Sage-Code Laboratory

Bee Data Processing

By using collections and control structures one can read, modify and store data. Bee has exquisite features to build collections and then access data elements as quick as possible to visit, extract, modify, combine or add new data.


In next chapters we will explain several design patterns that combine some of the knowledge you have so far. These examples are not yet tested but once we make a compiler this is how things should work.

Boxed values

A boxed value is a reference to a primitive type.

syntax Boxed value is an Array with a single element.

# define boxed values
make int ∈ [Z]; //boxed integer
make flt ∈ [R]; //boxed double float

boxing Boxing is the process of converting a primitive type to a reference.

make n ∈  Z;  //primitive integer 
make k ∈ [Z]; //boxed value
** check type of variable
print type(k);          //[Z]
print type(k) is Array; //1 = True
** boxing notation
alter k :=  n;  //auto-boxing
alter k := [n]; //explicit boxing
** comparison
print n = 0; //1 (true, initial value)
print n = k; //1 (true, same values)
print n ≡ k; //0 (false, different types)
** consequence
alter n := 2; //n = 2 (modify n)
print k;      //k = 0 (unmodified)
print k := 10; //auto-boxing
print n;       //n = 2 (unmodified)


Unboxing is the process of converting a reference to a primitive type. This will unwrap the value from the heap and stores it on the stack. Unboxing is always explicit. If you try to do implicit unboxing the compiler will signal an error.

make r := 10 ∈ [Z]; //reference to integer
make n := 0  ∈  Z;  //native type
** use data type like a function
alter n := Z(r);   //explicit unboxing (default notation)
alter n := r :> Z  //explicit unboxing (alternative notation)
** verify value identity
print n = r; //1 (true:  same values)
print n ≡ r; //0 (false: different types)
** consequence: variables are unbound
alter n += 2; //n = 12 (modified)
print r;      //r = 10 (unmodified)

Share vs copy

A reference can be shared between two variables. As a consequence, when one is modified the other is also modified.

example of sharing

A reference is shared using operator ":="

** create a reference using ":="
make  a := [1]; // create a reference
make  b :=  b;  // share a reference
** variable c is bound to a
pass if b = a; //1 (same values)
pass if b ≡ a; //1 (same location, same data type)
** consequence of sharing:
alter a := 2; // [2] (modify denoted value)
print a;      // [2] (new value is boxed)
print b;      // [2] (shared reference is modified)
pass if b = a; // will pass
pass if b ≡ a; // references are bound

example for cloning

** create a clone using "::"
make  a := [1]; // create a reference
make  b :: a;   // value [1]
pass if a  = b; //pass (same values)
fail if a ≡ b; //expect different locations
** consequence of cloning:
alter a := 3;
print a; // [3] (new value)
print b; // [1] (unmodified)
pass if a != b;       //no longer equal
pass if a !≡ b; //expect different locations

Array Operations


make test ∈ [R](10); //vector of 10 real numbers
make m := length(test)-1;
** array index start from 0
print test[0]; //first element
print test[m]; //last element
** alternative notation
print test[0];  //first element
print test[-1]; //last element
** array traversal 
make x := 0;
while (x < m) do
  alter test[i] := x;
  alter x += 1;
** print all elements of array
print test;




make a1 := [1, 2, 3]; //Initialized array
make a2 := [2, 3, 4]; //Initialized array
** addition between two Arrays "+" 
make a3 := a1 + a2; //[1,2,3,2,3,4]
** difference between two Arrays "-"
make a4 := l1 - l2; //[1]
make a5 := l2 - l1; //[4]
** intersection between two Arrays "&" 
make a6 := a1 ∩ a2; //[2,3]
** union between two Arrays "|" 
make a7 := a1 ∪ a2; //[1,2,3,4]


rule test_array:
  ** array  with capacity of 10 elements
  make my_array ∈ [Z](10);
  make m := my_array.capacity();
  make i := 0 ∈ N;
  ** traverse array and modify elements
  while i < m do
    alter my_array[i] := i;     
    alter i += 1;
  ** array  elements using escape template by index #[]
  print ("First element: #[1]"  ? my_array); 
  print ("Last element:  #[-1]" ? my_array);
  ** range of array elements are comma separated [1,2,3]
  print ("First two: #[1..2]"  ? my_array);
  print ("Lat two:   #[-2..-1]"  ? my_array);
  print ("All except lat two: #[1..-3]"  ? my_array);


This is the first element: 1   
This is the last element: 10   

resize Array capacity can be modified using union operator "+" or "+=". This will reset the array reference. That means it will not update any slice or other references you may have to this array.

** define new array and reference
make array := [0](10); 
make acopy := array; //copy reference
rule main():
  print array = acopy; //1 = True (same array)
  ** extend array with 10 more elements
  alter acopy    ++ [0](10); //10 new elements
  alter acopy[*] := 1; //modify all 
  ** print new array and reference
  print acopy;  //[1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1]
  print array;  //[0,0,0,0,0,0,0,0,0,0]
  print array = acopy; //0 = False (different arrays)

Array spreading

Array data can be used as arguments for feeding a function that receive variable arguments.

rule sum(*args ∈ Z) => (result: 0 ∈ Z): 
  given e <- args do 
    result += e;
make array := [1,2,3,4,5,6,7,8,9,10];
make s := sum(*array); //array spreading

Array decomposition

Array data can be assigned to multiple variables. Last elements can be captured using rest notation:

make array := [1,2,3,4,5];
make x, y, *other := [1,2,3,4,5]; //decomposition
rule main():
  print "x = #(n)" ? x;  // x = 1
  print "y = #(n)" ? y;  // y = 2
  print "other = #[*]" ? other; //other = [3,4,5]

Array slicing

A slice is a small view from a larger array, created with notation [n..m].


** declare array with capacity c
make array_name ∈ [element_type](c);
** unnamed slice can be used in expressions
print array_name[n..m]; 
** create named slice from array
make slice_name := array_name[n..m]; 

Where: n,m are 2 optional numbers, n ≥ 0, m <= capacity-1.


Anonymous slicing notation can be used to extract or modify specific elements from an array;

** initialized array
make a:= [0,1,2,3,4,5,6,7,8,9]; 
rule main():
  print a[1..-1];  // will print [0,1,2,3,4,5,6,7,8,9]
  print a[-3..-1]; // will print [7,8,9]
  print a[1..1];   // will print [0]
  print a[1..4];   // will print [1,2,3,4]
** modify first 4 elements
  alter a[1..4] += 2; 
** first 4 elements of (a) are modified
  print a; //[2,3,4,5,4,5,6,7,8,9]


Slicing notation can be used to create a view to original array.

** original array
make a:= [0](5); //[0,0,0,0,0]
** making two slices
make c := a[1..3]; //[0,0,0]
make e := a[4..5]; //[0,0]
rule main():
  ** modify all slice elements
  alter c[*] := 1;
  alter e[*] := 2;
  ** original array is modified
  print a; //[1,1,1,2,2]
  ** modify last 2 elements using anonymous slicing
  alter a[-2..-1] := [2,3];  
  print a; //[1,1,1,2,3]

Matrix Operations

Modify all elements of the matrix is possible using [*] and assign operator “ := ”

** a matrix having 2 rows and 2 columns
make M ∈ [Z](2,2);
rule main():
  M[*] := 100; //initialize all elements with 100
  print (M);   //[[100,100],[100,100]]
#define a shared matrix
make M ∈ [Z](2,2);
rule main():
** assign same value to all elements
  M[*] := 100;
** modify all elements
  M[*] += 10;
  print(M); //[[110,110],[110,110]]
** modify an entire row 
  M[1,*] := 0;
  M[2,*] := 1;
  print(M); //[[0,0],[1,1]]
** modify an entire column
  M[*,1] += 1;
  M[*,2] += 2;
  print(M); //[[1,2],[2,3]]

matrix addition Two matrices can be added to each other if they have the same dimensions.

** creation of matrix with 10 × 10 elements
make M  := [1](10,10) + [2](10,10); //type inference
** verify the result is a matrix of same dimensions  
pass if M = [3](10,10); //expected

Memory impedance

Matrices are multidimensional while computer memory is linear. This is an impedance mismatch that require mapping. Some computer languages organize matrices row by row and some others organize memory column by column. The difference between the orders lies in which elements of an array are contiguous in memory.

Row-major and column-major order

Transposition Passing a memory matrix from one computer language into another can require a transposition that can be a performance bottleneck. EVE uses row-major order therefore passing matrix arguments is the most efficient with Rust and C++ languages.

Matrix Traversal When you traverse elements use rows first, than you change the column. A processor will use the internal cache more efficient in this way. If the matrix is large this can be a significant performance issue.

Example: In this example we traverse all the rows then all the column, this is the most efficient way to traverse a matrix.

# define a matrix using unicode literal
make M := ⎡'a0','b0','c0'⎤
rule main():
  ** local control variables
  make row, col := 0;  // type inference: ∈ Z
  ** traverse matrix with index pattern     
  while col < 3 do     // traverse columns
    while row < 3 do   // traverse row first
      print M[row,col];
      alter row += 1;
    alter col += 1;
  ** traversal with visitor pattern
  given e <- M do
    print e; //element

Collection Builders

Set Builders

A set builder is a declarative structure used to produce a sub-set from a set. It can take elements from one set and filter them or translate them into new values using a map() that can be a deterministic rule.


Most common is to make a set from a range of values after we filter out some values:

make new_set  := { var | var ∈ range ∧ filter(var)};

Map rule:

More general we can use a map() rule to convert the source elements that can be a range or a list. The elements of the new set are calculated by the map() rule.

# simple builder
make set_name := { map(x) | x ∈ source ∧ filter(x)};



# define new sets of integer numbers
make test1, test2 ∈ {Z};
** populate the sets with new values
alter test1 := { x  | x ∈ (1..3)};
alter test2 := { x² | x ∈ (1..3)};
** expected result
fail if test1 ≠ {1,2,3};
fail if test2 ≠ {1,4,9};

Hash-Map Builder

A map builder can create also a hash map by using a "map" rule. A map is just a rule that create a value for each key. For example x² can be a map rule.


make map_name := { (key:map(key)) | (key ∈ source) ∧ filter(key)}



New map defined from a domain

# define hash-map using a map-builder
make  new_map := { (x:x²) | x ∈ (0.!10) ∧ (x % 2 = 0) }; 
rule main():
  print new_map; //{(0:0),(2:4),(4:16),(6:36),(8:64)}

Array Builder

Similar to a set builder you can initialize an array or matrix:

make array  := [ x | x ∈ (1..10:2) ]; //[1,3,5,7,9]

Logic Qualifiers

Logic quantification verify a domain to satisfy a condition. The two most common quantifiers are: "all" and "exists".


Qualifiers can be used as logical expressions in statements: { when, if, while etc. }.


∃ (x ∈ DS) ∧ condition(x);
∀ (x ∈ DS) ∧ condition(x);


** create a set of bit-masks
make here := {0b10011,0b10001,0b11101};
make verify ∈ L; //logical flag
** verify if any mask element has second bit from the end
alter verify := ∃(x ∈ here) ∧ (x ⊕ 0b10 = x);
** verify if all elements in Here have first bit from the end
alter verify := ∀(x ∈ here) ∧ (x ⊕ 0b01 = x);

Collection Casting

It is common for one collection to be created based on elements from another collection. Collection members can be copy into the new collection using collection builder:


make source := [0,1,2,2,2,2];
rule main():
  make set := { x | x ∈ source }; //eliminate duplicates
  print set; //{0,1,2} 

Collection Filtering

Build notation can use expressions to filter out elements during build.


make source := [0,1,2,3,4,5];
rule main()
  make set := { x | x ∈ source ∧ (x % 2 = 0) };
  print set; //{0,2,4} 

Collection Mapping

The elements in one set or list can be transformed by a function or expression to create a new collection.


make source := {0,1,2,3,4,5};
rule main():
  ** create Table pairs (key, value) for Table map   
  make target := {(x:x^2) | x ∈ source };
  print target; //{ 0:0, 1:1, 2:4, 3:9, 4:16, 5:25} 

List Operations

We can add elements to a list or remove elements from the list very fast:

List Concatenation

List concatenation is ready using operator “+”. This operator represent union. Therefore union act very similar to append, except we add multiple elements at the end of first list and we create a new list as result.

make a := ('a','b','c');
make b := ('1','2','3');
rule main():
  make c := a + b;
  print c; //('a','b','c','1','2','3');

Join built-in

The join function receive a list and convert elements into a string separated be specified character.

rule main():
  make str := join([1,2,3],',');
  print (str); //'1,2,3';

Split built-in

The join function receive a list and convert elements into a string separated be specified character.

rule main():
  make lst := split("1,2,3",",");
  print lst; //(1,2,3)

List as stack

A stack is a LIFO list of elements: LIFO = (last in first out)

make a := (1, 2, 3); //list
make last ∈ N;
rule main():
  ** append operator: "<+"
  alter a <+ 4; //(1,2,3,4)
  ** read last element
  alter last := a.tail; //last = 4
  ** delete operator "-="
  alter a -= last; //a = (1,2,3)

List as queue

A queue is a FIFO collection of elements: (first in first out)

make q := (1,2,3); 
make first: N;
rule main():
   ** enqueue new element into list "++" 
   alter q <+ 4; //(1,2,3,4)
   ** read first element using ":="
   alter first := a.head; //first = 1
   ** shift list to left with 1
   scrap a << 1; //a = (2,3,4)

Other built-ins

Following other rules should be available

Special attributes

A list has properties that can be used in logical expressions:

Collection Iteration

Collections have common rules that enable traversal using for statement.


Available for: {List, Table, Set} but not Array or Slice


rule main():
   make my_map := {("a":1),("b":2),("c":3)};
   given (key, value) <-;   my_map do
     print('("' + key + '",' + value +')');

Will print:


Hash collections

Hash tables are sorted in memory by key for faster search. It is more difficult to search by value because is not unique and not sorted. To search by value one must create a cycle and verify every element. This rule is very slow so you should never use it.


** check if a key is present in a hash collection
make my_map := {(1:'a'),(2:'b'),(3:'c')};
rule main()
   make my_key := 3;
   when my_key ∈ my_map do
     print("True"); //expected


make animals ∈ {S,S};
rule main():
  alter animals["Bear"] := "dog";
  alter animals["Kiwi"] := "bird";



Type inference


make animals := {}; //partial declaration
rule main():
  ** establish element types (S:X)
  alter animals["Rover"] := "dog";
  ** use direct assignment to create 2 more element
  alter animals["Bear"] := "dog";
  alter animals["Kiwi"] := "bird";



String: concatenation

Strings can be concatenated using:


** this is example of string concatenation
make str := ""; 
rule main():
  ** stupid fast concatenate two string as they are
  alter str := "this " + " string"; //"this  string"
  ** smart slower concatenation for path or url
  alter str := "this/  " / "  string";   // "this/string"
  alter str := "c:\this" . "is\path";         // "c:\this\is\path"
  alter str := "https:" . "";    // ""

path concatenation Two strings can be concatenated using concatenation operator "/" or "\". This operator is used to concatenate "path" strings or URL locations. Notice "\" is also escape character used for string templates.

make s := "";
rule main()
  alter s := "te/" / "/st"; //"te/st"
  alter s := "te/" \ "/st"; //"te\\st"
  alter s := "te"."st"; //"te\\st" or "te/st" depending on OS

String Generator

Replication operator: "*" will concatenate a string with itself multiple times:

** create string of 10 spaces
make s := ' ' * 10;


rule main():
  ** make a string from pattern 01
  make  a := "01" * 4;
  print a; //01010101;
  ** used in expression will generate string
  make  b := (a & ' ') * 4;
  print b; //01010101 01010101 01010101 01010101

String Pattern

It is common to create strings from a string pattern using operator "*".

make str := constant * n ∈ S(n);


make sep := '-' * 19;
rule main():
  print ('+' + sep + "-");
  print ('|   this is a test   |');
  print ('+' + sep + '+');


|  this is a test   |

Control codes

You can insert constants using notation $X or #(nn):


00 0x00 $NL Null
08 0x08 $BS Backspace
09 0x09 $HT Horizontal Tab
10 0x0A $LF Line Feed
11 0x0B $VT Vertical Tab
12 0x0C $FF Form Feed
13 0x0D $CR Carriage Return
27 0x1B $ES Escape
39 0x27 $AP Apostroph ''
34 0x22 $QM Quotation ""

String Interpolation

In computer programming, string interpolation is the process of evaluating a string literal named template that contains one or more placeholders. An interpolation expression is yielding a result in which the placeholders are replaced with their corresponding values.

We use notation "#()" or "#()[]" to create a placeholder template inside of a String or Text. You can use operator "?" to replace the placeholder with values from a data source. If placeholder is not found the result will contain the placeholder unmodified.



** next template uses #(n) placeholder
make template := "Duration:#(n) minutes and #(n) seconds";
make var1 := 4; 
make var2 := 55;
rule main():
  print template ? (var1,var2,...); //Duration:4 minutes and 55 seconds


** define two A codes
make x := 30; //Code ASCII 0
make y := 41; //Code ASCII A
rule main():
   ** template writing alternative
   print "#(n) > #(n)" ? (x,y); //"30 > 41" 
   print "#(a) > #(a)" ? (x,y); //"0 > A"  
   ** using two dots : to separate hour from minutes 
   print "#(n):#(n)" ? (10, 45); // 10:45
   ** using numeric format
   print "#(1,000.00)" ? (1000.45); // 1,234.56


Format template stings can use escape sequences:

"#(n)"   = natural number 
"#(z)"   = integer number
"#(r)"   = real number using default precision
"#(s)"   = single quoted string for string, symbol or number
"#(q)"   = double quoted string for string, symbol or number
"#(a)"   = ASCII symbol representation of code
"#(u)"   = Unicode symbol representation of code
"#(+)"   = UTF16 code point representation (U+HHHH) for symbol
"#(-)"   = UTF32 code point representation (U-HHHHHHHH) for symbol
"#(b)"   = binary number
"#(h)"   = hexadecimal number
"#(t)"   = time format defined by @time
"#(d)"   = date format defined by @date
"#[*]"   = display array elements (separated by comma)
"#[i]"   = search element by index [i]
"#[k]"   = search element by key value [k]


print "Numbers:   #(n) and #(n)" ? (10, 11);
print "Alpha:     #(a) and #(a)" ? (30, 41);
print "Strings:   #(s) and #(s)" ? ('odd','even');
print "Quoted:    #(q) and #(q)" ? ('odd','even');
print "Unicode:   #(u) and #(u)" ? (U+2260,U+2261);
print "Unicode:   #(q) and #(q)" ? (U+2260,U+2261);
print "Collection:#[*] and #[*]" ? ([1,2,3],{'a','b','c'});
print "Collection:#(s)[*] and #(q)[*]" ? ([1,2,3],{'a','b','c'});

Expected output:

Numbers:   10 and 11
Alpha:     0 and A
Strings:   'odd' and 'even'
Quoted:    "odd" and "even"
Unicode:   ≠ and ≡
Collection:1,2,3 and a,b,c
Collection:'1','2','3' and "a","b","c"


Large template

A large template can be stored into a file, loaded from file and format().

  1. Create a map collection of elements;
  2. Create the template text and store it in external file;
  3. Use a cycle to visit the template file row by row;
  4. Use template modifier: "?" to replace placeholders row by row;
  5. Alternative use format() build-in rule to replace all placeholders;

Using Hash:

make template1 := "Hey look at this #[key1] it #[key2]!";
make template2 := "Hey look at this #(s)[key1] it #(q)[key2]!";
make map       := {("key1":"test"),("key2":"works")};
rule main():
  print template.format(map);
  print template ? map;

Expect output:

Hey look at this test it works!
Hey look at this 'test' it "works"!

Using Set:

make  template := "Hey look at this #[0] it #[1]!";
make  my_set   := {"test","works"};
rule main():
  print template ? my_set; 

Expect Output:

Hey look at this test it works!

Numeric format

Number type is implementing format() rule. This rule has one string parameter that is optional.

# format signature
rule format(number ∈ R, pattern ∈ S) => (result ∈ S):

Where pattern cab gave two forms:

Note: Last pattern is depending on regional settings: $decimal:'.'/','

Alignment symbol "a" can be one of:

> is used to align to the right
< is used to align to the left
= is used to align to center

Format examples:

 "#(r)"       // real number, with default precision left align 
 "#(n)"       // natural number, unsigned left align
 "#(z)"       // integer number, with sign left align
 "#(10)"      // right align numeric with 10 digits padded with spaces
 "#(10.2)"    // 10 integer digits and 2 decimals, right padded with spaces
 "#(>_:10)"   // right align 10 digits padded with spaces
 "#(>0:10.2)" // right align padded to 10 integer digits and 2 decimals
 "#(>0:10,2)" // right align European numeric style with 2 decimals

Text rules:

Reading a Text:

Text is iterable by "row". The row separator CR or CRLF. So we can read a text line by line. You can use for iteration to check every line of text. Each row is a string. You can also parse a row word by word using a nested for.

Note: The text also support escape sequences like a normal string. However in a text literal we do not have to escape the single quote symbols: "'". We have to escape the double quotes like: "This is "quoted" text". This is very rare since quoted text should use symbols: "« »" like "«quoted»".


This was the Bee draft design for basic concepts. Thank you for reading it all. To watch this project growing we need your support. Contact us on Discord. We have a special channel where we discuss Bee design and construction. Our effort has mearely begun. There is a lot of testing and developing ahead of us.

Read next: Coroutines