#lang racket

;;; This file (ps7-postloop-tranform-fancy-starter.rkt) is a version of
;;; postfix-transform-fancy with some extra features relevant to
;;; CS251 Fall '18 PS7 Problem 1 (a solo problem). 
;;; Make a copy of this file for that problem and flesh out the missing parts. 

;;; PostLoop interpreter that views all commands (including exec)
;;; as stack transformers

;;; This "fancy" version includes the following features:
;;; 1. appropriate handling of all error cases, 
;;; 2. the ability to display step-by-step execution,
;;; 3. a general, extensible way to handle arithops and relops

;; Set this to #t to turn on printing of intermediate stacks; #f to turn it off
(define display-steps? #f)

;; Run the given PostLoop program on argument values, which form the initial stack
(define (postloop-run pgm args)
  (cond ((not (postloop-program? pgm))
         (error "Invalid PostLoop program" pgm))
        ((not (postloop-arguments? args))
         (error "Invalid PostLoop arguments" args))
        ((not (= (postloop-numargs pgm) (length args)))
         (error "Expected number of arguments does not
                 match actual number of arguments"
                (list (postloop-numargs pgm) (length args))))
        (else (let {[final-stack (postloop-exec-commands
                                  (postloop-commands pgm)
                                  args)]}
                (cond ((null? final-stack)
                       (error "Stack empty at end of program"))
                      ((not (non-sequence-value? (first  final-stack)))
                       (error "Top of final stack is not an integer or pair value"))
                      (else (first final-stack)))))))

;; Perform the stack transform of each command from left to right,
;; starting with init-stk, to yield the final stack. 
(define (postloop-exec-commands cmds init-stk)
  (begin (if display-steps? ; Only print intermediate stack if display-steps? is #t
             (printf "About to execute commands ~a on stack ~a\n" cmds init-stk)
             'do-nothing)
         (foldl (λ (cmd stk)
                  (let {[new-stk (postloop-exec-command cmd stk)]}
                    (begin (if display-steps? ; Only print step-by-step details if display-steps? is #t
                               (printf "  after executing ~a, stack is ~a\n" cmd new-stk)
                               'do-nothing)
                           new-stk)))   
                init-stk
                cmds)))

;; Execute a command on a stack to yield a new stack.
;; So each command can be viewed as a "stack transformer"
(define (postloop-exec-command cmd stk)
  (cond ((integer? cmd) (cons cmd stk))
        ((eq? cmd 'pop)
         (if (< (length stk) 1)
             (error "pop requires nonempty stack"
                    (list cmd stk))
             (rest stk)))
        ((eq? cmd 'swap)
         (if (< (length stk) 2)
             (error "swap requires stack with at least two values" (list cmd stk))
             (cons (second stk) (cons (first stk) (rest (rest stk))))))
        ((postloop-arithop? cmd)
         (cond ((< (length stk) 2)
                (postloop-run '(postloop 0 5 (add) for) '())(error "arithop requires two arguments" (list cmd stk)))
               ((or (not (integer? (first stk)))
                    (not (integer? (second stk))))
                (error "arithop requires two integers" (list cmd stk)))
               (else (cons ((postloop-arithop->racket-binop cmd) (second stk) (first stk))
                           (rest (rest stk))))))
        ((postloop-relop? cmd)
         (cond ((< (length stk) 2)
                (error "relop requires two arguments" (list cmd stk)))
               ((or (not (integer? (first stk)))
                    (not (integer? (second stk))))
                (error "relop requires two integers" (list cmd stk)))
               (else (cons ((postloop-relop->racket-binop cmd) (second stk) (first stk))
                           (rest (rest stk))))))
        ((eq? cmd 'nget)
         (if (< (length stk) 1)
             (error "nget requires one argument" stk)
             (let {[index (first stk)]}
               (cond ((not (integer? index))
                      (error "nget requires integer index" (list cmd stk)))
                     ((or (<= index 0)
                          (> index (length (rest stk))))
                      (error "nget index out of range" (list index (rest stk))))
                     (else 
                      (let {[valAtIndex (list-ref stk index)]}
                           ;; list-ref uses 0-based index, but haven't removed index from
                           ;; top of stack, so this works.
                        (if (non-sequence-value? valAtIndex)
                            (cons valAtIndex (rest stk))
                            (error "nget can't return a command sequence" valAtIndex)
                            )))))))
        ((eq? cmd 'sel)
         (cond ((< (length stk) 3)
                (error "sel requires three arguments" (list cmd stk)))
               ((not (integer? (third stk)))
                (error "sel test value must be an integer" (list cmd stk)))
               (else (cons (if (= (third stk) 0) (first stk) (second stk))
                           (rest (rest (rest stk)))))))
        ((postloop-command-sequence? cmd) (cons cmd stk))
        ((eq? cmd 'exec)
         ;; Treat executable sequence as a stack transform rather than appending the commands
         ;; in the sequence to commands portion of (stack * commands) configuration.
         (cond ((< (length stk) 1)
                (error "exec requires nonempty stack" (list cmd stk)))
               ((not (postloop-command-sequence? (first stk)))
                (error "exec requires executable sequence on top of stack" (list cmd stk)))
               (else (postloop-exec-commands (first stk) (rest stk)))))
        ;;----------------------------------------------------------------------
        ;; Extensions to PostFix for PS7 Problem 2 on PostLoop

        ((eq? cmd 'pair)
         (if (< (length stk) 2)
             (error "pair requires two arguments" stk)
             (let {[snd-val (first stk)]
                   [fst-val (second stk)]}
               (cond ((postloop-command-sequence? fst-val)
                      (error "first value of pair cannot be a command sequence" fst-val))
                     ((postloop-command-sequence? snd-val)
                      (error "second value of pair cannot be a command sequence" snd-val))
                     (else (cons (cons fst-val snd-val) (rest (rest stk))))))))

        ((eq? cmd 'fst)
         (if (< (length stk) 1)
             (error "fst requires one argument" stk)
             (let {[pair-val (first stk)]}
               (cond ((not (pair-value? pair-val))
                      (error "fst can only be applied to a pair value"))
                     (else (cons (car pair-val) (rest stk)))))))

        ((eq? cmd 'snd)
         (if (< (length stk) 1)
             (error "snd requires one argument" stk)
             (let {[pair-val (first stk)]}
               (cond ((not (pair-value? pair-val))
                      (error "snd can only be applied to a pair value"))
                     (else (cons (cdr pair-val) (rest stk)))))))

        ;; --------------------------------------------------
        ;; Put your code for handling the FOR command here:

        ((eq? cmd 'for)

         ;; REPLACE THIS STUB:
         (rest (rest stk))
         )

        ;; --------------------------------------------------
        ;; Handle case where no command matches
        
        (else (error "unrecognized command" cmd))
        
        ))

(define (postloop-loop-commands num seq stk)
  ;; Assume num is the nonnegative integer argument of a for loop
  ;; and seq is the command sequence argument of a for loop.
  ;; Returns the final stack that results from running the for loop
  ;; with these arguments starting with the initial stack stk
  ;; of values that *follow* these two arguments.

  stk ; Replace this stub!
  )
                                               
;;----------------------------------------------------------------------
;; General handling of arithops and relops

;; Begin with PostFix abstractions.
;; These are followed by PostLoop abstractions 
(define postfix-arithops
  (list (list 'add +)
        (list 'mul *)
        (list 'sub -)
        (list 'div (λ (a b)
                     (if (= b 0)
                         (error "division by 0 on" a)
                         (quotient a b))))
        (list 'rem (λ (a b)
                     (if (= b 0)
                         (error "remainder by 0 on" a)
                         (remainder a b))))
        ;; Could add more arithops here
        ))

(define (postfix-arithop? cmd)
  (assoc cmd postfix-arithops))

(define (postfix-arithop->racket-binop arithop)
  (second (assoc arithop postfix-arithops)))

(define postfix-relops
  (list (list 'lt <)
        (list 'eq =)
        (list 'gt >)
        ))
        
(define (postfix-relop? cmd)
  (assoc cmd postfix-relops))

(define (postfix-relop->racket-binop relop)
  (let {[boolop (second (assoc relop postfix-relops))]}
    (lambda (x y) (if (boolop x y) 1 0))))

;;----------------------------------------------------------------------
;; Postfix/Postloop Syntax abstractions

(define (postfix-program? sexp)
  (and (list? sexp)
       (>= (length sexp) 2)
       (eq? (first sexp) 'postfix)
       (integer? (second sexp))
       (postfix-command-sequence? (rest (rest sexp)))))

(define (postfix-command-sequence? sexp)
  (and (list? sexp)
       (forall? postfix-command? sexp)))

(define (postfix-command? sexp)
  (or (integer? sexp)
      (postfix-command-sequence? sexp)
      (postfix-arithop? sexp) ; defaults are: add mul sub div rem (but could add more)
      (postfix-relop? sexp) ; defaults are: lt eq gt (but could add more)
      (member sexp  '(pop swap nget sel exec))
      ))

(define (postfix-numargs pgm) (second pgm))
(define (postfix-commands pgm) (rest (rest pgm)))

(define (postfix-arguments? sexp)
  (and (list? sexp)
       (forall? integer? sexp)))

;; Postloop abstractions
(define (postloop-command-sequence? sexp)
  (and (list? sexp)
       (forall? postloop-command? sexp)))

(define (postloop-command? sexp)
  (or (integer? sexp)
      (postloop-command-sequence? sexp)
      (postfix-arithop? sexp) ; defaults are: add mul sub div rem (but could add more)
      (postfix-relop? sexp) ; defaults are: lt eq gt (but could add more)
      (member sexp '(pop swap nget sel exec
                     pair fst snd for ;; Added for postloop
                     ))
      ))

(define (postloop-program? sexp)
  (or (postfix-program? sexp) ; Regular postfix program
      (and (list? sexp)
           (>= (length sexp) 2)
           (eq? (first sexp) 'postloop)
           (integer? (second sexp))
           (postloop-command-sequence? (rest (rest sexp))))))

(define (postloop-arguments? sexp)
  (and (list? sexp)
       (forall? non-sequence-value? sexp)))

;;; All of the following postloop helper functions/variables are synonyms
;;; for their postfix counterparts. 
(define postloop-numargs postfix-numargs)
(define postloop-commands postfix-commands)
(define postloop-arithops postfix-arithops)
(define postloop-arithop? postfix-arithop?)
(define postloop-arithop->racket-binop postfix-arithop->racket-binop) 
(define postloop-relops postfix-relops)
(define postloop-relop? postfix-relop?)
(define postloop-relop->racket-binop postfix-relop->racket-binop)

;;----------------------------------------------------------------------
;; Postloop value abstractions

(define (pair-value? val)
  (and (pair? val)
       (non-sequence-value? (car val))
       (non-sequence-value? (cdr val))))

(define (non-sequence-value? val)
  (or (integer? val) (pair-value? val)))
         
;;----------------------------------------------------------------------
;;; Helper functions

;; Higher-order helper function from PS4
(define (forall? pred xs)
  (if (null? xs)
      #t
      (and (pred (first xs))
           (forall? pred (rest xs)))))

;;----------------------------------------------------------------------
;;; PostFix Examples

;; Sample program from lecture
(define pf1 '(postfix 2 2 nget 0 gt (sub) (swap 1 nget mul add) sel exec))

#|
> (postfix-run pf1 '(3 5))
About to execute commands (2 nget 0 gt (sub) (swap 1 nget mul add) sel exec) on stack (3 5)
  after executing 2, stack is (2 3 5)
  after executing nget, stack is (5 3 5)
  after executing 0, stack is (0 5 3 5)
  after executing gt, stack is (1 3 5)
  after executing (sub), stack is ((sub) 1 3 5)
  after executing (swap 1 nget mul add), stack is ((swap 1 nget mul add) (sub) 1 3 5)
  after executing sel, stack is ((sub) 3 5)
About to execute commands (sub) on stack (3 5)
  after executing sub, stack is (2)
  after executing exec, stack is (2)
2
|#

#|
> (postfix-run pf1 '(3 -5))
About to execute commands (2 nget 0 gt (sub) (swap 1 nget mul add) sel exec) on stack (3 -5)
  after executing 2, stack is (2 3 -5)
  after executing nget, stack is (-5 3 -5)
  after executing 0, stack is (0 -5 3 -5)
  after executing gt, stack is (0 3 -5)
  after executing (sub), stack is ((sub) 0 3 -5)
  after executing (swap 1 nget mul add), stack is ((swap 1 nget mul add) (sub) 0 3 -5)
  after executing sel, stack is ((swap 1 nget mul add) 3 -5)
About to execute commands (swap 1 nget mul add) on stack (3 -5)
  after executing swap, stack is (-5 3)
  after executing 1, stack is (1 -5 3)
  after executing nget, stack is (-5 -5 3)
  after executing mul, stack is (25 3)
  after executing add, stack is (28)
  after executing exec, stack is (28)
28
|#

;; Sum-of-squares program 
(define sos
  '(postfix 2 ; let's call the arguments a and b, from top down
            1 nget ; duplicate a at top of stack
            mul ; square a
            swap ; stack now has b and a^2 from top down
            1 nget mul ; square b
            add ; add b^2 + a^2 and return
            ))

#|
> (postfix-run sos '(3 4))
About to execute commands (1 nget mul swap 1 nget mul add) on stack (3 4)
  after executing 1, stack is (1 3 4)
  after executing nget, stack is (3 3 4)
  after executing mul, stack is (9 4)
  after executing swap, stack is (4 9)
  after executing 1, stack is (1 4 9)
  after executing nget, stack is (4 4 9)
  after executing mul, stack is (16 9)
  after executing add, stack is (25)
25
|#


;;----------------------------------------------------------------------
;;; PostLoop Examples

;; ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;; PostLoop programs from Problem 1b:
(define postloop-pgm1 '(postloop 1 0 2 nget (pair) for))
(define postloop-pgm2 '(postloop 1 0 2 nget (swap 10 mul add) for))

;; ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;; PostLoop programs from Problem 1c:

;; You are given postloop-sum
(define postloop-sum '(postloop 1 ; this program takes 1 argument,
                                  ; a nonnegative integer N, and returns
                                  ; the sum of integers from N down to 1. 
                                0 ; initial value of summation accumulator
                                2 nget ; get current integer of loop
                                (add) ; add current integer into accumulator
                                for) ; perform the for loop 
                                 )

;; Replace these stubs with commented, working PostLoop programs
(define postloop-fact '(postloop 1))
(define postloop-expt '(postloop 2))
(define postloop-pairs-up '(postloop 1))
(define postloop-fib '(postloop 1))

;; ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
;; Replace this stub for PS7 Extra Credit Problem 2:
(define postloop-sum-between '(postloop 2))

;;----------------------------------------------------------------------
;;; PostLoop Testing

(define loop-tests
  (list

        ;; -------------------------------------------------------
        ;; PS7 Problem 1b

        (list 'postloop-pgm1
              postloop-pgm1
              '(((0) 0)
                ((1) (0 . 1))
                ((2) ((0 . 2) . 1))
                ((3) (((0 . 3) . 2) . 1))
                ((4) ((((0 . 4) . 3) . 2) . 1))
                ((5) (((((0 . 5) . 4) . 3) . 2) . 1))
                ))

        (list 'postloop-pgm2
              postloop-pgm2
              '(((0) 0) ((1) 1) ((2) 21) ((3) 321) ((4) 4321) ((5) 54321)))

        ;; -------------------------------------------------------
        ;; PS7 Problem 1c
        (list 'postloop-fact
              postloop-fact
              '(((0) 1) ((1) 1) ((2) 2) ((3) 6) ((4) 24) ((5) 120)))

        (list 'postloop-expt
              postloop-expt
              '(((2 0) 1) ((2 1) 2) ((2 2) 4) ((2 3) 8) ((2 4) 16) ((2 5) 32)
                ((3 0) 1) ((3 1) 3) ((3 2) 9) ((3 3) 27) ((3 4) 81) ((3 5) 243)
                ((4 2) 16)
                ((5 2) 25) ((5 3) 125)
                ((-3 0) 1) ((-3 1) -3) ((-3 2) 9) ((-3 3) -27) ((-3 4) 81) ((-3 5) -243)
                ((-5 2) 25) ((-5 3) -125)))

        (list 'postloop-pairs-up
              postloop-pairs-up
              '(((0) 0)
                ((1) (0 . 1))
                ((2) ((0 . 1) . 2))
                ((3) (((0 . 1) . 2) . 3))
                ((4) ((((0 . 1) . 2) . 3) . 4))
                ((5) (((((0 . 1) . 2) . 3) . 4) . 5))
                ))

        (list 'postloop-fib
              postloop-fib
              '(((0) 0) ((1) 1) ((2) 1) ((3) 2) ((4) 3) ((5) 5)
                ((6) 8) ((7) 13) ((8) 21) ((9) 34) ((10) 55)))

        ;; -------------------------------------------------------
        ;; PS7 Extra Credit Problem 1
;        (list 'postloop-sum-between
;              postloop-sum-between
;              '(((0 5) 15) ((0 100) 5050) ((17 17) 17)
;                ((3 7) 25) ((-7 -3) -25) ((-3 4) 4) ((-4 3) -4) ((-3 3) 0)
;                ((7 3) 0) ((-3 -7) 0)))
 
        ))

(define (test-loop name pgm test-cases)
  (display "\n--------------------------------------------------\n")
  (printf "Testing ~a\n" name)
  (for-each (λ (test-case)
              (let* {[args (first test-case)]
                     [expected (second test-case)]
                     [actual (postloop-run pgm args)]}
                (if (equal? actual expected)
                    (printf "Passed! Args: ~a; Expected/Actual Result: ~a\n"
                            args
                            actual)
                    (printf "***FAILED! Args: ~a;\n  Expected Result: ~a;\n  Actual Result ~a\n"
                            args
                            expected
                            actual))))
            test-cases))

(define (test-loops test-cases)
  (for-each (λ (test-case) (apply test-loop test-case))
            test-cases))

;; Uncomment this for PS7 Problem 1d
; (test-loops loop-tests)