History log of /seL4-l4v-10.1.1/HOL4/examples/category/limitScript.sml
Revision Date Author Comments
# d0ecd297 02-Aug-2016 Michael Norrish <Michael.Norrish@nicta.com.au>

Fix category theory scripts in light of pat_assum rename


# 7106a911 09-Jan-2015 Michael Norrish <Michael.Norrish@nicta.com.au>

Fixes to category theory example in light of 92317114


# 35c28065 22-Jun-2011 Ramana Kumar <ramana.kumar@gmail.com>

remove TruePrefix from category theory example


# f76448c7 03-Jun-2011 Ramana Kumar <ramana.kumar@gmail.com>

Update to category theory example.

Main new result is a Yoneda embedding into the category of zfset-valued
presheaves, whose properties are (mostly) simply inherited from the
simpler embedding into the category of (predicate-)set-valued
presheaves.


# a3013634 19-May-2011 Ramana Kumar <ramana.kumar@gmail.com>

More work on categoryTheory example

Highlights include:
- proof that an embedding is essentially injective on objects
- one direction of the proof that an equivalence of categories is full,
faithful, and essentially surjective on objects
- proof that the binary product functor is a functor; characterization
of binary products


# 65992c65 10-May-2011 Ramana Kumar <ramana.kumar@gmail.com>

Major reworking of categoryTheory example

Major changes include:

- Reuse a polymorphic type of "morphisms" for morphisms in a category as
well as for functors and natural transformations. The category record
no longer has dom and cod fields.

- Only store the id_map in a category (and the comp map) because the dom
and cod of these morphisms is forced.

- O'Keefe style treatment of the category of sets: have a separate
category of sets for each HOL type (so really a subcategory of the
real category of sets). Have not yet linked this up with a
Katovsky-style zfset theory (would want to exhibit embeddings).

- Use overloading and Parse rules for nicer syntax.

- Split category theory into category, functor, and nat_trans theories.

- Make many (all?) partial functions extensional, that is, explicitly
set to ARB outside their domain (so that they are comparable).

- Use the constants 'full' and 'faithful' and (new) 'inj_obj' to
characterize the Yoneda embedding. Katovsky said it was injective on
objects in "YonedaEmbedding", which is the wrong term.

- Start a theory of limits (barely started).