PPP Exercises: Subtyping and Contravariance

Exercise:

1. Define a function 'printPerson' that displays persons. Use this representation for persons:
   

   Let Person = 
      Tuple
         name :String
         age :Int
      end;
   

2. Define a function 'printPersonList' that displays a list of persons using the already defined function 'printPerson'. Use either your polymorphic list tuple considered in the exercise 'Parametric Polymorphism' or the module 'list' (see files 'bulkenv/List.ti' and 'bulkenv/list.tm' for included functions).

3. The following type 'Student' is a subtype of 'Person', meaning that a value of type 'Student' may be used wherever a value of type 'Person' is valid. Define the functions 'printStudent' and 'printStudentList'. Use the already defined 'printPerson' as far as possible.
   

   Let Student = 
      Tuple
         name :String
         age :Int
         term :Int 
      end;
   

4. Change the implementation of 'printPerson' so that it returns the printed person as result:
   

   let printPerson(p :Person) :Person = begin ... p end;
   

   Can we now define 'printStudent' as following?
   

        
   let printTerm(term :Int) = 
      print.string("term  " <> fmt.int(term));
   
   let printStudent(s :Student) =
      begin
          printTerm(printPerson(s).term)
          print.ln()
      end;
   

   What further modification in 'printPerson' would be required and why?

5. Consider the following functions:
   

   let printPerson(p :Person) :Person = begin ... p end;
   let printStudent(s :Student) :Student = begin ... s end;
   

   Now consider a person and a student:
   

   let p :Person = tuple ... end;
   let s :Student = tuple ... end;
   

   and the following four functions:
   

   let a(p :Person  print(:Person) :Person) :Person = print(p);
   let b(p :Person  print(:Person) :Student) :Student = print(p);
   let c(s :Student  print(:Student) :Person) :Person = print(s);
   let d(s :Student  print(:Student) :Student) :Student = print(s);
   

   Can you tell which of the possible 16 combinations between these functions having 'p' or 's' as first parameter and 'printPerson' or 'printStudent' as second parameter are valid with respect to Tycoon subtyping rules and what are the reasons of errors (in case of multiple errors, consider the first)?

      
   				STATUS		REASON
   a(p printPerson)			
   
   a(p printStudent)	
    
   a(s printPerson)	
   
   a(s printStudent)	
   
   b(p printPerson)	
   
   b(p printStudent)               
   
   b(s printPerson)							        
   
   b(s printStudent)               
          
   c(p printPerson)		
   
   c(p printStudent)	
   
   c(s printPerson)		
   
   c(s printStudent)		
    
   d(p printPerson)	
   
   d(p printStudent)
   
   d(s printPerson)
   
   d(s printStudent)