[Haskell-cafe] A Modest Records Proposal
Gregory Collins
greg at gregorycollins.net
Sun Apr 1 16:40:01 CEST 2012
Whoosh? :-)
On Sun, Apr 1, 2012 at 3:54 PM, Greg Weber <greg at gregweber.info> wrote:
> Hi Gershom,
>
> This sounds very interesting even if I have no idea what you are
> talking about :)
> Please create a proposal linked from this page:
> http://hackage.haskell.org/trac/ghc/wiki/Records
> The first thing you should probably do is explain the programmer's
> point of view. That ensures that we are all going through the
> requirements phase correctly.
> I can assure you that haskell prime would not accept a records change
> until it is first implemented in GHC or another Haskell compiler.
>
> Thanks,
> Greg Weber
>
> On Sat, Mar 31, 2012 at 11:14 PM, Gershom B <gershomb at gmail.com> wrote:
> > The records discussion has been really complicated and confusing. But
> > I have a suggestion that should provide a great deal of power to
> > records, while being mostly[1] backwards-compatible with Haskell 2010.
> > Consider this example:
> >
> > data A a = A{a:a, aa::a, aaa :: a -> A (a -> a)}
> > data B a = B{aaa :: a -> A (a -> a), a :: A}
> >
> > Now what is the type of this?
> >
> > aaaa aaaaa a aa = aaaaa{a = a, aaa = aa}
> >
> > Using standard Haskell typeclasses this is a difficult question to
> > answer. The types of aaaa for A and B do not unify in an obvious way.
> > However, while they are intensionally quite distinct, they unify
> > trivially extensionally. The obvious thing to do is then to extend the
> > type system with extensional equality on record functions.
> >
> > Back when Haskell was invented, extensional equality was thought to be
> > hard. But purity was thought to be hard too, and so were Monads. Now,
> > we know that function existentionality is easy. In fact, if we add the
> > Univalence Axiom to GHC[2], then this is enough to get function
> > existensionality. This is a well-known result of Homotopy Type
> > Theory[3], which is a well-explored approach that has existed for at
> > least a few years and produced more than one paper[4]. Homotopy Type
> > Theory is so sound and well understood that it has even been
> > formalized in Coq.
> >
> > Once we extend GHC with homotopies, it turns out that records reduce
> > to mere syntactic sugar, and there is a natural proof of their
> > soundness (Appendix A). Furthermore, there is a canonical projection
> > for any group of fields (Appendix B). Even better, we can make "."
> > into the identity path operator, unifying its uses in composition and
> > projection. In fact, with extended (parenthesis-free) section rules,
> > "." can also be used to terminate expressions, making Haskell friendly
> > not only to programmers coming from Java, but also to those coming
> > from Prolog!
> >
> > After some initial feedback, I'm going to create a page for the
> > Homotopy Extensional Records Proposal (HERP) on trac. There are really
> > only a few remaining questions. 1) Having introduced homotopies, why
> > not go all the way and introduce dependent records? In fact, are HERP
> > and Dependent Extensional Records Proposal (DERP) already isomorphic?
> > My suspicion is that HERP is isomorphic, but DERP is not. However, I
> > can only get away with my proof using Scott-free semantics. 2) Which
> > trac should I post this too? Given how well understood homotopy type
> > theory is, I'm tempted to bypass GHC entirely and propose this for
> > haskell-prime. 3) What syntax should we use to represent homotopies?
> > See extend discussion in Appendix C.
> >
> > HTH HAND,
> > Gershom
> >
> > [1] To be precise, 100% of Haskell 2010 programs should, usually, be
> > able to be rewritten to work with this proposal with a minimal set of
> > changes[1a].
> >
> > [1a] A minimal set of changes is defined as the smallest set of
> > changes necessary to make to a Haskell 2010 program such that it works
> > with this proposal. We can arrive at these changes by the following
> > procedure: 1) Pick a change[1b]. 2) Is it minimal? If so keep it. 3)
> > are we done? If not, make another change.
> >
> > [1b] To do this constructively, we need an order. I suggest the lo
> > mein, since noodles give rise to a free soda.
> >
> > [2] I haven't looked at the source, but I would suggest putting it in
> > the file Axioms.hs.
> >
> > [3] http://homotopytypetheory.org/
> >
> > [4] http://arxiv.org/
> >
> >
> > *Appendix A: A Natural Proof of the Soundness of HERP
> >
> > Take the category of all types in HERP, with functions as morphisms.
> > Call it C. Take the category of all sound expressions in HERP, with
> > functions as morphisms. Call it D. Define a full functor from C to D.
> > Call it F. Define a faithful functor on C and D. Call it G. Draw the
> > following diagram.
> >
> > F(X)----F(Y)
> > | |
> > | |
> > | |
> > G(X)----G(Y)
> >
> > Define the arrows such that everything commutes.
> >
> >
> > *Appendix B: Construction of a Canonical Projection for Any Group of
> Fields.
> >
> > 1) Take the fields along the homotopy to an n-ball.
> > 2) Pack them loosely with newspaper and gunpowder.
> > 3) Project them from a cannon.
> >
> > In an intuitionistic logic, the following simplification is possible:
> >
> > 1) Use your intuition.
> >
> >
> > *Appendix C: Homotopy Syntax
> >
> > Given that we already are using the full unicode set, what syntax
> > should we use to distinguish paths and homotopies? At first, I thought
> > we could avoid providing any syntax for homotopies at all. Haskell is
> > a language with type inference, so we should just be able to infer
> > paths and homotopies behind the scenes by adding homotopies to the
> > type system. That's a very nice answer in theory. But in the real
> > world, when we're writing code that solves actual problems,
> > theoretical niceties break down. What if a user wants to use a
> > nonstandard homotopy?
> >
> > Why should we stop them just because we're too lazy to come up with a
> > good syntax? I then realized that we keep running out of syntax
> > because we've limited ourselves to unicode. Instead, I propose we add
> > a potentially infinite universe of identifiers: youtube videos. For
> > example, the higher inductive type for a circle can be written as:
> >
> > homotopyType http://www.youtube.com/watch?v=dQw4w9WgXcQ where
> > Base ::: http://www.youtube.com/watch?v=dQw4w9WgXcQ
> > Loop ::: http://www.youtube.com/watch?v=J---aiyznGQ Base Base
> >
> > Note that the urls do not use SSL. For portability reasons, I propose
> > that SSL only be enabled as an optional extension.
> >
> > _______________________________________________
> > Glasgow-haskell-users mailing list
> > Glasgow-haskell-users at haskell.org
> > http://www.haskell.org/mailman/listinfo/glasgow-haskell-users
>
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--
Gregory Collins <greg at gregorycollins.net>
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