How to automate the modification of code?

I have a large piece of code consisting of thousands of equations. Example of two connective lines, corresponding to lines 998 and 999 is

sum(x[i]*y[i]for i in 1:n) == 15;
sum(z[i]*x[i]for i in 1:n) == 30;

I would like to replace such lines with the following

sum(x[i]*y[i]for i in 1:n) - 15 >= -s[998];
sum(x[i]*y[i]for i in 1:n) - 15 <=  s[998];

sum(z[i]*x[i]for i in 1:n) - 30 >= -s[999];
sum(z[i]*x[i]for i in 1:n) - 30 <=  s[999];

How to automate this process?

Solution

Substitutions

Our first step is to transform each individual line:

sum(x[i]*y[i]for i in 1:n) == 15;

into this:

sum(x[i]*y[i]for i in 1:n) - 15 >= -s[998];

While doing it in one command would be a nice parlor trick, we will do it in several easier to follow steps.

== to -

Here is our first command, it is very simple:
```
:%s/==/-<CR>
```
- : enters command-line mode.
- % is the range of lines on which to execute the following command. Here, % is a shortcut for 1,$ (from line 1 to last line), thus "every line".
- s is the "substitute" command, see :help :s.
- /== is what you want to substitute.
- /- is what you want to substitute it with.
- Press <CR> (ENTER) to execute the command.
In plain english: "substitute every == with -".

We should get something like:
```
sum(x[i]*y[i]for i in 1:n) - 15;
sum(z[i]*x[i]for i in 1:n) - 30;
```
; to >= -s[XXX];

Here is our second command:
```
:%s/;/ >= -s[XXX];
```
Where we substitute every ; with a generic >= -s[XXX];. This is also quite simple.

In plain english: "substitute every ; with >= -s[XXX];.

We should get something like:
```
sum(x[i]*y[i]for i in 1:n) - 15 >= -s[XXX];
sum(z[i]*x[i]for i in 1:n) - 30 >= -s[XXX];
```
XXX to line number

Here is our third command:
```
:%s/XXX/\=line('.')
```
The big change between this command and the other ones is that the replacement part is dynamic. With \=, we use an expression that is evaluated during each execution instead of a fixed string. line('.') is a vimscript function that returns a line number, which is exactly what we want between those brackets.

In plain english: "substitute every XXX with the current line number".

We should get something like:
```
sum(x[i]*y[i]for i in 1:n) - 15 >= -s[998];
sum(z[i]*x[i]for i in 1:n) - 30 >= -s[999];
```

Duplication

Here we duplicate each line with a single command:

:g/^/t.|s/-s/ s

:g is the :help :global command.
/^/ matches every line so the following command will be executed on every line.
t is the :help :t command.
. represents the current line.
| separates two commands.
s/-s/ s removes the - before the s on the duplicated line.

In plain english: "mark every line, then copy each marked line below itself, then remove that leading - before the s".

We should get something like:

sum(x[i]*y[i]for i in 1:n) - 15 >= -s[998];
sum(x[i]*y[i]for i in 1:n) - 15 >=  s[998];
sum(z[i]*x[i]for i in 1:n) - 30 >= -s[999];
sum(z[i]*x[i]for i in 1:n) - 30 >=  s[999];

One last thing

We use one last command to add a line between our blocks:

:g/ s[/put=''

Every line matching s[ is marked.
We use :help :put to append an empty line.

In plain english: "put an empty line after each line with s[".

We should get something like:

sum(x[i]*y[i]for i in 1:n) - 15 >= -s[998];
sum(x[i]*y[i]for i in 1:n) - 15 >=  s[998];

sum(z[i]*x[i]for i in 1:n) - 30 >= -s[999];
sum(z[i]*x[i]for i in 1:n) - 30 >=  s[999];

What did we learn?

how to perform simple substitutions with :help :substitute,
the notion of :help :range,
how to use an expression in the replacement part (the usual gateway drug to vimscript) with :help sub-replace-\=,
how to execute arbitrary commands on lines matching a specific pattern with :help :global,
how to copy a given line to a given address with :help :t,
how to put some text, here an empty string, below the current line with :help :put,
how to separate commands with :help :|.