General Computer Science 320201 GenCS I & II Lecture ... - Kwarc

P instruction comment P instruction comment
0 LOAD 1 ACC : = a 10 MOVE ACC IN1 IN1: = IN1 +1
1 MOVE ACC IN1 IN1: = a 11 MOVE IN2 ACC
2 LOAD 2 ACC : = b 12 ADDI 1
3 MOVE ACC IN2 IN2: = b 13 MOVE ACC IN2 IN2: = IN2 +1
4 LOAD 0 ACC : = n 14 LOAD 0
5 JUMP= 13 if n = 0 then stop 15 SUBI 1
6 LOADIN 1 0 ACC : = P (IN1) 16 STORE 0 P (0): = P (0) − 1
7 STOREIN 2 0 P (IN2): = ACC 17 JUMP − 12 goto step 5
8 MOVE IN1 ACC 18 STOP 0 Stop
9 ADDI 1
Lemma 454 We have P (0) = n − (i − 1), IN1 = a + i − 1, and IN2 = b + i − 1 for all
(1 ≤ i ≤ n + 1). (the program does what we want)
proof by induction on n.
Definition 455 The induction hypotheses are called loop invariants.
c○: Michael Kohlhase 280
3.4.2 A Stack-based Virtual Machine
We have seen that our register machine runs programs written in assembler, a simple machine
language expressed in two-word instructions. Machine languages should be designed such that on
the processors that can be built machine language programs can execute efficiently. On the other
hand machine languages should be built, so that programs in a variety of high-level programming
languages can be transformed automatically (i.e. compiled) into efficient machine programs. We
have seen that our assembler language ASM is a serviceable, if frugal approximation of the first
goal for very simple processors. We will (eventually) show that it also satisfies the second goal by
exhibiting a compiler for a simple SML-like language.
In the last 20 years, the machine languages for state-of-the art processors have hardly changed.
This stability was a precondition for the enormous increase of computing power we have witnessed
during this time. At the same time, high-level programming languages have developed considerably,
and with them, their needs for features in machine-languages. This leads to a significant
mismatch, which has been bridged by the concept of a virtual machine.
Definition 456 A virtual machine is a simple machine-language program that interprets a slightly
higher-level program — the “byte code” — and simulates it on the existing processor.
Byte code is still considered a machine language, just that it is realized via software on a real
computer, instead of running directly on the machine. This allows to keep the compilers simple
while only paying a small price in efficiency.
In our compiler, we will take this approach, we will first build a simple virtual machine (an ASM
program) and then build a compiler that translates functional programs into byte code.
Virtual Machines
Question: How to run high-level programming languages (like SML) on REMA?
Answer: By providing a compiler, i.e. an ASM program that reads SML programs (as data)
and transforms them into ASM programs.
But: ASM is optimized for building simple, efficient processors, not as a translation target!
Idea: Build an ASM program VM that interprets a better translation target language
(interpret REMA+VM as a “virtual machine”)
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