THUNKIT

=THUNKIT(anything)
anything
numbers, text, arrays, LAMBDAs, etc.
Allows passing values by "storing" them inside a LAMBDA
T

tboulden

Board Regular
Joined
Jan 14, 2021
Messages
73
Office Version
  1. 365
Platform
  1. Windows
Link to Wikipedia on thunks

Excel Formula: 
=LAMBDA(x,LAMBDA(x))

Some LAMBDA helpers have limitations on what can be returned due to constraints based on the shape of the starting array. For example, if some calculation creates a series of 2-d arrays, Excel will throw an error if we try to pass those back through SCAN/BYROW/BYCOL. Thunking a value by wrapping it in a LAMBDA with no parameter "stores" a complex value in a single cell in an array, which can be passed around in calculations; we trade error-handling constructions for thunking.

I'll add some helper functions for use with thunks soon.

LAMBDA_pairwise_thunks_summarize_pivot.xlsx
ABCDEFG
1
2=LAMBDA(x,LAMBDA(x))("anything")#CALC!
3=LAMBDA(x,LAMBDA(x))("anything")()anything
4
5=LET( thunkIt,LAMBDA(x,LAMBDA(x)), thunkIt(10) )#CALC!
6
7
8
9=thunkIt(10)()10
10
11=thunkIt(SEQUENCE(4,4))#CALC!
12=thunkIt(SEQUENCE(4,4))()1234
135678
149101112
1513141516
16
17=MAP(SEQUENCE(4), LAMBDA(num,CHAR(SEQUENCE(num,num,65,1))))#CALC!
18
19
20=LET( thunks, MAP(SEQUENCE(4), LAMBDA(num, thunkIt(CHAR(SEQUENCE(num,num,65,1))))), REDUCE(,thunks, LAMBDA(stacked,thunk, vStack(IFERROR(stacked(),stacked),thunk()))) )A
21AB
22CD
23ABC
24DEF
25GHI
26ABCD
27EFGH
28IJKL
29MNOP
thunkIt
Cell Formulas
RangeFormula
B2:B3,B20,B17,B11:B12,B9,B5B2=FORMULATEXT(C2)
C2C2=LAMBDA(x,LAMBDA(x))("anything")
C3C3=LAMBDA(x,LAMBDA(x))("anything")()
C5C5=LET( thunkIt,LAMBDA(x,LAMBDA(x)), thunkIt(10) )
C9C9=thunkIt(10)()
C11C11=thunkIt(SEQUENCE(4,4))
C12:F15C12=thunkIt(SEQUENCE(4,4))()
C17C17=MAP(SEQUENCE(4), LAMBDA(num,CHAR(SEQUENCE(num,num,65,1))))
C20:F29C20=LET( thunks, MAP(SEQUENCE(4), LAMBDA(num, thunkIt(CHAR(SEQUENCE(num,num,65,1))))), REDUCE(,thunks, LAMBDA(stacked,thunk, vStack(IFERROR(stacked(),stacked),thunk()))) )
Dynamic array formulas.
 
Upvote 0
expandThunks - Retrieve and stack stored thunks in row-major order.
Excel Formula: 
=LAMBDA(array_of_thunks,
    IF(
        AND(ROWS(array_of_thunks)=1,COLUMNS(array_of_thunks)=1),
            INDEX(array_of_thunks,1,1)(),
        LET(
            expand_rows,
                BYROW(array_of_thunks,
                    LAMBDA(row_,
                        thunkIt(
                            REDUCE(
                                ,
                                row_,
                                LAMBDA(stacked,thunk,
                                    hStack(IFERROR(stacked(),stacked),thunk())
                                )
                            )
                        )
                    )
                ),
            IF(
                ROWS(array_of_thunks)=1,
                    INDEX(expand_rows,1,1)(),
                LET(
                    stack_expanded_rows,
                        REDUCE(
                            ,
                            IF(COLUMNS(array_of_thunks)=1,array_of_thunks,expand_rows),
                            LAMBDA(stacked,thunk,
                                vStack(IFERROR(stacked(),stacked),thunk())
                            )
                        ),
                    stack_expanded_rows
                )
            )
        )
    )
)

alignExpandThunks - Adjust dimensions of thunked arrays and ensure INDEX(thunk,1,1)() lines up with others in same row and column.
Excel Formula: 
=LAMBDA(array_of_thunks,
    LET(
        getDimCt,
            LAMBDA(dim,
               LAMBDA(thunk,
                   CHOOSE(dim,ROWS(thunk()),COLUMNS(thunk())))),
        row_cts,MAP(array_of_thunks,getDimCt(1)),
        col_cts,MAP(array_of_thunks,getDimCt(2)),
        max_row_ct_by_row,BYROW(row_cts,LAMBDA(row_,MAX(row_))),
        max_col_ct_by_col,BYCOL(col_cts,LAMBDA(col_,MAX(col_))),
        row_idxs,
          pairWise(max_row_ct_by_row,max_col_ct_by_col,
            LAMBDA(x,y,thunkIt(QUOTIENT(SEQUENCE(x,y)-1,y)+1))),
        col_idxs,
          pairWise(max_row_ct_by_row,max_col_ct_by_col,
            LAMBDA(x,y,thunkIt(MOD(SEQUENCE(x,y)-1,y)+1))),
        aligned,
          MAP(array_of_thunks,row_idxs,col_idxs,
            LAMBDA(thunk,row_idx,col_idx,
              thunkIt(
                IFERROR(
                  INDEX(thunk(),row_idx(),col_idx()),
                  "")))),
        expandThunks(aligned)
    )
)
LAMBDA_pairwise_thunks_summarize_pivot.xlsx
ABCDEFGHIJKLMNOPQRSTUVWXYZAA
1ABABCABABC
2DEFDEF
3ABCDABCDEABCDABCDE
4EFGHFGHIJEFGHFGHIJ
5IJKLKLMNOIJKLKLMNO
6PQRSTPQRST
7ABCDEFABCDEFGABCDEFABCDEFG
8GHIJKLHIJKLMNGHIJKLHIJKLMN
9MNOPQROPQRSTUMNOPQROPQRSTU
10STUVWXVWXYZ[\STUVWXVWXYZ[\
11YZ[\]^]^_`abcYZ[\]^]^_`abc
12defghijdefghij
expandThunks
Cell Formulas
RangeFormula
A1:M12A1=expandThunks(MAP(SEQUENCE(3,2), LAMBDA(num, thunkIt(CHAR(SEQUENCE(num,num+1,65,1))))))
O1:AA12O1=alignExpandThunks(MAP(SEQUENCE(3,2), LAMBDA(num, thunkIt(CHAR(SEQUENCE(num,num+1,65,1))))))
Dynamic array formulas.
 
I keep coming back to this page every time I'm doubting if I understand thunking in Lambda. I think it might be (finally) starting to sink in! Thanks for writing this up. It's an invaluable resource.
 
Hi tboulden,

I was wondering if this "thunkit" method can be further extrapolated to a multi-layer (more than 2 levels) thunking like LAMBDA(x,LAMBDA(x, LAMBDA(x))) and even LAMBDA(x,LAMBDA(x, LAMBDA(x, LAMBDA(x)))) etc.?

Of course we hardly encounter such complex calculations in practice. I just wanted to push it a little further and see how for example a 3-layer array thunking plays out.

Appreciate if you could shed some light and give an example if possible.

Many thanks.

Vince
 
vincethesun said:
Hi tboulden,

I was wondering if this "thunkit" method can be further extrapolated to a multi-layer (more than 2 levels) thunking like LAMBDA(x,LAMBDA(x, LAMBDA(x))) and even LAMBDA(x,LAMBDA(x, LAMBDA(x, LAMBDA(x)))) etc.?

Of course we hardly encounter such complex calculations in practice. I just wanted to push it a little further and see how for example a 3-layer array thunking plays out.

Appreciate if you could shed some light and give an example if possible.

Many thanks.

Vince
Click to expand...
Perhaps, but I think for it to be truly useful, it will depend on the problem being addressed. What experimenting have you done? The recycling of x as the parameter means that essentially all values passed in are lost except the last one, so not sure what the specific value is in this example.
 
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