Archive for July, 2008

CCC-ness of the category of containers

Friday, July 11th, 2008 by Hancock

Paul Levy seems to have taken an interest in the category of containers, and in particular in whether or not it is a CCC. (Like [Set,Set], in which it faitfully and fully embeds.)

In his thesis, Pierre Hyvernat proved that (interaction structures, which are essentially) indexed containers provide a model of multiplicative linear logic, which is to say tensor (><), lolly (-o) and bang (!). A while ago, we "back-ported" at least tensor and lolly to the category of (plain 'ole) containers. I'm not 100% sure, but I think we backported the bang. (The details are in the containers blog, which seems to be defunct.) It would follow that if we define the exponential of containers so that (A -> B) = (!A)-oB, we’d get what ought to be the exponential. Some slightly inebriated investigations last night persuaded me that it could well work out. The question arises of relating this construction to Paul L’s one — it looks prima facie
a bit different. Paul’s centres round partial functions. Mine centres round bags.

The discussion was mostly about the details of the bang construction, eg. the right way to deal with multisets constructively. (Pierre used finitely indexed families modulo permutations of the index set.) Thorsten had a vague memory that decidability of equality was needed somewhere. Indeed, this rings some kind of bell. The moral was that one should try to stay out of the pub long enough to nail this stuff down.

Agda compiler and FFI

Friday, July 4th, 2008 by Nils Anders Danielsson

Today I discussed Agda’s compiler and FFI.

braincurry

Thursday, July 3rd, 2008 by Tom Nielsen

Last Friday, I presented the braincurry project, which is my attempt, with assistance from Henrik Nilsson, to create a domain specific language to define and execute experiments and simulations related to cellular neuroscience. I spent a bit of time introducing neurons, dendrites, axons, synapses and the problem of synaptic integration (given a pattern of inputs to a neuron, can we predict its outputs?) I also talked briefly about the preparation I am currently working on in Tom Matheson’s lab in Leicester, the locust visual system and the influence of locust swarming on agriculture and crop failure.

Experiments with invertebrates and in particular insects can include an large number of modalities, including visual, auditory and olfactory sensory stimulation, intracellular or extracellular recording from multiple neurons, and movement observation – all at the same time. I presented a prototype language for defining these experiments and their associated analyses.

I restrict myself to experiments that consists of trials, i.e. finite episodes during which a set of stimuli (visual, waveforms of currents to be injected into neurons, etc) are presented and responses (neuron spikes, etc) are recorded. Analog input and output is controlled from a simple FFI binding to the Comedi library, which in turns controls a National Instruments data acquisition board. All aspects of the stimuli must be known before the beginning of the trial, so there are no dynamic or reactive components, although stimuli can be influenced by the outcome of previous trials. This restriction suggests a very simple definition of a trial, which is a list of trial specifications:


%format dots = &#8220;\ldots&#8221;

> type Trial = [TrialSpecification]
> data TrialSpecification  = RecordWaveform Channel
>                           | PlayVideo dots
>                           | PlayAudio dots

In addition, I would like to be able to specify analyses that are performed online, ie immediately after a trial has concluded. I can implement this in an untyped manner by giving names to recordings and additionally specify names as inputs and outputs of analyses. First I define a results data type:


%format dots = &#8220;\ldots&#8221;

> data Result  = ResWaveform [Double]
>              | ResNumber Double
>              | ResBool Bool | dots
> type Name = String

And modify TrialSpecification


%format dots = &#8220;\ldots&#8221;

> data TrialSpecification
>   = RecordWaveform Channel Name
>   | PlayVideo dots
>   | PlayAudio dots
>   | Analysis Name (Result -> Result) Name

One advantage of this approach is that I do not have to specify the order in which analyses are carried out if they depend on one another; their dependencies can be resolved automatically, although not in a type-safe manner. Trials are also very easy to compose. We discussed various possibilities for defining a type-safe trial, including monads and GADTs. I talked a bit about how this language may allow me to use parametrised trials to define general higher order trials that can determine, for instance, whether any one trial parameter influences some experimental outcome.