Apply a function to every element in a list to every element in another list

Question

I'd like a more elegant way to write the following two functions, ideally in one :

applyOperatorBetweenVariableLists:: [Variable] -> String -> [Variable] -> [Variable]
applyOperatorBetweenVariableLists firstList operator secondList = concat $ map (test firstList operator) secondList

test:: [Variable] -> String -> Variable -> [Variable]
test firstVariables operator secondVariable = concat $ map (applyOperatorBetweenVariables secondVariable operator) firstVariables

The declaration of applyOperatorBetweenVariables is :

applyOperatorBetweenVariables:: Variable -> String -> Variable -> [Variable]

I'm quite sure there must be a Prelude Function that does exactly this, or a very elegant way to write it.

Answer 1

This can be done concisely with a do block:

applyOperatorBetweenVariableLists firstList operator secondList = do
  secondVariable <- secondList
  firstVariable <- firstList
  applyOperatorBetweenVariables secondVariable operator firstVariable

If you wanted to be even more concise, you could reorder the arguments to both applyOperatorBetweenVariableLists and applyOperatorBetweenVariables , and then use either liftJoin2 or bind2 to implement it (like my final sentence below but with it in place of liftA2 ).

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My original answer was wrong, as it left a layer of nesting (ie, should have done an extra concat or join ):

That's almost just liftA2 , but your arguments are in a weird order. Here's how you'd implement what you wrote in terms of that:

import Control.Applicative (liftA2)
applyOperatorBetweenVariableLists firstList operator secondList = liftA2 (flip applyOperatorBetweenVariables operator) secondList firstList

From that definition, it should be clear how you could change and simplify that to applyOperatorBetweenVariableLists = liftA2 . applyOperatorBetweenVariables applyOperatorBetweenVariableLists = liftA2 . applyOperatorBetweenVariables just by reordering the arguments to it and to applyOperatorBetweenVariables .