Exercises

Do a step by step hand evaluation of the following Jam expressions:

1.  
      let or      := map x,y to if x then true else y;
          member  := map x,l to if null?(l) then false
                                else or(x = first(l), member(x, rest(l)));
      in member (1, cons(1, null))
   

   Do it one time using call-by-value and another time using call-by-name

2.    let or      := map x,y to if x then true else y;
          member  := map x,l to if null?(l) then false
                                else or(x = first(l), member(x, rest(l)));
           zeroes := cons(0, zeros);
      in member (1, zeros)
   

   Do it one time using call-by-value/lazy-cons evaluation and another time using call-by-name/lazy-cons

3.    let or      := map x,y to if x then true else y;
          member  := map x,s to if null?(s) then false
                                else or(x = first(s), member(x, rest(s)));
           countup := map x to cons(x, countup(1+x));
      in member (1, countup(0))
   

   Do it one time using call-by-value/lazy-cons evaluation and another time using call-by-name/lazy-cons

Note: the lazy semantics for cons are reflected by three changes to our evaluation rules:

cons(M,N) is a value for all expressions M,N.

first(cons(M,N)) = M

rest(cons(M,N)) = N

Note that this semantics corresponds to lazy call-by-name. For functional Jam, the difference between lazy call-by-name call-by-need can only be detected because the equality operator is not purely functional (when comparing functions). None of our examples will involve this operation.