I thought I should have a look at clojure.core.reducers in case there was 
an answer there - but this all still looks eager whereas I need something 
like a lazy reduction which applies a given function to its accumulator and 
each input to give it's new accumulator, which is output on each step...

Jules


On Sunday, 27 November 2022 at 19:00:48 UTC Jules wrote:

> Guys,
>
> I've found myself needing a function that I am sure cannot be an original 
> but I'm not aware of it existing anywhere...
>
> It is a cross between 'map', 'reduce' and 'iterate'...
>
> Given a function 'f' and a sequence 's' it would return you  a sequence of 
> :
> ```
> [(f s[0]) (f (f s[0]) s[1]) (f (f (f s[0]) s[1]) s[2]) ...]
> ```
>
> or, more concretely, e.g.:
> ```
> util-test> (stateful-map + [0 1 2 3 4 5])
> [0 1 3 6 10 15]
> util-test> 
> ```
>
> I have a couple of approaches to it - one using reduce:
>
> ```
> (defn stateful-map-1 [f [h & t]]
>   (reduce
>    (fn [acc v]
>      (conj acc (f (last acc) v)))
>    [h]
>    t))
> ```
>
> and another, mapping using a stateful function:
>
> ```
> (let [secret (Object.)]
>   (defn stateful-mapper [f]
>     (let [state (volatile! secret)] (fn [v] (vswap! state (fn [old new] 
> (if (= secret old) (f new) (f old new))) v)))))
>
> (defn stateful-map-2 [f s]
>   (mapv (stateful-mapper f) s))
> ```
>
> The former feels more idiomatic whereas the latter (although uglier) is 
> more efficient and has the added benefit of being able to be used for 
> general map-ing which is important as I want to use this approach to 
> transduce a clojure.async.channel.
>
> It could, of course, be expressed directly as a transducer but it feels 
> like something simpler that should only be lifted to a transducer as and 
> when needed (see test below) ...
>
> Here is my working testsuite:
>
> ```
> (deftest stateful-map-test
>   (testing "reduction"
>     (is
>      (=
>       [0 1 3 6 10 15]
>       (stateful-map-1 + [0 1 2 3 4 5]))))
>   (testing "mapping stateful function"
>     (is
>      (=
>       [0 1 3 6 10 15]
>       (stateful-map-2 + [0 1 2 3 4 5]))))
>   (testing "transduction"
>     (is
>      (=
>       [0 1 3 6 10 15]
>       (sequence (map (stateful-mapper +)) [0 1 2 3 4 5])))))
> ```
>
> Am I missing a standard way of doing this in Clojure ? Or is a stateful 
> function the best answer ?
>
> Interested in your thoughts,
>
>
> Jules
>
>

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