;; CS 3520
;; Fall 2001
;; HW 1 example solution

1.1

*  (1 + (2 - 3))
-> (1 + -1)
-> 0


*  f(x) = (x + x)   f((4 + 5))
-> f(x) = (x + x)   f(9)
-> f(x) = (x + x)   (9 + 9)
-> f(x) = (x + x)   18

*  g(y) = (y - 1)   h(z) = (z + g(z))   h(17)
-> g(y) = (y - 1)   h(z) = (z + g(z))  (17 + g(17))
-> g(y) = (y - 1)   h(z) = (z + g(z))  (17 + (17 - 1))
-> g(y) = (y - 1)   h(z) = (z + g(z))  (17 + 16)
-> g(y) = (y - 1)   h(z) = (z + g(z))  33


1.2

* + : not a program

* (1 + 2) : a program

         1 in <num>    2 in <num>
        -----------   -----------
        1 in <expr>   2 in <expr>
        -------------------------
           (1 + 2)  in  <expr>
           -------------------
           (1 + 2)  in  <prog>

* 1 + 2 : not a program (missing parens)

* f(x) = f(x) f(x) : a program
                                   x in <id>
                                  -----------
                       f in <id>  x in <expr>                x in <id>
                       ----------------------               -----------
 f in <id>  x in <id>       f(x) in <expr>       f in <id>  x in <expr>
 --------------------------------------------    ----------------------
         f(x) = f(x)  in <defn>                     f(x)  in  <expr>
 ----------------------------------------------------------------------
                    f(x) = f(x) f(x)  in  <prog>

* f(x) = 1   (1 + 1)   g(x) = 2   (2 + 2) : not a program (extra expression
                                            between definitions)

* f(x) = 1   g(x) = 1   (1 - 1) : a program

                       1 in <num>                         1 in <num>   1 in <num>  1 in <num>
                      -----------                        -----------  ----------- -----------
f in <id>  x in <id>  1 in <expr>  g in <id>  x in <id>  1 in <expr>  1 in <expr> 1 in <expr> 
---------------------------------  ---------------------------------  -----------------------
       f(x) = 1 in <defn>                  g(x) = 1 in <defn>             (1 - 1) in <expr>
---------------------------------------------------------------------------------------------
                             f(x) = 1 g(x) = 1 (1 - 1)  in  <prog>