On 9/20/21, James Bowery <jabow...@gmail.com> wrote: > Functions are degenerate Relations. Anyone that starts from a functional > programming perspective has already lost the war.
Some concepts seem to be functions more naturally, for example in programming you return a single value instead of a set of values. You either perform an action or not. But I see that relations do play a central role in categorical logic. > Here's a question for ya'll: > > What is the Relational generalization of Curry-Howard? Let me see... a relation is a sub-object of the Cartesian product of two domains or types, such as A × B. A sub-object of A × B is a new type, call it R, whose elements are propositions such as aRb or R(a,b). According to the book "Lectures on the CHI", a relation, such as R, is a type constructor, a proposition, such as aRb, is a dependent type. The type constructor returns a new type aRb for each a ∈ A and b ∈ B. ------------------------------------------ Artificial General Intelligence List: AGI Permalink: https://agi.topicbox.com/groups/agi/T74958068c4e0a30f-Mab2bdb14214795d205a9ec13 Delivery options: https://agi.topicbox.com/groups/agi/subscription
