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import Enum

def bread(p), do: p |> String.split("/") |> split(-1) |> bread_()

defp bread_({[], _}), do: []
defp bread_({p, [s]}), do: [{s, join(p ++ [s], "/")}] ++ (p |> split(-1) |> bread_())

bread("/path/to/segment") #=>
 [{"segment", "/path/to/segment"}, {"to", "/path/to"}, {"path", "/path"}]

this is inefficient, but easy to follow and short. I opt for easy here because this will never be time critical.
“Fast-readability” is also a kind of fast code.