5.2 A Register-Machine Simulator - SICP Comparison Edition

In order to gain a good understanding of the design of register machines, we must test the machines we design to see if they perform as expected. One way to test a design is to hand-simulate the operation of the controller, as in exercise 5.5. But this is extremely tedious for all but the simplest machines. In this section we construct a simulator for machines described in the register-machine language. The simulator is a JavaScript program with four interface functions. The first uses a description of a register machine to construct a model of the machine (a data structure whose parts correspond to the parts of the machine to be simulated), and the other three allow us to simulate the machine by manipulating the model:

make_machine($register$-$names$, $operations$, $controller$)
constructs and returns a model of the machine with the given registers, operations, and controller.
set_register_contents($machine$-$model$, $register$-$name$, $value$)
stores a value in a simulated register in the given machine.
get_register_contents($machine$-$model$, $register$-$name$)
returns the contents of a simulated register in the given machine.
start($machine$-$model$)
simulates the execution of the given machine, starting from the beginning of the controller sequence and stopping when it reaches the end of the sequence.

As an example of how these functions are used, we can define gcd_machine to be a model of the GCD machine of section 5.1.1 as follows:

const gcd_machine =
    make_machine(
        list("a", "b", "t"),
        list(list("rem", (a, b) => a % b),
             list("=", (a, b) => a === b)),
        list(
          "test_b",
            test(list(op("="), reg("b"), constant(0))),
            branch(label("gcd_done")),
            assign("t", list(op("rem"), reg("a"), reg("b"))),
            assign("a", reg("b")),
            assign("b", reg("t")),
            go_to(label("test_b")),
          "gcd_done"));

The first argument to make_machine is a list of register names. The next argument is a table (a list of two-element lists) that pairs each operation name with a JavaScript function that implements the operation (that is, produces the same output value given the same input values). The last argument specifies the controller as a list of labels and machine instructions, as in section 5.1.

To compute GCDs with this machine, we set the input registers, start the machine, and examine the result when the simulation terminates:

set_register_contents(gcd_machine, "a", 206);

"done"

set_register_contents(gcd_machine, "b", 40);

"done"

start(gcd_machine);

"done"

get_register_contents(gcd_machine, "a");

This computation will run much more slowly than a gcd function written in JavaScript, because we will simulate low-level machine instructions, such as assign, by much more complex operations.

Exercise 5.7 Use the simulator to test the machines you designed in exercise 5.4.

There is currently no solution available for this exercise. This textbook adaptation is a community effort. Do consider contributing by providing a solution for this exercise, using a Pull Request in Github.