Translating Expressions to Stack Machine

Connection to Postfix

Example: translate expression

(a*b + b*c + a*c) * 2

into posftix form.


     +     2
  *     +
 a b  *   *
     b c a c

Postfix expression:

a b * b c * + a c * + 2 *

Translated expression:

  iload slot_a
  iload slot_b
  iload slot_b
  iload slot_c
  iload slot_a
  iload slot_c

Compare to cubeArea in Compiled Expression Examples

In compiled code what corresponds to:

  • '+'
  • '*'
  • variables, like a,b,c
  • constants, like 2

Conclusion: Translating expressions to stack machine is like printing expression in postfix form.

Translation Rules

For constant $c$,

    [\![ c ]\!] = List(\textbf{bipush}(c))

The iconst is just special case of bipush

Translation for operations:

    [\![ e_1 * e_2 ]\!] = [\![ e_1 ]\!] ::: [\![ e_2 ]\!] ::: List([\![*]\!])

and similarly for other operations.

  • we will sometimes omit List(…) when it is clear from the context

Intuition: to evaluate e1 * e2, an interpreter would

  • evaluate e1
  • evaluate e2
  • perform operation on these two values

Compiled code should do the same

  • generate code that will evaluate e1 and store it somewhere
  • generate code that will evaluate e2 and store it somewhere else
  • retrieve these two values and perform the operation on them

In stack machine, “somewhere” is an appropriate part of the stack

  • we need to know that “somewhere” and “somewhere else” are different
  • what would happen if compile code “ate” stack before and removed previous value?

Properties of generated code for expression:

  • do not erase anything that was on the stack
  • increase stack exactly by one, and leave the result of the expression on the stack