[TYPES] Fwd: When types appeared in programming languages

[PATRICK BROWNE]

Simone,
I enjoyed your review of types. Have you looked at Joseph Goguen's paper
Type as Theories[1].
He presents three descriptions of types: 1)as sets, 2)as algebras, 3)as
theories.
I believe that algebraic languages like CafeOBJ and Maude support all three
approach to types.
Types as sets: Using *sorts*, which can be arrange in a lattice of sorts.
Types as algebras: Tight modules with carrier set, and concrete operations
using initial semantics
Types as theories: Loose modules representing theories with axioms stating
properties e.g. partial order, monoid.
                   Types are logical theories, presented by axioms, whose
properties can be explored by logical deduction.
Regards,
Pat
[1]
http://www.google.ie/url?sa=t&rct=j&q=&esrc=s&source=web&cd=4&cad=rja&uact=8&ved=0CDQQFjADahUKEwib3eGM1MbIAhXC6xQKHcsLA4A&url=http%3A%2F%2Fciteseerx.ist.psu.edu%2Fviewdoc%2Fdownload%3Fdoi%3D10.1.1.16.2241%26rep%3Drep1%26type%3Dps&usg=AFQjCNGjxJGhAumTd7mV0iNovz3eKUco3g&bvm=bv.105039540,d.d24

On 14 October 2015 at 10:26, Simone Martini <simone.martini at unibo.it> wrote:

> [ The Types Forum, http://lists.seas.upenn.edu/mailman/listinfo/types-list
> ]
>
> Last year, there has been a thread on this mailing list on the role (and
> concept) of types in programming languages, started by this msg of Vladimir
> Voevodsky:
>         http://lists.seas.upenn.edu/pipermail/types-list/2014/001745.html
>
> Stimulated from that thread (which showed that there was little consensus
> on when types appeared, and with which meaning), I wrote a little essay,
> suggesting that the emergence of the concept of type in computer science is
> relatively independent from the logical tradition, until the Curry-Howard
> isomorphism will make an explicit bridge between them.
>
> I presented the paper last week at History and Philosophy of Computing
> 2015, in Pisa.
>
>         http://arxiv.org/abs/1510.03726
>
> Comments, remarks, and especially critiques would be much welcomed from
> the members of this list.
>
> Best,
> -s.
> ---------------------------------------------------
> Simone Martini
> Universita' di Bologna
> Dip. di Informatica - Scienza e Ingegneria
> Italy
>
> www.cs.unibo.it/~martini
>

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