Given that most Excel users would not dream of employing one thunk, you might well ask why even consider nested thunks!  The use case explored here is to return all the combinations by which one might choose m objects from n (not just a count of options =COMBIN(n, m), but the actual combinations)  Knowing that sometimes allows one to deploy an exhaustive search of options to determine the best strategy for a task.

Before considering the task further, one might ask ‘what is a thunk; isn’t it far too complicated to be useful?‘  All it is, is a LAMBDA function that evaluates a formula when used, the same as any other function.  The formula could be an expensive calculation or, rather better, no more than a simple lookup of a term from a previously calculated array.  The point is, that whilst ‘arrays of arrays’ are not currently supported in Excel, an array of functions is fine, after all, an unrun function is little more than a text string.  Only when evaluated, does one recover an array.

In the example challenge, each cell contains an list/array of binary numbers, which might itself run into the hundreds of terms.  A ‘1’ represents a selected object whilst a ‘0’ is an omitted object.  Rather like the counts of combinations obtained from Pascal’s triangle, each cell is derived from the contents of the cell to the left and the cell above.  This is SCAN on steroids, accumulating array results in two directions.  Running down the sheet, the new combination contains those of the above cell, but all the objects are shifted left and an empty slot appears to the right.  These values are appended to those from the left, in which the member objects are shifted left but the new object is added to the right.

So the challenge is to build a 2D array, each member of which is itself an array.  The contents of each cell is represented by a thunk; each row is therefore an array of thunks which, for REDUCE to treat it as a single entity, requires it to be securely tucked inside its own LAMBDA, to become a thunk containing thunks.  Each pair of rows defined by REDUCE is itself SCANned left to right to evaluate the new row.

By comparison the 2D SCAN required for the Levenshtein distance which measure the similarity of text strings was a pushover.  I am not expecting a great amount of discussion to stem from this post but, if it encourages just a few to be a little more adventurous in the way they exploit Excel, its job will be done!

p.s. The title of this discussion borrows from the Double Diamond advert for beer in the 1960s

​Given that most Excel users would not dream of employing one thunk, you might well ask why even consider nested thunks!  The use case explored here is to return all the combinations by which one might choose m objects from n (not just a count of options =COMBIN(n, m), but the actual combinations)  Knowing that sometimes allows one to deploy an exhaustive search of options to determine the best strategy for a task. Before considering the task further, one might ask ‘what is a thunk; isn’t it far too complicated to be useful?’  All it is, is a LAMBDA function that evaluates a formula when used, the same as any other function.  The formula could be an expensive calculation or, rather better, no more than a simple lookup of a term from a previously calculated array.  The point is, that whilst ‘arrays of arrays’ are not currently supported in Excel, an array of functions is fine, after all, an unrun function is little more than a text string.  Only when evaluated, does one recover an array. In the example challenge, each cell contains an list/array of binary numbers, which might itself run into the hundreds of terms.  A ‘1’ represents a selected object whilst a ‘0’ is an omitted object.  Rather like the counts of combinations obtained from Pascal’s triangle, each cell is derived from the contents of the cell to the left and the cell above.  This is SCAN on steroids, accumulating array results in two directions.  Running down the sheet, the new combination contains those of the above cell, but all the objects are shifted left and an empty slot appears to the right.  These values are appended to those from the left, in which the member objects are shifted left but the new object is added to the right. So the challenge is to build a 2D array, each member of which is itself an array.  The contents of each cell is represented by a thunk; each row is therefore an array of thunks which, for REDUCE to treat it as a single entity, requires it to be securely tucked inside its own LAMBDA, to become a thunk containing thunks.  Each pair of rows defined by REDUCE is itself SCANned left to right to evaluate the new row. By comparison the 2D SCAN required for the Levenshtein distance which measure the similarity of text strings was a pushover.  I am not expecting a great amount of discussion to stem from this post but, if it encourages just a few to be a little more adventurous in the way they exploit Excel, its job will be done! p.s. The title of this discussion borrows from the Double Diamond advert for beer in the 1960s  Read More

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