To write a valid program, you have to know the grammar/language.

That just specifies things using some form, typically BNF.

Start by specifying all the valid words in the language (numbers,
'for', 'while', 'if', 'true', 'false', that kind of thing).

Then specify how you can build things like sentences and paragraphs
(in programming 'expressions' and usually 'blocks'), and what valid
combinations of those form a complete program.

for example:

Expr := for (<SimpleExpr>; <SimpleExpr>; <SimpleExpr>) Block
            | if <SimpleExpr> then Block else Block

where the SimpleExpr and Block both refer to other ways of writing
little paragraphs in the language, with different limitations on what
you're allowed to include.

The BNF form is read as

Expr := <stuff> | <otherstuff>

"an Expr [equivalent to, say, 'sentence', or 'clause', or whatever] is
built from <stuff> OR <otherstuff>".


This specifies every program you can write in the language which is
correct for that language. Just like writing a strict grammar for
French or German or whatever, only considerably simpler :)

That's syntax.

The next thing you want to do is assign meaning to your programs. You
want to know what's going to happen when you write something that is
grammatically correct. So to do that you specify the
semantics. Typically they'll be written down in natural language, but
pedants can find enormous numbers of holes and "undefined" cases if
you do that.

So for example, in natural language you might write down that:

'if <cond> then <ThenExpr> else <ElseExpr>' behaves as follows:

the system will evaluate <cond>. It should turn out to be "true" or
"false". If it turns out to be something else ("four", or "hello"),
spit out an error. If it turns out to be "true", then execute the
<ThenExpr>. If it turns out ot be false then execute the <ElseExpr>.

The stuff I was doing with Acute in Cambridge, that was specifying
semantics formally, and inventing/implementing a language
(implementing it means writing a program which knows both the language
we invented, and a language the computer already knows, and can
translate the former into the latter, more or less).

Why would we do that? Why have more than one language?

You know they say the Eskimoes have forty-seven words for snow? Or
something like that? And the Japanese have about five words for "you",
/and/ different versions of all their verbs according to
politeness. Languages evolve to be good at expressing certain types of
things. Programming languages are the same.

There's also a question of how fast the computer can do something, and
that depends on how compactly the translator can translate the
original language. Which sort of depends on how close to the
computer's natural language the programming language is. Languages
that are easier for humans to use tend to result in the computer doing
things more slowly. Although that's getting less so nowadays.