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 Scheme JavaScript program with four interface procedures. 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) 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) 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) get_register_contents($machine$-$model$, $register$-$name$)
  returns the contents of a simulated register in the given machine.
• (start machine-model) 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 procedures functions are used, we can define gcd-machine gcd_machine to be a model of the GCD machine of section 5.1.1 as follows:

Original	JavaScript
(define gcd-machine (make-machine '(a b t) (list (list 'rem remainder) (list '= =)) '(test-b (test (op =) (reg b) (const 0)) (branch (label gcd-done)) (assign t (op rem) (reg a) (reg b)) (assign a (reg b)) (assign b (reg t)) (goto (label test-b)) gcd-done)))	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 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 Scheme procedure 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:

Original	JavaScript
(set-register-contents! gcd-machine 'a 206) done	set_register_contents(gcd_machine, "a", 206); "done"

Original	JavaScript
(set-register-contents! gcd-machine 'b 40) done	set_register_contents(gcd_machine, "b", 40); "done"

Original	JavaScript
(start gcd-machine) done	start(gcd_machine); "done"

Original	JavaScript
(get-register-contents gcd-machine 'a) 2	get_register_contents(gcd_machine, "a"); 2

This computation will run much more slowly than a gcd procedure function written in Scheme, 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.

Add solution

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.