Is the use of $\to$ for both implication and function typing just a happy coincidence or was notation changed?

Question

Due to the Curry-Howard correspondence; Implication and Function Types are isomorphic. The symbol $\to$ is used for both. There is an intuitive sense why you would choose an arrow to mean implication and there it also makes sense why you would choose to use an arrow to indicate the domain and codomain of a function.

What I am curious about is did we originally use different symbols for these concepts and then change them so that they where the same or we where just lucky?

Answer 1

Yes, some sort of coincidence based on intuition, as you said: "from... to..." vs "if... then...".

The implication sign slowly emerged: previously the symbol $\supset$ was widely used.

See Principia Mathematica and Material implication.