Illustration of what happens with our compiler:
Grammar (subset of Tiny):

     M  -->  S { S } '$'
     S  -->  A  |  P
     A  -->  lower-case '=' E ';'
     P  -->  '<' ( E  ';'  |  'N' ';') 
     E  -->  T {('+'  |  '-') T}
     T  -->  F {('*'  |  '/') F}
     F  -->  '(' E ')'  |  lower-case  |  digit

Example Tiny program:

   ex0.t: Tiny program (should print 7 or 7.0):
   < 7; $

Parser works on virtual parse tree:

   The address of '7' is 7*8 = 56 bytes past start of M.
   This address is calculated inside F.
   It is returned from F to T to E to A.

         M
         | \
         S  \
         |  '$'
         P
       / | \
      /  |  \
    '<'  E  ';'
         | | 56
         T ^
         | | 56
         F ^
         | | 56
        '7'

Your parsing program:  Calls M at the top level.

M():
    Output first part of framework

    Call S()
    Since next == '$', Tiny program done

    Output second part of framework

S():
    Because next is '<', call A()

P():
    Scan past '<'
    Get return value from E: res = E()
    56 is returned
    Output 3 MIPS instructions:
        "     li      $v0, 3\n"
        "     l.d     $f12, 56($s1)\n"
        "     syscall\n"
    (A alway prints the same, except for
     the "56" which comes from the call to E)

Execute Tiny compiler:

   Redirect Tiny source in; redirect MIPS output out:

       % python tiny.py < ex0.t > ex0.s

   ex0.s: my final MIPS program:

Final MIPS output from compiler:

### compiled by Neal Wagner on
#     Tue Oct 28 20:29:57 2014
main:   move    $s7, $ra
        la      $s1, M # data addr
# Print your name
        li      $v0, 4
        la      $a0, Name
        syscall
### Compiled code starts here

# Output M[7]                  --+
        li      $v0, 3           |
        l.d     $f12, 56($s1)    +---  generated code
        syscall                  |
                               --+
# Stuff at end
        move    $ra, $s7
        jr      $ra  # ret to sys
# data declarations
        .data
        .align  3
M:      .double 0.,1.,2.,3.,4.,5.
        .double 6.,7.,8.,9. # cons
        .space  208  # a to z
        .space  1000 # 125 temps
Blank:  .asciiz " "
NewL:   .asciiz "\n"
Tab:    .asciiz "\t"
Name:   .asciiz "Executed by Neal Wagner\n"

(Execute MIPS program. '%' = Linux prompt, red = MIPS output)

% spim ex0.s
SPIM Version 7.4 of January 1, 2009
Copyright 1990-2004 by James R. Larus (larus@cs.wisc.edu).
All Rights Reserved.
See the file README for a full copyright notice.
Loaded: /usr/lib/spim/exceptions.s
Executed by Neal Wagner
7%

(final note: if we wanted to print a newline at the end,
we would have included another Tiny statement:  < N;  )