Intermediate Representations

You can’t really write a translator, or even an iterpreter, for a complex language, without using an intermediate representation.

What is an IR?

An intermediate representation is a representation of a program “between” the source and target languages. A good IR is one that is fairly independent of the source and target languages, so that it maximizes its ability to be used in a retargetable compiler.

Why use an IR?

We use intermediate representations for at least four reasons:

  1. Because translation appears to inherently require analysis and synthesis.
  2. To break the difficult problem of translation into two simpler, more manageable pieces.
  3. To build retargetable compilers:
    • We can build new back ends for an existing front end (making the source language more portable across machines).
    • We can build a new front-end for an existing back end (so a new machine can quickly get a set of compilers for different source languages).
    • We only have to write $2n$ half-compilers instead of $n(n-1)$ full compilers. (Though this might be a bit of an exaggeration in practice!)
  4. To perform machine independent optimizations.

Types of Intermediate Representations

Intermediate representations are usually:

We’ll use a running example code fragment to illustrate various options.

while (x < 4 * y) {
    x = y / 3 >> x;
    if (y) print x - 3;

Semantic Graph

We’ve seen this before:



Tuples are stored as on the left column, but usually rendered as on the right.

(JUMP, L2)                          goto L2
(LABEL, L1)                    L1:
(SHR, 3, x, t0)                     t0 := 3 >> x
(DIV, y, t0, t1)                    t1 := y / t0
(COPY, t1, x)                       x := t1
(JZ, y, L3)                         if y == 0 goto L3
(SUB, x, 3, t2)                     t2 := x - 3
(PRINT, t2)                         print t2
(LABEL, L3)                    L3:
(LABEL, L2)                    L2:
(MUL, 4, y, t4)                     t4 := 4 * y
(LT, x, t4, t5)                     x := t4 < t5
(JNZ, t5, L1)                       if t5 != 0 goto L1

Stack Code

    goto L2
    load y
    load_constant 3
    load x
    store x
    load y
    jump_if_zero L3
    load x
    load_constant 3
    load x
    load_constant 4
    load y
    jump_if_not_zero L1

Types of Tuple-Based Representations

Genenerally we recognize three levels of tuple sophistication:

Operands look a lot like the source language, with structured objects like arrays and structs.
There are no structured objects, but still target language independent
Operands are extremely close to target language

Here is a running C++ example to illustrate all three:

double a[20][10];
for (int i = 0; i < n; i += di)
    a[i][j+2] = j;



(COPY, 0, i)                        i := 0
(LABEL, L1)                    L1:
(JGE, i, n, L2)                     if i >= n goto L2
(INDEX, a, i, t0)                   t0 := a[i]
(ADD, j, 2, t1)                     t1 := j + 2
(INDEX, t0, t1, t2)                 t2 := t0[t1]
(COPY_TO_DEREF, j, t2)              *t2 := j
(INCJUMP, i, di, L1)                i += di, goto L1
(LABEL, L2)                    L2:



When constructing a medium level IR, the IR generator must be told about the sizes of source language datatypes. Assume here that doubles require 8 bytes and ints require 4 bytes:

(COPY, 0, i)                        i := 0
(LABEL, L1)                    L1:
(JGE, i, n, L2)                     if i >= n goto L2
(MUL, i, 80, t0)                    t0 := i * 80
(ADD, a, t0, t1)                    t1 := a + t0
(ADD, j, 2, t2)                     t2 := j + 2
(MUL, t2, 8, t3)                    t3 := t2 * 8
(ADD, t1, t3, t4)                   t4 := t1 + t3
(COPY_TO_DEREF, j, t4)              *t4 := j
(ADD, i, di, i)                     i := i + di
(JUMP, L1)                          goto L1
(LABEL, L2)                    L2:

Some languages will require bounds checking on arrays and a different treatment of for-loops.



Suppose in our example we know the target is a RISC processor with no memory operations. Variable $j$ can go in r1 and $n$ in r2 and $di$ in r3. They’re not changed in this loop, so we needn’t save them at the end. We might get something like:

(LDC, 0, r0)                        r0 := 0
(LOAD, j, r1)                       r1 := j
(LOAD, n, r2)                       r2 := n
(LOAD, di, r3)                      r3 := di
(LOAD, a, r4)                       r4 := a
(LABEL, L1)                    L1:
(JGE, r0, r2, L2)                   if r0 >= r2 goto L2
(MUL, r0, 80, r5)                   r5 := r0 * 80
(ADD, r4, r5, r6)                   r6 := r4 + r5
(ADD, r1, 2, r7)                    r7 := r1 + 2
(MUL, r7, 8, r8)                    r8 := r7 * 8
(ADD, r6, r8, r9)                   r9 := r6 + r8
(TOFLOAT, r1, f0)                   f0 := tofloat r1
(STOREIND, f0, r9)                  *r9 := f0
(ADD, r0, r3, r0)                   r0 := r0 + r3
(JUMP, L1)                          goto L1
(LABEL, L2)                    L2:


Some structures generally associated with IRs include:

Control Flow Graphs


A control flow graph is a graph whose nodes are basic blocks and whose edges are transitions between blocks.

Basic Blocks

A basic block is a:

... in the abscence of hardware faults, interrupts, crashes, threading problems, etc.

To locate basic blocks in flattened code:

Example Control Flow Graph

     goto L2
     t0 := 3 >> x
     t1 := y / t0
     x := t1
     if y == 0 goto L3
     t2 := x - 3
     print t2
     t4 := 4 * y
     x := t4 < t5
     if t5 != 0 goto L1


Single Static Assignment


Example IRs

Here are a few things that qualify as intermediate representations, or, at least, things a compiler front-end may output:

The intermediate language for the many source and target languages of the GNU Compiler Collection.
Descriptive Intermediate Attributed Notation for Ada. No longer used by major Ada compilers.
The intermediate language of early Pascal compilers. Stack based. Responsible for wide adoption of Pascal in the 1970s.
Java Virtual Machine
Another virtual machine specification. Almost all Java compilers use this format. So do nearly all Scala, Ceylon, Kotlin, and Groovy compilers. Hundreds of other languages use it as well. JVM code can be interpreted, run on specialized hardware, or jitted.
One I made up myself.
Common Intermediate Langauge. Langauges in Microsoft’s .NET framework (such as C+, VB.NET, etc.) compile to CIL, which is then assembled into bytecode.
Why not? It’s widely available and the whole back end is already done within the C compiler.
Kind of like using C, but C-- is designed explicitly to be an intermediate language, and even includes a run-time interface to make it easier to do garbage collection and exception handling. Seems to be defunct.
The new hotness. Much more than just a VM.
The Swift Intermediate Language. Here is a nice presentation on SIL.
A low-level subset of JavaScript.
Web Assembly
An efficient and fast stack-based virtual machine.

A JVM Example


An LLVM Example


An SIL Example


A Web Assembly Example

A C++ function:

unsigned gcd(unsigned x, unsigned y) {
  while (x > 0) {
    unsigned temp = x;
    x = y % x;
    y = temp;
  return y;

Compiled to Web Assembly:

  (type $type0 (func (param i32 i32) (result i32)))
  (table 0 anyfunc)
  (memory 1)
  (export "memory" memory)
  (export "_Z3gcdjj" $func0)
  (func $func0 (param $var0 i32) (param $var1 i32) (result i32)
    (local $var2 i32)
    block $label0
      get_local $var0
      br_if $label0
      loop $label1
        get_local $var1
        get_local $var0
        tee_local $var2
        set_local $var0
        get_local $var2
        set_local $var1
        get_local $var0
        br_if $label1
      end $label1
      get_local $var2
    end $label0
    get_local $var1

Case Study: An IR for C

Let’s design our own tuple-based IR for C. Why? C is such a simple language, an IR is fairly easy to design. Why is C so simple?

Thus, the following tuples are sufficient:

  x ← y                               (COPY, y, x)
  x ← &y                              (COPY_FROM_REF, y, x)
  x ← *y                              (COPY_FROM_DEREF, y, x)
  *x ← y                              (COPY_TO_DEREF, y, x)
  x ← unaryop y                       (uop, y, x)
  x ← y binaryop z                    (binop, y, z, x)
  x ← y[i]                            (COPY_FROM_ARRAY_ELEM, y, i, x)
  x[i] ← y                            (COPY_TO_ARRAY_ELEM, y, x, i)
  goto L                              (JUMP, L)
  if x relop y goto L                 (Jop, x, y, L)
  param x                             (PARAM, x)
  call p, n                           (CALL, p, n)