[TYPES] types

Vladimir Voevodsky vladimir at ias.edu
Mon May 12 13:47:26 EDT 2014


I am reading Russell's texts and the more I investigate them the more it seems to me that the concept of types as we use it today has very little with how types where perceived by Russell or Church.

For them types were a restriction mechanism. As Russell and Whitehead write:

"It should be observed that the whole effect of the doctrine of types is negative: it forbids certain inferences which would otherwise be valid, but does not permit any which would otherwise be invalid."

The types which we use today are a constructive tool. For example, types in Ocaml are a device without which writing many programs would be extremely inconvenient.

I am looking for a historic advice - when and where did types appear in programming languages which were enabling rather than forbidding in nature?


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