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[cellml-discussion] A typed lambda calculus system for CellML


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  • From: r.britten at auckland.ac.nz (Randall Britten)
  • Subject: [cellml-discussion] A typed lambda calculus system for CellML
  • Date: Thu, 7 Aug 2008 14:31:06 +1200
> >>> MathML operators for dealing with types:
> >>> ----------------------------------------
> >>> - "Creating types which represent the product space of two (or more)
> >>>
> >> other
> >>
> >>> types. For example, given the types real_metre and real_second,
creates
> >>>
> >> the
> >>
> >>> type for both a real_metre and real_second." Couldn't you refer to
> >>>
> >> "product"
> >>
> >>> rather than "product space"?
> >>>
> >> I mean product space in the sense that the set of acceptable values for
> >> the type is the cartesian product of the sets of possible values of the
> >> types the operator is applied to. So for example, a variable of the
> >> product space type of real_metre x real_second could take the value
(5m,
> >> 10s).
> >>
> >
> > Ok, though I am now wondering when such a product would be useful to
have.
> >
> Any time you have two or more pieces of information that are so tightly
> coupled they should be in one variable instead of two, or when you want
> to put that information onto a list. Complex numbers, Cartesian
> co-ordinates, and similar sorts of tightly coupled structured
> information would be likely applications.

Just a thought: a function of two variables, one of which is in metres and
the other in seconds could also be viewed as a function of a single variable
whose type is the ordered pair.
e.g. function calculateSpeed(distanceTravelled[metres], timeTaken[seconds])
could also be calculateSpeed( distanceAndSpeed[ metre x second ])

We might want to consider that for functions of multiple variables. Same
goes for returning multiple values from a function.

Overall, though I think it takes some work to digest Andrew's document, I
think he has done an excellent job. Well done, Andrew.

Andrew, please could you recommend some lambda calculus introduction
resources.

Regards,
Randall




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