Index of /~stough/705/coursedir/fib

 Name                    Last modified      Size  Description
 Parent Directory                             -   
 fib-test                05-Mar-2009 16:31  961   
 fib-test-output         12-Mar-2009 16:40  1.8K  
 fib-untyped.txt         05-Mar-2009 16:31  1.7K  

fib-untyped.txt contains an implementation in the untyped lambda calculus
of the Fibonacci function:

  let rec fib n =
        if n = 0
        then 0
        else if n = 1
             then 1
             else fib(n - 2) + fib(n - 1)
  in fib

To run it on input n, put the contents of fib-untyped.txt in a file,
and follow it with

  c_n
  (lambda x. lambda y. y x)
  (lambda x. x);

Then give the untyped lambda calculus interpreter the new file as
its input.  The output should look like

  (lambda y.
     y
     (lambda y'.
        y'
        (lambda y''.
           y''
           ... (lambda x.x) ...)))

where the number of occurrences of lambda y -- with
some number of primes on y -- is fib n.  (There was no reason that
the primes were necessary, but the lambda calculus interpreter adds them.)

The Linux/Mac OS X shell script fib-test automates the process of
creating the input to the untyped lambda calculus interpreter.
Running

  fib-test fib-untyped.txt n

puts the text described above in the file fib-test-output.

For example, running

  fib-test fib-untyped.txt 3

will put the text

  ( /* beginning of fib code */
  ...
  /* end of fib code */ )

  (lambda s. lambda z. s(s(s z))) /* 3 */
  (lambda x. lambda y. y x)
  (lambda x. x);

in fib-test-output.  Giving this file to the untyped lambda calculus
interpreter should produce the output (formatted slightly differently)

  (lambda y.
     y
     (lambda y'.
        y'
        (lambda x.x)))

because fib 3 = 2.