BigSpill: A 97‑Function Excel LAMBDA Library for Dynamic Arrays

Patrick2788​ 

Nice job with the Triple and Quad versions. I like how many of your custom functions are built upon one or more of your core array reshaping functions (e.g. Echoλ, Resizeλ, RepeatRowsλ, etc.). Would a Quint adaptation be written in a similar fashion to Quad?

For Cartesian products, I do tend to agree with m_tarler​ 's point that it may be easier to adapt Pairwiseλ for multiple arrays if it wasn't limited to vectors from the onset. Regarding 'fixed arity', I agree it can get a bit messy, what with LAMBDA's inability to declare the last argument as a ParamArray; however, with a reasonable number of optional array arguments, and a bit of LAMBDA trickery, it is possible to filter out omitted arguments. For example, a simple CrossJoinλ function and its CrossJoinMultλ companion might be:

CrossJoinλ = LAMBDA(array1,array2,
    HSTACK(
        CHOOSEROWS(array1,TOCOL(SEQUENCE(ROWS(array1))*EXPAND(1,,ROWS(array2),1))),
        CHOOSEROWS(array2,TOCOL(SEQUENCE(,ROWS(array2))*EXPAND(1,ROWS(array1),,1)))
    )
);

CrossJoinMultλ = LAMBDA(array1,array2,[array3],[array4],[array5],[array6],[array7],[array8],
    LET(
        vec, VSTACK(LAMBDA(array1),LAMBDA(array2),LAMBDA(array3),LAMBDA(array4),LAMBDA(array5),LAMBDA(array6),LAMBDA(array7),LAMBDA(array8)),
        arr, FILTER(vec,1-MAP(vec,LAMBDA(arg,ISOMITTED(arg())))),
        REDUCE(INDEX(arr,1,1)(),DROP(arr,1),LAMBDA(acc,val,CrossJoinλ(acc,val())))
    )
);

Which could be used as follows:

=CrossJoinMultλ(Animals,Letters,Colors,Numbers)

// this would have the same basic effect as:
=CrossJoinλ(CrossJoinλ(CrossJoinλ(Animals,Letters),Colors),Numbers).

I've also toyed with the idea of a generalized ParamArrayλ function, e.g.:

CrossJoinParrλ = LAMBDA(array1,array2,[param_array],
    IF(
        ISOMITTED(param_array),
        CrossJoinλ(array1,array2),
        REDUCE(
            CrossJoinλ(array1,array2),
            FILTER(param_array,1-MAP(param_array,LAMBDA(arg,ISOMITTED(arg())))),
            LAMBDA(acc,val,CrossJoinλ(acc,val()))
        )
    )
);

ParamArrayλ = LAMBDA(_1,[_2],[_3],[_4],[_5],[_6],[_7],[_8],[_9],[_10],[_11],[_12],[_13],[_14],[_15],[_16],
    VSTACK(
        LAMBDA(_1),LAMBDA(_2),LAMBDA(_3),LAMBDA(_4),LAMBDA(_5),LAMBDA(_6),LAMBDA(_7),LAMBDA(_8),
        LAMBDA(_9),LAMBDA(_10),LAMBDA(_11),LAMBDA(_12),LAMBDA(_13),LAMBDA(_14),LAMBDA(_15),LAMBDA(_16)
    )
);

Which would look something like this:

=CrossJoinParrλ(Animals,Letters,ParamArrayλ(Colors,Numbers))

But it's not very intuitive and would likely require a bit more error handling than usual to make it bullet-proof.

Just something to chew on. Kind regards.

p.s. PeterBartholomew1​ said:

David's Braille challenge was interesting but I didn't get to a point where I could publish it. The OP deserved more discussion.

Sorry Peter, I should have given it more time before posting my solution, but it's still an open discussion. Feel free to post your complete solution there... I'd love to see it!