A piece of the Rosetta stone

Posted in Category theory, Math, Programming by Mike Stay on 2007 December 20
category lambda calculus pi calculus Turing machine
objects types structural congruence classes of processes \mathbb{N}\times S^*, where \mathbb{N} is the natural numbers and S^* is all binary sequences with finitely many ones.
a morphism an equivalence class of terms a specific reduction from one process state to the next a specific transition from one state and position of the machine to the next
dinatural transformation from the constant functor (mapping to the terminal set and its identity) to a functor generated by hom, products, projections, and exponentials (if they’re there) combinator reduction rule (covers all reductions of a particular form) tape-head update rule (covers all transitions with the current cell and state in common)
products product types parallel processes multiple tapes
internal hom exponential types all types are exponentials? ?
Model of the category in Set A set of values for each data type and a function for each morphism between them A set of states for each process and a single evolution function out of each set. ?

This won’t be appearing in our Rosetta stone paper, but I wanted to write it down. What flavor of logic corresponds to the pi calculus? To the Turing machine?


One Response

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  1. Another piece of the stone « reperiendi said, on 2007 December 28 at 1:40 pm

    […] piece of the stone A few days ago, I thought that I had understood pi calculus in terms of category theory, and I did, in a […]

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