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The "utility" of the lambda calculus, in my opinion, comes down to Church's original choice of terminology. He did not call the things denoted by lambda "functi
by DonaldPShimoda 2y ago
The "utility" of the lambda calculus, in my opinion, comes down to Church's original choice of terminology. He did not call the things denoted by lambda "functions"; rather, they were abstractions. What makes the lambda calculus so cool is that it lets us see that abstraction is the root of all computation, at least through one perspective (as opposed to the Turing point of view). Learning the lambda calculus directly will allow you to appreciate functions ("abstractions") and use them more effectively; you can reason about their computation and composition.
- andoando 2y agoI dont quite think of functions and abstractions as the same. Abstractions seem to do more with having a self referential property. Though I suppose that can be seen as the identity function f->f. IIRC Church was heavily influenced by Turing and vice versa.
- 082349872349872 2y agoMight the terminology have been due to early awareness of the cardinality problem associated with the abstractions (D->D) being a subset of the values (D)?