Notebooks such as Jupyter give programming languages a level of interactivity approaching that of spreadsheets. I present here an idea for a programming language specifically designed for an interactive environment similar to a notebook. It aims to combining the power of a programming language with the usability of a spreadsheet. Instead of free-form code, the user creates fields / columns, but these can be combined into tables and object classes. By decoratively cycling through field elements, loops and other programming constructs can be created. I give examples from classical computer science, machine learning and mathematical finance, specifically: Nth Prime Number, 8 Queens, Poker Hand, Travelling Salesman, Linear Regression, VaR Attribution

1. Idea for Interactive Programming Language
Lincoln Hannah - July 2018
Notebooks such as Jupyter give programming languages a level of interactivity approaching that of spreadsheets.
I present here an idea for a programming language specifically designed for an interactive environment similar to a notebook.
It aims to combining the power of a programming language with the usability of a spreadsheet.
Instead of free-form code, the user creates fields / columns, but these can be combined into tables and object classes.
By declaratively cycling through field elements, loops and other programing constructs can be created.
I give examples from classical computer science, machine learning and mathematical finance, specifically:
Nth Prime Number, 8 Queens, Poker Hand, Travelling Salesman, Linear Regression, VaR Attribution
Input
Output
Name Formula Comments
X 5:9:2 5 7 9 Array 5 to 9 by 2
Xby2 2*X 10 14 18 increment by 1 if increment omitted
Y 4: { Y^2 < 30 } 4 5 {} indicates a do while condition
like a do while loop
Z 1:1000 1 2 3 4 5 996 997 998 999 1000
MyCol Data ABC Hello 123
Function Fn( Arg1, Arg2 ) Arg1 + 2 * Arg2 In-line function definition
Function fibonacci( n=10 ) MultiLine
1:n 1 2 3 4 5 11 12 13 14 15
fib fib.prev + fib.prev(2) 1 1 2 3 5 89 144 233 377 610
Return fib.last 610
fibonacci( 4:7 ) 3 5 8 13
My_Dict Dictionary
key 4:6 4 5 6
value Data four five six
X 5 7 9 5 7 7 9 5 7 9 Fields in adjacent rows (X and Y)
Y 4 4 4 5 5 4 4 5 5 5 whithout a specified join, does a cross-join.
Xby2 10 14 18 10 14 14 18 10 14 18 produces every combination of X and Y so
My_Dict( Y ) four four four five five four four five five five Can be used like nested loops
MyCol ABC ABC ABC ABC ABC 123 123 123 123 123
XbyY X*Y 20 28 36 25 35 28 36 25 35 45
Fn( X, Y ) 13 15 17 15 17 15 17 15 17 19
Multiple blank lines indicates end of
multi-line function
Values - First 5 Values - Last 5
Data keyword allows vaulues to be
entered directly
Default argument values (n=10)
allow example function output to be
shown within function definition.
Useful for debugging.

2. Outer_Join( X, Y ) 4 5 7 9
X 5 7 9
Y 4 5
Concat( X, Y ) 5 7 9 4 5
X_filled Str(X) 5 7 9 Manual1 haha
Y 4 2
CountX count( X ) 3
MaxX max( X ) 9
X 5 7 9
SumY sum( Y ) 9 9 9
SumXbyY sum( XbyY ) 45 76 81
FirstMatch( X ) <= 6 <=8 CatchAll
X_bucket_1st up_to_6 up_to_8 Some_Other
X 5 7 9
Y_bucket_1st up_to_6 up_to_8 Some_Other
AllMatch( X ) <= 8 <=10
X_bucket_All up_to_8 up_to_10
X 5 7 5 7 9
X_bucket_All up_to_8 up_to_8 up_to_10up_to_10up_to_10
AllMatch( X ) <= 8 <= 8 >8
Above.AND.AllMatch( Y ) ==4 ==5 CatchAll
lable A B C
X 5 7 5 7 9 9
Y 4 4 4 4 4 5
lable A A B B C C
I New MyClass( Arg1=1 ) 1
I.Arg2 1
I.Const 1.2
I.Out1 8.2
Id Generated automatically. Arg2 not
speified so gets default value from
class definition.

3. W New MyClass( Arg1=X, Arg2=Y) 1 2 3 2 4 12 18 7 14 21
X 1 2 3 1 2 2 3 1 2 3
Y 1 1 1 2 2 6 6 7 7 7
W.Out1 6.2 8.2 10.2 9.2 11.2 23.2 25.2 24.2 26.2 28.2
W.Out2 0.2 1.4 2.6 -0.8 0.4 -3.6 -2.4 -5.8 -4.6 -3.4
M1 New Matrix( nRows=3, nCols=2 ) 1
M2 New Matrix( nRows=1, nCols=2 ) 1 Alternate notatation
M1.Row 1 2 1 2 1 2
M1.Col 1 1 2 2 3 3
M1.Value Data 10 11 12 13 14 15
M2.Col 1 1
M2.Row 1 2
M2.Value Data 3 3
M3 M1.Product( M2 )
M3.Row 1 2 3
M3.Col 1 1 1
M3.Value 63 75 87
Class MyClass
ID ID-Generator 1
Arg1 Decimal 1
Arg2 Decimal 1
Const Static Decimal 1.2
Out1 Const + 2 * Arg1 + 3 * Arg2 6.2
Out2 Const * Arg1 - Arg2 0.2
Data keyword allows values to be
entered in data area
Static Data indicates cannot be
overridden when instantiated. Data
without Static are default values
only. Fields will be input (white)
Every class has an id. (like the
primary Key of a table) ID shown if
no field selected, as per Z and W
above.
Arguments set to columns / vectors
so a column of Ojbects created with
generated IDs - 1 to 21.

4. NameSpace MathLibrary
Class Matrix
ID ID-Generator 1
nRows Data 2
nCols Data 2
Row 1 : nRows 1 2
Col 1 : nCols 1 2
Row 1 2 1 2
Col 1 1 2 2
Value Data 0 0 0 0
Row==Col 1 2
Trace Value 0 0
Add Method returns Matrix
M2 Argument Matrix 1
Return New Matrix( nRows= This.nRows, nCols= This.nCols) 1
Error_If nRows != M2.nRows Error( "number of Rows must match to add Matricies" )
Error_If nCols != M2.nCols Error( "number of Columns must match to add Matricies" )
Row == M2.Row == Return.Row
Col == M2.Col ==Return.Col
Return.Value Value + M2.Value
Transpose Method returns Matrix
Return New Matrix( nRows = This.nCols, nCols=This.nRows) 1
Return.Row == This.Col
Return.Col == This.Row
Return.Value This.Value
Product Method returns Matrix
Right Argument Matrix
Return New Matrix( nRows= This.nRows, nCols= Right.nCols)
Error_If nCols != Right.nRows Error( "number of Columns of left matrix must match number of Rows of Right matrix." )
This.Col == Right.Row
Return.Value sum( This.Value * Right.Value )
Fields created within method only
visible within method (Privative
Errors produced if user tries to add
matricies of unmatched dimensions
Left, Right, Add automatically joined
on Row and Column Due to matching
Default values set in class definition
can be overwritten.

5. Class Primes
Is_Prime Method returns Boolean
x Argument Integer 32
i 2 : { i > sqrt( x ) } 1 2 3 4 5
Mod_x x mod i == 0 TRUE TRUE FALSE TRUE FALSE
x 1 >1
Return TRUE OR( Mod_x )
Nth_Prime Method returns Integer
n Argument Integer 5
i 1: {Count_Primes == n} 1 2 3 4 5 6 7
Count_Primes Is_Prime( i ) + Count_Primes.prev(First=0) 1 2 3 3 4 4 5
Return Last( i ) 7
NameSpace Poker
Class Card
ID ID-Generator 1
Suit Possible_Values Data 4 Hearts Diamonds Clubs Spades
Number Possible_Values Data 13 Two Three Four Five Six Ten Jack Queen King Ace
Class Hand
ID ID-Generator 1
C New( 5 ) Card 1 2 3 4 5
C.Suit Data Hearts Diamonds Clubs Spades Spades
C.Number Data Five Five Five Five Six
Four_of_a_Kind count( distict( C.Suit ) ) >= 4 TRUE
Three_of_a_Kind count( distict( C.Suit ) ) >= 3 TRUE
Pair count( distict( C.Suit ) ) >= 2 TRUE
Full_House Count( Distict( C.Suit ) ) >= 2 TRUE
Non static Data - set defaults to test
formulas

6. NameSpace Chess
Class Position
D1 Possible_Values 1:8 1 2 3 4 5 6 7 8
D2 Possible_Values 1:8 1 2 3 4 5 6 7 8
Class Queen
Pos New Position 1
Pos.D1 Default 6
Pos.D2 Default 4
Cross1 New Position( D1= Pos.D1, D2=1:8 ) 1 2 3 4 5 6 7 8
Cross2 New Position( D2= Pos.D1, D1=1:8 ) 1 2 3 4 5 6 7 8
Diag1 New Position 1 2 3 4 5 6
Diag1.D1 1 + max( 0 ,D2-D1) : 8 - max(0 ,D2-D1) 1 2 3 4 5 6
Diag1.D2 Diag1.D1 + D2 - D1 3 4 5 6 7 8
Diag2 New Position 1 2 3 4 5 6 7
Diag2.D1 max( 1 , x+y - 8 ) : min( 8, x+y-1 ) 2 3 4 5 6 7 8
Diag2.D2 Reverse( Diag2.D1 ) 8 7 6 5 4 3 2
Take_Pos Concat( Cross1 , Cross2 , Diag1 , Diag2 ) 1 2 3 4 29 27 28 29
Take_Pos Concat Cross1 Cross2 Diag1 Diag2 Alternative notation
Take_Pos_Col Method
Col Argument Integer 7
Take_Pos.D1 == Col
Return Distinct( Take_Pos.D2 ) 3 4 5

7. Class 8_Queen
Queens New Queen 1 2 3 4 5 6 7 8
Queens.ID 1:8 1 2 3 4 5 6 7 8
Queens.D1 Queens.ID 1 2 3 4 5 6 7 8
X New 8_Queen
X.Queens[1].D2 All 1 2 3 4 5 6 7 8
i 2:8 2 3 4 5 6 7 8
X.Queens[i].D2 All ~ X.Queens[1: i-1].Take_Pos_Col(i)
X.ID 1 1 1 1 1 1 1 1 2 2
X.Queens.D1 1 2 3 4 5 6 7 8 1 2
X.Queens.D2 * * * * * * * * * *
X.ID 1 2 3 4 5 88 89 90 91 92
Pivot
1 2 1 1 4 5 5 5 6 5 4
2 4 7 7 1 1 1 7 3 3 6
3 6 4 5 5 8 8 1 1 1 8
4 8 6 8 8 5 6 4 8 7 2
5 3 8 2 2 2 3 2 4 2 7
6 7 2 4 7 7 7 8 2 8 1
7 1 5 6 3 3 2 6 7 6 3
8 5 3 3 6 6 4 3 5 4 5
X.Queens.D2
X.Queens.D1

8. NameSpace Travelling Salesman
Import_Data C:Test.CSV
Start_City Hull Hull Hull Leeds Leeds Bath
End_City Leeds Bath Slaugh Bath Slaugh Slaugh
Time 2.2 3.4 4.2 6.3 4.2 2.2
Start_City_* concat( Start_City, End_City ) 1 1 1 2 2 2 3 4 3 4
End_City_* concat( End_City, Start_City ) 2 3 4 3 4 1 1 1 2 2
Time_* concat( Time, Time ) 2.2 3.4 4.2 6.3 4.2 2.2 3.4 4.2 6.3 4.2
Cities distinct( Start_City_* ) 1 2 3 4
Perms New Permutations( Items = Cities )
Perms All Class Members
Perms.Permutation 1 1 1 1 2 23 24 24 24 24
Perms.Item 1 2 3 4 1 2 4 3 2 1
Perms.Permutation 1 1 1 1 2 23 24 24 24 24
Start_City_* == Perms.Item 1 2 3 4 1 2 4 3 2 1
End_City_* == If( Permutation.Next == Permutation, Item.Next, Item.Prev(3)2 3 4 1 3 4 3 2 1 4
Time 2.2 6.3 2.9 9.1 7.5 5.8 1.5 6.3 2.2 4.2
Perms.Permutation 1 2 3 4 5 20 21 22 23 24
Total_Time Sum( Time ) 38.1 18.2 27.1 37.8 1.5 16.7 3.0 22.0 27.0 8.0
Min_Total_Time Min( Total_Time ) 5
Min_Time_Perm Perms.Permutation 13
Min_Time_Perm 13 13 13 13
Perms.Item 2 1 3 4

9. NameSpace Linear Regression
Function variance( x ) ( sum( x^2 ) - sum( x )^2 )/ (count(x) -1 )
Function covar( x, y ) ( sum( x*y ) - sum(x)*sum(y) )/ (count(x) -1 )
Function slope( x, y ) covar( x, y ) / variance( x )
Function intercept( x, y ) mean( y ) - mean( x ) * slope( x, y )
Import_Data C:Daily_Temp_Training_Data.CSV
Daily_Temp 20 13 19 15 27 18 28 25 13 25
Next_Day_Temp 24 13 23 19 28 21 31 30 13 29
Temp_Slope slope( Daily_Temp, Next_Day_Temp ) 0.55
Temp_Intercept intercept( Daily_Temp, Next_Day_Temp ) 11
Import_Data C:Daily_Temp_Test_Data.CSV
Daily_Temp 16 29 15 10 10 10 23 29 20 23
Predicted_Next_Day_Temp Temp_Intercept + Temp_Slope * Daily_Temp 20 27 19 17 17 17 24 27 22 23
NameSpace VaR Attribution
Import_Data C:Historical_Simulation.CSV
Rate_Schock_ID 1 1 1 1 1 500 500 500 500 500
Trade_ID 1 2 3 4 5 221 222 223 224 225
PandL 26.53 1.89 16.98 49.23 23.90 17.50 45.38 46.61 37.93 45.27
Quantile Data 95%
Number_of_Shocks count( Rate_Schock_ID ) 500
VaR_Rank Quantile * Number_of_Schocks 475
Total_PandL sum( PandL ).descending 323.0 321.5 320.3 316.8 313.9 309.4 308.6 308.4 308.2 306.6
Ordered_IDs Rate_Shock_ID 335 405 209 102 409 168 116 138 379 339
Quantile_Schock_ID Ordered_IDs.rank( Q_Rank ) 245
Quantile_Schock_ID 245
Trade_ID 1 2 3 4 5 221 222 223 224 225
Trade_VAR_Attribution PandL 113 133 141 169 140 145 182 139 172 140