CS 3520 Homework 6   - Due October 14

This homework is due October 14, 8:00 AM.

Exercise 6.1, Lazy Lists

Implement an interpreter with lazy evaluation and the following grammar:

  <CNSFAL> = <number>
          | {+ <CNSFAL> <CNSFAL>}
          | {- <CNSFAL> <CNSFAL>}
          | <id>
          | {fun {<id>} <CNSFAL>}
          | {<CNSFAL> <CNSFAL>}
          | {if0 <CNSFAL> <CNSFAL> <CNSFAL>}
          | {cns <CNSFAL> <CNSFAL>}
          | {fst <CNSFAL>}
          | {rst <CNSFAL>}

That is, a language with single-argument functions and application, an if-zero conditional, and cons, first, and rest operations. The language does not include recursive bindings. Also, unlike the PLAI languages, the rest of a cons need not be a list (and we don't bother with an empty-list constant).

Implement your interpreter with the PLAI Advanced language, not a lazy language.

Evaluation of the interpreted langauge must be lazy, however. In particular, if a function never uses the value of an argument, then the argument expression should not be evaluated. Similarly, if the first or rest of a cons cell is never needed, then the first or rest expression should not be evaluated.

See the lecture slides for most of the code you will need, not including cns, fst, and rst. You can implement either call-by-name (no caching of forced values) or call-by-need; the tests will be simple enough that caching won't matter.

As in HW 5, provide a parse function and a interp-expr function. The interp-expr function should return 'cons for a cons result.

  (test (interp-expr (parse 10))
        10)
  (test (interp-expr (parse '{+ 10 17}))
        27)
  (test (interp-expr (parse '{- 10 7}))
        3)
  (test (interp-expr (parse '{{fun {x} {+ x 12}}
                              {+ 1 17}}))
        30)
  
  (test (interp-expr (parse '{{fun {x}
                                   {{fun {f}
                                         {+ {f 1}
                                            {{fun {x}
                                                  {f 2}}
                                             3}}}
                                    {fun {y} {+ x y}}}}
                              0}))
        3)
  
  (test (interp-expr (parse '{if0 0 1 2}))
        1)
  (test (interp-expr (parse '{if0 1 1 2}))
        2)
  
  (test (interp-expr (parse '{cns 1 2}))
        'cons)
  (test (interp-expr (parse '{fst {cns 1 2}}))
        1)
  (test (interp-expr (parse '{rst {cns 1 2}}))
        2)
  
  ;; Lazy evaluation:
  (test (interp-expr (parse '{{fun {x} 0}
                              {+ 1 {fun {y} y}}}))
        0)
  (test (interp-expr (parse '{fst {cns 3
                                       {+ 1 {fun {y} y}}}}))
        3)
  (test (interp-expr (parse '{fst {cns 5
                                       ;; Infinite loop:
                                       {{fun {x} {x x}}
                                        {fun {x} {x x}}}}}))
        5)
  
  (test (interp-expr 
         (parse 
          '{{fun {mkrec}
                 {{fun {fib}
                       ;; Call fib on 4:
                       {fib 4}}
                  ;; Create recursive fib:
                  {mkrec
                   {fun {fib}
                        ;; Fib:
                        {fun {n}
                             {if0 n
                                  1
                                  {if0 {- n 1}
                                       1
                                       {+ {fib {- n 1}}
                                          {fib {- n 2}}}}}}}}}}
            ;; This is call-by-name mkrec
            ;;  (simpler than call-by-value):
            {fun {body-proc}
                 {{fun {fX}
                       {fX fX}}
                  {fun {fX}
                       {body-proc {fX fX}}}}}}))
        5)
  
  (test (interp-expr 
         (parse 
          '{{fun {mkrec}
                 {{fun {nats-from}
                       {{fun {list-ref}
                             ;; Call list-ref on infinite list:
                             {{list-ref 4} {nats-from 2}}}
                        ;; Create recursive take:
                        {mkrec
                         {fun {list-ref}
                              ;; list-ref:
                              {fun {n}
                                   {fun {l}
                                        {if0 n
                                             {fst l}
                                             {{list-ref {- n 1}} {rst l}}}}}}}}}
                  ;; Create recursive nats-from, which generates
                  ;;  an infinite list of numbers:
                  {mkrec
                   {fun {nats-from}
                        ;; nats-from:
                        {fun {n}
                             {cns n {nats-from {+ n 1}}}}}}}}
            ;; This is call-by-name mkrec:
            {fun {body-proc}
                 {{fun {fX}
                       {fX fX}}
                  {fun {fX}
                       {body-proc {fX fX}}}}}}))
        6)