Re: [isabelle] Where to learn about HOL vs FOL?

On 2/1/2013 3:41 PM, "Mark" wrote:
Does that clear anything up?

I was sort of speaking of maybe where I was a year ago, but "the problem" is still there to a certain extent.

So I count 30 folders for the "HOL section" of books, then there's the non-HOL logic folders, where I count 49 folders, along with the ML folders, 14 of those, and the Isabelle section with about 14 top level folders, but many subfolders by author or web page.

Before tying into the last paragraph, in the document kanaskskis-8-logic.pdf, I point out the semi-formal BNF grammar describing a HOL4 type, page 11, and then the first BNF grammar describing a term, page 15, followed by the second BNF grammar of a term.

I now ask, "Where is the semi-formal definition of a Isabelle type and term?"

If you said, "If you understand the HOL4 definitions of a type and term, then you basically understand Isabelle's".

To that I would reply, "But I'm not interested in studying 2 or 3 or 4 other HOL's to get a general understanding of Isabelle's logic, I'm interested in studying one logic to get a precise understanding of the one logic that I'm using."

"The problem" is represented by another question. "What is the clear learning path for learning about a particular HOL so that a person can use that HOL in a theorem assistant, and do that within a reasonable period of time, and not just end up with a foggy notion of ideas?"

The answer is that, for self-education, there is no clear path. It's not clear what is essential, and what is an unneeded tangent. But that's not anyone's fault. It just indicates that the market is not mature.

In a mature market, speaking analogously, you don't have to learn C, to learn C++, to learn Java, when it's Java that you're going to be using. In a mature market, people have written lots of books to start you wherever you want to start.

Now to something of a positive nature. The name for your HOL Zero site on my hard drive is "hoZ", and I downloaded the latest glossary, which is now named "hoZ__Glossary 130202.pdf".

It occurred to me that I can tweak it to fit my own preferences, so I saved it to PDF, and with Acrobat, I can add a bookmark entry for each of the terms, and make them sub-bookmarks of their first character. Doing that, I'll be able to see the trees, and not just the forest.

There are many mini-lessons in there that don't demand a big investment of time, so thanks for that.


I think it can get quite confusing because different people use the same
names for different things, and different names for the same things, and
sometimes the same people do this too!

"HOL" can mean "higher-order logic" (referring to one or more of various
logics that are higher-order), or it can mean "the HOL logic" (Mike Gordon's
particular higher-order logic, implemented by HOL4, Isabelle/HOL, HOL Light,
ProofPower and HOL Zero).  Other theorem provers such as Coq, PVS and IMPS
implement other higher-order logics.  So the logic described in the HOL4
logic manual really is the same as HOL Light's, etc, the only difference
being that they are built up in different ways (i.e. they start with a
different initial set of axioms and primitive inference rules, but these
axiomatisations are just different ways of defining the same logic).
Does that clear anything up?


on 1/2/13 2:23 PM, Gottfried Barrow<gottfried.barrow at>  wrote:

On 1/31/2013 1:46 PM, Yannick Duchêne (Hibou57) wrote:
Seems available on‑line; here is a link for the paper you suggest:
(the page also has a link at the top, for a PDF version)
There's a newer dated version, 20 December 2007, at the author's web
site. The published one says "received in revised form 6 August 2007".

When the gurus try to succinctly describe Isabelle/HOL, they'll many
times just use the phrase "simply typed lambda calculus".

But if they have time to type a few extra characters, they might add the
phrase "with polymorphism".

If you keep talking long enough, another one might pop in and throw in
the term "type classes".

Because there's no HOL which has yet won the HOL wars, then they use
external, historical vocabulary to begin the description of their HOL,
but then have to start attaching their own internal vocabulary to the

For someone looking for a label to label HOL with, as a starting place
to learn about HOL, it can get confusing.

If you see the phrase "simple type theory" in the title of Farmer's
paper, then you might ask, "Ah, is this what's going to tell me what
Isabelle/HOL is? Because 'simple type theory' sounds suspiciously like
'simply typed lambda calculus'".

Being an authoritative prophet, I can now say that in the future, the
HOL's which win out in the HOL wars will be the standard themselves, and
the references will be to the 700 page textbooks which formalize,
starting with the basics, what the logic of these HOLs are.

For HOL4 they already have that in their logic manual (to what degree I
can't say), which I thought would be the perfect place to learn about
Isabelle/HOL's formal logic, but it's not, it's the perfect place to
learn about HOL4's formal logic:

For completeness, I quote from Mark's glossary to show how the gurus
have to do a lot qualifying when they try to explain things:

simply-typed : (adj)  Relating to type systems that are relatively simple
are not, for example, dependently-typed.  There is considerable variation
precise intended meaning of "simply-typed" in contemporary usage: in some
polymorphism is not a disqualifying factor, in other usages polymorphism
a disqualifying factor if it caters for the quantification of type
and in other usages still any form of polymorphism is a disqualifying
To avoid confusion, the usage of this term is avoided in HOL Zero, its
documentation and elsewhere in this glossary.

Still looking at Gottfried's list.
In addition to collecting books, I also rip web pages for past,
educational courses on Isabelle. I haven't had time to study any of this
right now. I'm making enough progress just stumbling along. I'll get
more sophisticated later. Some of these are linked to from the official
Isabelle site, many of them aren't.

Regards, GB

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