On Fri, Oct 18, 2019 at 3:29 PM Olivier Binda <[email protected]> wrote:

> I have started looking at the Peano file and understanding mm0.
>
> This looks a lot like function signatures, with abstract/concrete bodies.
> So Mephistolus statements like "( v1w -> v2w )" might be viewed as a
> function im (v1w v2w : wff) : wff = $( v1w -> v2w )$
>

That depends on what you mean. A "term" or "def" is used to define a new
expression constructor, like implication. That looks like this:

term im: wff > wff > wff;
infixr im: $->$ prec 25;

That declares implication as a right arrow (right associative), and from
this point on you are permitted to write things like "v1w -> v2w" in
statements. It is basically the equivalent of metamath's

wi $a wff ( ph -> ps ) $.

statement.

This is by contrast to theorem statements and hypotheses, which in metamath
usually come after a "|-" symbol. In MM0 these appear in "axiom" and
"theorem" statements, like this one:

theorem syl (a b c: wff) (h1: $ a -> b $) (h2: $ b -> c $): $ a -> c $;

This says that given proofs of a -> b and b -> c, we get a proof of a -> c.
In MM0 this ends right away with a semicolon, and in MM1 the proof is given
afterwards as a lisp expression:

theorem syl (a b c: wff) (h1: $ a -> b $) (h2: $ b -> c $): $ a -> c $ =
(proof...);

These are exactly analogous to the theorems that take up the majority of
the space in MM databases like set.mm.

-- 
You received this message because you are subscribed to the Google Groups 
"Metamath" group.
To unsubscribe from this group and stop receiving emails from it, send an email 
to [email protected].
To view this discussion on the web visit 
https://groups.google.com/d/msgid/metamath/CAFXXJSudWF%3Do5MzERFqFNXRRLZbqfaH%2BTb9J_%3DTgG%2B0Rqsyd7A%40mail.gmail.com.

Reply via email to