One of the exciting topic in the course of computer science
is mathematical theory of parsing.
After learning the basics of the theory,
it is a very good Exercise to design a small language and
write a compiler or interpreter for the language.
If you do not like to write a compiler for real CPU,
the stackmachine `sm1` will be a good target
machine.
For example, the language may accept the input

12345678910111213*(256+2)and the interpreter or the compiler generate the following code for

(12345678910111213).. (256).. (2).. add mul messageOne can easily write an arbitrary precision calculator by using

Exercise 1: parse a set of linear equations like
`2x+3y+z = 2; y-z =4; `, output the equation in the matrix form
and find solutions.

Exercise 2:
Modify the calculator `hoc` so that it can use `sm1` as the
backend engine.
The calculator `hoc` is discussed in the book:
Kerningham and Pike, Unix programming environment.

The stackmachine `sm1` provides a very strong virtual machine for
object oriented system by the dictionary tree.
We can easily implement a language, on which Java-like object
oriented programming mechanism is installed,
by using `sm1`.
Here is a sample program of `kan/k0`, which is an object oriented
language and works on `sm1`.
I taught a course on writing mathematical softwares
in a graduate school with `k0`.

class Complex extends Object { local re, /* real part */ im; /* imaginary part*/ def new2(a,b) { this = new(super.new0()); re = a; im = b; return(this); } def real() { return(re); } def imaginary() { return(im); } def operator add(b) { return( new2(re+b.real(), im+b.imaginary()) ); } def operator sub(b) { return( new2(re-b.real(), im-b.imaginary()) ); } def operator mul(b) { return(new2( re*b.real()-im*b.imaginary(), re*b.imaginary()+im*b.real())); } def operator div(b) { local den,num1,num2; den = (b.real())^2 + (b.imaginary())^2 ; num1 = re*b.real() + im*b.imaginary(); num2 = -re*b.imaginary()+im*b.real(); return(new2(num1/den, num2/den)); } def void show() { Print(re); Print(" +I["); Print(im); Print("]"); } def void showln() { this.show(); Ln(); } }

` a = Complex.new2(1,3); `

` a: `

1 +I[3]

` a*a: `

-8 +I[6]

Nobuki Takayama 2020-11-24