of the lambda abstraction by the argument :
  

  

• performing -reduction substituting in the body of the lambda abstraction by the argument :
  

  

• evaluating `IF'-expression returning the `yes'-branch:
  

  

• evaluating the multiplication:
  

  

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