Epilogue

The Epigram meeting went underground today due to the AUT strike. Despite a surprise picketter having taken up temporary residence on Conor’s downstairs sofa we weathered the shouts of “Scab!” and made it safely to Conor’s study.

Topics of discussion:

1. Further consideration of the advice provided to us by team gtk2hs on Friday.
2. Edwin is here and keen to build on his experiment of circumventing ghc’s typechecker to utilise the STG Machine for compiling Epigram programs. Expect further news on this later in the week.

Three things on the slate this week

• Datatypes for OTT: the current implementation loses canonicity if you use the notion of datatype from the pre-OTT days, so we need to bring this up to date. Peter Morris and I have a plan bearing a certain resemblance to what’s going on in the Indexed Containers paper; we also have a longer term plan, with an even stronger resemblance to the same, but that’s another story.
• Hierarchical proof state for Ecce: my Oleg theory of holes has the annoying problem that objects only have private subobjects (within so-called ‘guesses’); subobjects which need to be visible get λ-lifted and exported to the global context, resulting in a flattening of the elaboration tree, a loss of sharing, you name it. Just do a proof-state dump in Epigram 1 (META-RET, then look in *Epigram-bin*) if you don’t know what I’m talking about. So the plan is to do away with guesses in favour of hierarchically stored but fully λ-lifted holes and definitions. With a twist: we use a relative mode of naming, omitting the parameters held in common between reference and referent. So although these things are globally global, locally they look local. Oh, wait and see…
• Dummy elaborator for high-level source code. Joel has refactored the grammar and the parser; Peter has refactored the scoper; we just need to reassemble the pieces we had before and we have a basis to build a real UI. We might have the beginnings of a non-dummy elaborator soon enough too.

…is the new injunction which we shall doubtless take as seriously as we take anything. With that in mind, I have begun to exploit the page facility of this blog to produce some user documentation for Ecce, so that the intrepid might have fun and games of one sort or another. I, er, encourage my fellow developers to keep this stuff accurate, warts and all.

I’ve been thinking for a while that it ought to be possible to get Epigram to write out haskell code for ghc to compile, suitably annotated with unsafeCoerce# so as to get past the type checker. I finally got around to experimenting with this the other day; you can see some of the results here (generated from this).

This code is (mostly, apart from the Haskell interface glue at the top) generated by a tool I’m working on for a completely different reason from my usual noddy test functions: factorial, variadic adder and vector sum. I’ve tested it on some more complex code, but this example (factorial in particular) gives some idea of how fast it goes (about 1 second to compute 9! on my machine). Perhaps if I get a moment later this week I’ll try to make a more interesting program.

(more…)

Needed to do a bit of hacking at the weekend, so I just sorted out the naming mechanism to allow and generate the x^n notation. Try typechecking lam X : * => lam X : X => X and lam X : * => lam X : X => X^1.

Next mission, a very simple interactive editor for proof states, given by (Cursor (Key UId Reference)) for now, but we’ll go tree-structured later. In the first instance, this should just have holes and lets, with refinement and undo as the basic operations. This requires the ability to propagate an update. Before long, though, we’ll want to have parametrised things, and a hierarchical structure. We should be able to knock up a serviceable toy in fairly short order.

OK, I think I have a plan. I’m gonna

• hack in Bool and W directly, leaving ‘data’ alone for the moment
• add the relevant extra eliminators for equations (dom, cod, sym)
• make coe go into functions, pairs and trees
• add a constructor for extensionality

If that works out, it’s time to rethink data, then remove Bool and W. I’ll keep youse posted.

I’m following a plan to get us to stage 2 of the equality story: proof irrelevance. I’ll update this post as I go, but so far I’ve

• split Term into syntactic stuff (still Term) and semantic stuff (new file Value)
• lumped the contents of Equality into Value and removed Equality
• threaded a freshroot through eval and everything which calls it (no fun at all)
• added source and target to coe and coh
• made the computational behaviour of coe and coh compare source with target if the proof isn’t already refl
• made normal proofs of equations equal
• made spine comparison of coe just compare sources and targets, rather than (irrelevant) proofs
• did some very basic testing
• pushed the changes
• gone in search of a drink

I’m trying to keep Epitome sane as I go.

Meeting:

• Thorsten should type:
  1. darcs get http://sneezy.cs.nott.ac.uk/darcs/term
  2. cd term
  3. chmod +x Setup.hs
  4. ./Setup.hs configure --prefix=$HOME
  5. ./Setup.hs build
  6. ./Setup.hs install --user
  7. (and providing $HOME/bin is in your path:) epigram
• The next job in term is to build equality in these steps:
  1. Propositional equality
     
     coersions between equal types (and the proof that these are coherant)
     
     and the structural rule for application
     
  2. Proof-irrelevance for equality, to do this right we need to decide equality during evaluation (if we do not have a proof of an equation but it’s homogeneous, then we win anyway). The upshot is Equality.lhs and eval from Term.lhs need to be in the same file.
  3. Observational equavalence, at some point (sooner rather than later) we’ll include the structural rule for :
     
     Thorsten pointed out that is rule can be derived from substution of equals for equals plus the more primitive:
     
     Having this gives OTT a simpler core, but Conor prefers the first version because it is easier to program with.

I just had the following interaction with the version I just pushed:

*ParseEvalCheckRender> parseit synthit
input:
Nat => => data X : * where <z> : X ; <s> : all x : X => X
two => => <s <s <z>>> : Nat
plus => => lam m => lam n => m elim{Nat} (lam x => Nat)
% n
% (lam x => lam xh => <s xh>) :
% all m : Nat => all n : Nat => Nat
---
plus two two
STOP

<s <s <s <s <z>>>>>
data X : * where <z> : X ; <s> : all x : X => X


Some sort of progress, I think.

1. UI. Some interest from Nick Thomas. Joel is planning an experiment with gtk2hs.
2. Using darcs is working very well. Discussed structure our darcs repos.
3. Status of Epigram 2. We have been hacking the core recently. The afore mentioned ‘Up’ and ‘Down’ terms are in with the supporting parser, (not very) pretty printer,type checker equality checker. Peter has been implementing datatypes. Next is the equality type, and then on to wrapping it in a representation of holes.
4. Thorsten discussed injectivity of type constructors.
5. Move to the board to discuss 3 further. Specifically Conor proposes a short path to making something go. Two main areas: a) Finishing Core and moving on to theorem prover. b) Concrete syntax, comms protocol.

6. Division of work. Joel and Wouter to look at concrete syntax and comms. James and Peter to look at core and theorem proving.
7. The advantages of supporting observational type theory sooner rather than later will afford us simplifications in the implementation. (Thorsten to go into more detail about this on the blog).

I’ve just completed the upgrade of the blog software to Wordpress 2.0, fun. The shouldn’t be too much new stuff to get used to, the admin pages look different but are fairly similar in content.

You may notice that I’ve swapped darcs activity in for cvs, this time round it doesn’t use the hack of commenting on a dummy post and uses rss instead, try clicking on on of the patches to find out why.

If you find any bugs, leave a comment and I’ll fix.