4 ms·
Now I'm thinking what the type of the Dirac delta function is. I'm leaning to something like: (X (R -> R) ((R -> R) -> (R -> R))) -> R where we are given a fun
by thrown_22 4y ago
Now I'm thinking what the type of the Dirac delta function is.
I'm leaning to something like: (X (R -> R) ((R -> R) -> (R -> R))) -> R where we are given a function (R -> R) on which it acts and a linear operation (R -> R) -> (R -> R), like integration, which acts on it and gives us a single real number as the answer.
- johnbcoughlin 4y agoThis is basically correct, the theory of distributions can be presented in terms of linear functionals. A functional is a map that takes a function and returns a scalar. I'm not sure how to encode linearity in your type system though...
- thrown_22 4y ago>I'm not sure how to encode linearity in your type system though... You don't really, the same way that a regular function R->R has no specific type information that tells you ti's linear or not, e.g. both x and sin(x^2) have the same type.