Hi Pat, you might be interested in Agda [1] and the tutorial "Dependently Typed Programming in Agda" [2]. I'm just reading the tutorial and it helps me a lot with understanding the concept.
Also if you'd like to have a deeper understanding of the underlying theory, I'd suggest reading Barendregt's "Lambda Calculi with Types" [3]. Best regards, Petr [1] http://wiki.portal.chalmers.se/agda/ [2] http://www.cse.chalmers.se/~ulfn/papers/afp08/tutorial.pdf [3] http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.26.4391 and ftp://ftp.cs.kun.nl/pub/CompMath.Found/HBKJ.ps.Z On Fri, Oct 09, 2009 at 02:11:30PM +0100, pat browne wrote: > Hi, > I am trying to understand the concept of dependent types as described in > Haskell literature (Hallgren 2001),(Hinze,Jeuring et al. 2006). I am > particularly interested in understanding two flavours of dependency > mentioned by Hinze et al: > 1) Types depending on values called dependent types > 2) Types depending on types called parametric and type-indexed types > > I think that ascending levels of abstraction are important here: values > - types - classes (Hallgren 2001). Here is a Haskell example of the use > of DT: > > class Named object name | object -> name where > name :: object -> name > > instance (Eq name, Named object name) => Eq object where > object1 == object2 = (name object1) == (name object2) > > I think that the intended semantics are: > 1) Objects have names and can be compared for equality using these names. > 2) Two objects are considered equal (identical) if they have the same name. > 3) The type of a name depends on the type of the object, which gets > expressed as a type dependency (object -> name). > I am not sure about the last semantic it might be interpreted as "the > named object depends on..". This may indicate a flaw in my understanding > of DT. > > I am aware that dependent types can be used to express constraints on > the size of lists and other collections. My understanding of Haskell's > functional dependency is that object -> name indicates that fixing the > type object should fix the type name (equivalently we could say that > type name depends on type object). The class definition seems to show a > *type-to-type* dependency (object to name), while the instance > definition shows how a name value is used to define equality for objects > which could be interpreted as a *value-to-type* dependency (name to > object) in the opposite direction to that of the class. > > My questions are: > Question 1: Is my understanding correct? > Question 2: What flavour of DT is this does this example exhibit? > > Best regards, > Pat > > > Hallgren, T. (2001). Fun with Functional Dependencies. In the > Proceedings of the Joint CS/CE Winter Meeting, Varberg, Sweden, January > 2001. > Hinze, R., J. Jeuring, et al. (2006). Comparing Approaches to Generic > Programming in Haskell. Datatype-generic programming: international > spring school, SSDGP 2006. > > _______________________________________________ > Haskell-Cafe mailing list > Haskell-Cafe@haskell.org > http://www.haskell.org/mailman/listinfo/haskell-cafe _______________________________________________ Haskell-Cafe mailing list Haskell-Cafe@haskell.org http://www.haskell.org/mailman/listinfo/haskell-cafe
