; Problem Set 4

; To do this problem set you should take your copy of m1-story.lisp and make a
; copy of everything from the top through the defun of compile.  Save that
; fragment of m1-story.lisp as problem-set-4-answers.lisp.  Then edit it to
; answer these two questions.  By the way, it is very common in software
; development that you are asked to take an existing system and modify it!


; Problem 4-1: Extend M1 so that it supports the IFNE instruction.  The
; semantics of (IFNE x) is that it adds x to the pc if the top of the stack is
; not equal to 0; otherwise control passes to the next instruction.  In any case,
; the topmost item on the stack is removed.

; Problem 4-2: Change the M1 compiler to support two new features:
; a new test, namely the equality of two integer-valued expressions,
; and an IF statement.  In particular the two syntactic changes
; are

; <test>         := ( <expr> > <expr>) | (<expr> = <expr>)

; <stmt>         := ( <var> = <expr> ) |
;                   ( while <test> <stmt*>) |
;                   ( if <test> ( <stmt*> )
;                               ( <stmt*> ) ) |
;                   ( return <expr> )

; where:

;  the semantics of the new <test>, ( <expr> = <expr> ), is that it is true if
;  the two <expr>s evaluate to the same integer and false otherwise.  You may
;  assume that all <expr>s evaluate to integers; and

;  the semantics of ( if <test> ( <stmt*> ) ( <stmt*> ) ) is that if <test>
;  evaluates to true the first sequence of statements is evaluated, otherwise
;  the second is evaluated.

; I strongly advise you to test your compiler, but that is not necessary for
; full credit.

; Obscure Hint: ACL2 will probably have trouble admitting your modified version
; of collect-vars-in-stmt*, collect-vars-in-stmt, stmt*! and stmt!.  That is
; because it doesn't know this simple fact:

; (defthm hack-lemma
;  (implies (car stmt)
;           (consp stmt)))

; I advise you to insert this lemma in your script just before the
; mutual-recursion event defining collect-vars-in-stmt*.