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Re: Axiom musings...


From: Tim Daly
Subject: Re: Axiom musings...
Date: Sun, 8 Dec 2019 23:55:58 -0500

The Axiom Sane compiler is being "shaped by the hammer
blows of reality", to coin a phrase.

There are many goals. One of the primary goals is creating a
compiler that can be understood, maintained, and modified.

So the latest changes involved adding multiple index files.
These are documentation (links to where terms are mentioned
in the text), code (links to the implementation of things),
error (links to where errors are defined), signatures (links to
the signatures of lisp functions), figures (links to figures),
and separate category, domain, and package indexes.

The tikz package is now used to create "railroad diagrams"
of syntax (ala, the PASCAL report). The implementation of
those diagrams follows immediately. Collectively these will
eventually define at least the syntax of the language. In the
ideal, changing the diagram would change the code but I'm
not that clever.

Reality shows up with the curent constraint that the
compiler should accept the current Spad language as
closely as possible. Of course, plans are to include new
constructs (e.g. hypothesis, axiom, specification, etc)
but these are being postponed until "syntax complete".

All parse information is stored in a parse object, which
is a CLOS object (and therefore a Common Lisp type)
Fields within the parse object, e.g. variables are also
CLOS objects (and therefore a Common Lisp type).
It's types all the way down.

These types are being used as 'signatures' for the
lisp functions. The goal is to be able to type-check the
compiler implementation as well as the Sane language.

The parser is designed to "wrap around" so that the
user-level output of a parse should be the user-level
input (albeit in a 'canonical" form). This "mirror effect"
should make it easy to see that the parser properly
parsed the user input.

The parser is "first class" so it will be available at
runtime as a domain allowing Spad code to construct
Spad code.

One plan, not near implementation, is to "unify" some
CLOS types with the Axiom types (e.g. String). How
this will happen is still in the land of design. This would
"ground" Spad in lisp, making them co-equal.

Making lisp "co-equal" is a feature, especially as Spad is
really just a domain-specific language in lisp. Lisp
functions (with CLOS types as signatures) would be
avaiable for implementing Spad functions. This not
only improves the efficiency, it would make the
BLAS/LAPACK (see volume 10.5) code "native" to Axiom.
.
On the theory front I plan to attend the Formal Methods
in Mathematics / Lean Together conference, mostly to
know how little I know, especially that I need to know.
http://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/

Tim



On 11/28/19, Jacques Carette <address@hidden> wrote:
> The underlying technology to use for building such an algebra library is
> documented in the paper " Building on the Diamonds between Theories:
> Theory Presentation Combinators"
> http://www.cas.mcmaster.ca/~carette/publications/tpcj.pdf [which will
> also be on the arxiv by Monday, and has been submitted to a journal].
>
> There is a rather full-fledged prototype, very well documented at
> https://alhassy.github.io/next-700-module-systems/prototype/package-former.html
>
> (source at https://github.com/alhassy/next-700-module-systems). It is
> literate source.
>
> The old prototype was hard to find - it is now at
> https://github.com/JacquesCarette/MathScheme.
>
> There is also a third prototype in the MMT system, but it does not quite
> function properly today, it is under repair.
>
> The paper "A Language Feature to Unbundle Data at Will"
> (https://alhassy.github.io/next-700-module-systems/papers/gpce19_a_language_feature_to_unbundle_data_at_will.pdf)
>
> is also relevant, as it solves a problem with parametrized theories
> (parametrized Categories in Axiom terminology) that all current systems
> suffer from.
>
> Jacques
>
> On 2019-11-27 11:47 p.m., Tim Daly wrote:
>> The new Sane compiler is also being tested with the Fricas
>> algebra code. The compiler knows about the language but
>> does not depend on the algebra library (so far). It should be
>> possible, by design, to load different algebra towers.
>>
>> In particular, one idea is to support the "tiny theories"
>> algebra from Carette and Farmer. This would allow much
>> finer grain separation of algebra and axioms.
>>
>> This "flexible algebra" design would allow things like the
>> Lean theorem prover effort in a more natural style.
>>
>> Tim
>>
>>
>> On 11/26/19, Tim Daly <address@hidden> wrote:
>>> The current design and code base (in bookvol15) supports
>>> multiple back ends. One will clearly be a common lisp.
>>>
>>> Another possible design choice is to target the GNU
>>> GCC intermediate representation, making Axiom "just
>>> another front-end language" supported by GCC.
>>>
>>> The current intermediate representation does not (yet)
>>> make any decision about the runtime implementation.
>>>
>>> Tim
>>>
>>>
>>> On 11/26/19, Tim Daly <address@hidden> wrote:
>>>> Jason Gross and Adam Chlipala ("Parsing Parses") developed
>>>> a dependently typed general parser for context free grammar
>>>> in Coq.
>>>>
>>>> They used the parser to prove its own completeness.
>>>>
>>>> Unfortunately Spad is not a context-free grammar.
>>>> But it is an intersting thought exercise to consider
>>>> an "Axiom on Coq" implementation.
>>>>
>>>> Tim
>>>>
>



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