Bee use several kind of data types described below. Use these links to jump to a particular data type. Use browser back-button to revisit a particular data type:
Bee is using a gradual typing system. We think dynamic typing is more fragile and prone to errors. Therefore Bee is a strongly typed language with type inference. That means any data is constrained by fixed "data type" rules.
Bee has predefined data types. You can create new data types based on predefined types using a type declaration. You can create sub-types or composite types having new constraints and rules that can improve data validation further.
A data type can be manipulated using rules and operators. You can have a variable of type: Type. To detect a data type of any variable you can use the introspection function type().
Primitive data types are defined using one capital letter. This may be unusual in Computer Science but standard in Mathematics. Therefore Bee uses this convention.
Alias | Code | Description + Default representation |
---|---|---|
Boolean | B | Boolean or 8 bit number, 0 = False, >= 1 True |
Alpha | A | Alpha-numeric E-ASCII ('0'..'9') ('a'..'Z') |
Unicode | U | Unsigned 32 bit, max: U-FFFFFFFF (UTF32) |
Rational | Q | Fix point representation number: like 1/2. Notation: Q(14,17) |
Natural | N | Unsigned large positive integer 64 bit [0..+] |
Integer | Z | Signed large integer 64 bit [-..+] Z(64) |
Real | R | Double precision float 64 bit (-..+) R(64) |
These are symbolic representations for primitive data types:
Example | Type | Literal characters |
---|---|---|
'a' | A | (+-) & (0..9) & (a..z) & (A..Z) |
'Ω' | U | (Δ Λ Φ Γ Ψ Ω Σ Π π ⊥ ǁ α β ɣ ε δ μ ω ...) |
"str" | S | (∀ UTF8) |
0b0,0b1 | B | (0,1) & B |
1234567890 | N | (0,1,2,3,4,5,6,7,8,9) |
+0 | Z | (-+) & (0,1,2,3,4,5,6,7,8,9) |
'a','b' | A | ASCII (0x00..OxFF) |
U+FFFF | U | (U+) & (0,1,2,3,4,5,6,7,8,9) & ABCDEF |
U-FFFFFFFF | U | (U-) & (0,1,2,3,4,5,6,7,8,9) & ABCDEF |
0.05 | R | (-.) & (0,1,2,3,4,5,6,7,8,9) |
-1/2 | Q | (-/) & (0,1,2,3,4,5,6,7,8,9) |
1E10 | R | (-1E)& (0,1,2,3,4,5,6,7,8,9) |
1e10 | R | (-1e)& (0,1,2,3,4,5,6,7,8,9) |
note
Special types have an alias starting with capital letter. These types are embeded in the language and contribute to language coherence. All these types are actually references to memory structures:
Alias | Type | Description |
---|---|---|
Complex | C | Double precision pair of double float numbers (9r+9j) |
String | S | UTF8 encoded double quoted string "α β ɣ ε δ μ ω" |
Date | D | "DD/MM/YYYY" |
Time | T | "hh:mm,ms" |
Lambda | L | Lambda expression or function. |
Bee define a collection literal using a special notation based on brackets. These types are going to be explained later in another page. We mention these types here because they represent types.
delimiter | collection types |
---|---|
() | List |
[] | Array / Matrix |
{} | Set / Map / Object / Ordinal |
User can define type alias using operators ":" and sub-types using operator "<:" (inheritance). Usr can specify type of variables explicit usin operator ∈
** declare new type alias
type Type_Identifier: type_descriptor <: super_type;
** declare variables using type alias
new var_name ∈ Type_Identifier;
** declare many variables using type alias
new var_name, var_name ... ∈ Type_Identifier;
A range is a notation that designate a sub-set of consecutive integer numbers between two limits: lower limit and upper limit included in round parenthesis and separated by two dots (..) or (!).
range ::= (min..max); range ::= (min.!max); -- exclude upper limit range ::= (min!.max); -- exclude lower limit
#integer domain
rule main:
print (0..5); -- 0,1,2,3,4,5
print (0.!5); -- 0,1,2,3,4
print (0!.5); -- 1,2,3,4,5
pass if 32667 ∈ (0..+); -- expect to pass
pass if -32668 ∈ (-..0); -- expect to pass
return;
Ranges can use symbols that are ASCII or Unicode. In this case the symbols must be included in single quotes: 'X' or use U+ notation:
** sub-type declarations
type .Digit: ('0'..'9') <: Z;
type .Capital: ('A'..'Z') <: A;
type .Lowercase:('a'..'z') <: A;
type .Latin: (U+0041..U+FB02) <: U;
rule main:
** following statements should pass
pass if '0' ∈ Digit;
fail if 'x' ∈ Capital;
pass if 'X' ∈ Capital;
pass if 'e' ∈ Latin;
return;
Domain is very similar to range except a domain has a ratio. This is the difference, the numbers are not integers, can be fractional or Q umber.
type Domain: (min..max:ratio) <: Super_Type;
** generate rational numbers
print (0..1:1&\4); -- 0&\4, 1&\4, 2&\4, 3&\4, 1
** generate float numbers
print (0..1:0.25); -- 0.00, 0.25, 0.50, 0.75, 1.00
Constants literals bound to identifiers using keyword "set".
** using explicit type
set constant_name: constant_literal ∈ type_name;
** using implicit type
set constant_name := constant_literal;
#define symbol constants
set forall1: U+2200 ∈ A; -- Symbol: ∀
set forall2: U-00002200 ∈ U; -- Symbol: ∀
Variables are defined using type inference and these operators:
operator | purpose |
---|---|
∈ | declare variable/element type |
: | define | block start | pair up operator |
: | set initial value (require type in declarations) |
:= | type inference | share a reference | assign operator |
:: | deep copy | duplicate object | cloning operator |
** primitive variable declarations with type
new var_name ∈ type_name; -- declaration only type without initial value
new var_name: value ∈ type_name; -- declaration with initial value and type
** Variable declaration using type inference
new var_name := expression; -- expression ":=" do not require type hint ("∈").
** Multiple variables can be define in one single line using comma separator:
new var1, var2 ... ∈ TypeName; -- default initial values
new var1, var2 ... := Expression; -- use type inference for all initial values
** Initialize multiple variables, of the same type (type is required)
new var1:con1, var2:con2 ... ∈ TypeName;
One can modify variables using alter statement.
#fragment of code
new a:10, b:0 ∈ Z; -- initialize two variables
let b := a + 1; -- modify b using binding operator :=
let b += 1; -- modify b using modifier +=
expect b = 12; -- check if b has proper value
** declare a public constant
set .PI: 3.14 ∈ R;
rule main:
** declare a single variable
new a ∈ Z; -- Integer
** declare multiple variables
new (x,y):0 ∈ R; -- Double
new (q,p):0 ∈ L; -- Logic
** using modifiers
let a := 10; -- modify value of: a == 10
let a += 1; -- increment value of: a == 11
let a -= 1; -- decrement value of: a == 10
** modify two variables using one single constant
let x, y := 10.5;
** modify two variables using two constants
let q, p := True, False;
** swapping two variables
let p, q := q, p;
return;
When data type mismatch you must perform explicit conversion.
** data conversion
rule main:
new a:0, b:20 ∈ Z;
new v:10.5, x:0.0 ∈ R;
** explicit conversion
let a:=v :> N;
print a; -- truncated to 10
** explicit conversion
let x := b :> R;
print x; -- expect 20.00
return;
Bee define A as single UTF-8 code point with representation: U+HH
rule main:
new a, b ∈ A; -- ASCII
new x, y ∈ B; -- Binary integer
let a :='0'; -- ASCII symbol '0'
let x := a :> B; -- convert to binary 30
let y := 30; -- decimal code for '0'
let b := y :> A; -- convert to ASCII symbol '0'
return;
You can use symbol ":=" to initialize variables using type inference.
** declare constants
set i := 4; -- integer constant
set r := 2.5; -- real constant
set q := 1&\8; -- rational constant
** declare variables
new x := 0; -- integer number
new y := 0.0; -- real number
new z := 0\1; -- rational number
We can use variable type to validate expression type.
** using type inference
rule main:
new a := 0; -- integer variable
new b := 0.0; -- real variable
let a:= 10.5; -- error: explicit conversion is required
return;
You can use operator "∈" to verify data type:
rule main:
new a := 0 ∈ Z;
** expected: Integer
expect a ∈ Z;
return;
Boolean type is Bee is native numeric of type B. However we also implement native two constants True, False that are publicly available in core library
** overwrite the default values
set False = 0;
set True = 1;
Printing native Boolean values is going to print numbers. Type B can support a number between 0b0 and 0b00000001. Therefore printing this type is done using notation 0b0 and 0b1.
** printing Boolean values
rule main:
print False; -- 0b0
print True; -- 0b1
return;
You can convert B to a number, safely. You can convert a number to B explicit using cast operator: number :> B.
The number will loose all it's significance and become 0b1 or 0b0.
Bee uses several familiar logic operators from mathematics:
Precedence: { ¬, ∧, ∨ }. Symbol ¬ will apply first, symbol ∨ will apply last.
bitwise
In Bee we define special operators to perform bitwise operations. One opperator is overwrite: ⊕. This operator (xor) can operate on both, logical values or expressions and also on integer numbers.
# bitwise operations
print 4 | 3; -- out:7 is because 100 | 011 = 111 = 7;
print ~4; -- out:3 is because: 100 ~ 100 = 011 = 3;
print 4 & 7; -- out:4 is because: 100 & 111 = 100 = 4;
print 4 ⊕ 4; -- out:0 is because: 100 ⊕ 100 = 000 = 0;
print 1 << 2; -- out:2 is because: 001 << 2 = 100 = 4;
print 6 >> 2; -- out:1 is because: 110 >> 2 = 001 = 1;
Comparison operators will create a Boolean response: 1 = True or 0 = False. Also, the equivalent and belonging operators will create a Boolean response. You can combine them to create Boolean expressions.
rule main:
new (x, y):4 ∈ Z; -- primitive integer
** value comparison
print x = 4; -- 1 (equal)
print x ≡ 4; -- 1 (identical)
print x = y; -- 1 (equal)
print x ≡ y; -- 1
print x ≠ 5; -- 1 (different)
print x!≡ 5; -- 1 (not identical)
** reference ordering
print x ≥ y; -- 1: x and a are actually equal
print x ≥ 4; -- 1: greater or equivalent to 4
print x ≤ 4; -- 1: less than or equivalent to 4
print x > 4; -- 0: not greater than 4
print x < 4; -- 0: not less than 4
** arithmetic expressions have primitive results
print x - 4 = 0; -- 1
print x - 4 ≡ 0; -- 1
return;
singleton
Primitive types are unique. That means they are equivalent. A literal or constant is equivalent to another literal having the same value.
** primitive values are singleton
print 1 ≡ 1; -- 1
print "s" ≡ "s"; -- 1
** alternative operator have the same significance
print 1 == 1; -- 1
print "s" == "s"; -- 1
Precedence:
Logic operators have greater precedence than comparison operators.
Logical expression have value { 0 = False, 1 = True }
** define constants based on Boolean values
set f: False;
set t: True;
rule main:
** expressions with single operant
print f; -- 0
print ¬ t; -- 0
** expressions with two operands
print (f = t); -- 0
print (f ≡ t); -- 0
print (f ≠ t); -- 1
print (f < t); -- 1
print (f > t); -- 0
print (f ∧ t); -- 0
print (f ∨ t); -- 1
print (f ⊕ t); -- 1
return;
coercion Any numeric expression can be converted to a logic value using coercion operator ":>" (easy to memorize if you think is like an arrow).
set (a: 0.0, b: 1.5) ∈ R;
rule main:
new (x, y) ∈ B;
let x := a :> B; -- 0
let y := b :> B; -- 1
return;
design
** logical values are numeric
print True ≡ 1; -- 1
print False ≡ 0; -- 1
** logical values do not compute
print False - True; -- Error
print True + True; -- Error
** Null value is not True
print Null ≡ True -- 0
** Null value is not False
print Null ≡ False -- 0
Type inference is a logical deduction of data type from constant literals.
Each literal has associated a default type, induced by operators {":=", "::"}.
** string expressions
new c := 'a' ; -- type = A
new s := '∈' ; -- type = U
new s := "str" ; -- type = S
** numeric expressions
new i := 0; -- type = Z
new j := 0.50; -- type = R
** define synonyms for logic constants
set f := False; -- type B
set t := True; -- type B
** multiple variables get same value
new (x, y, z) := 5; -- type = Z for all
** multiple variables get multiple values
new int, rea := -4, 4.44;
print type(int); -- Z
print type(rea); -- R
Composite structures are using () [] and {} to create different data types. Next you can study some examples. We wil explain later all these types: List, Map, Array, Object. All of these are also called Bee collections.
** boxed integer (type = Z)
new i := [10]; -- array of one value = 10!
** array with capacity of 4 integers: Z
new d := [1,2,3,4];
** array with capacity of 10 real numbers: R = 0.00
new e := [0.00](10);
** list of one value (Z)
new a := (1);
** list of integers (Z)
new b := (1,2);
** list of symbols (type = A)
new l := ('a','b');
** list of Unicode symbol (type = U)
new u := ("Δ", "Λ", "Γ");
** 2d matrix with capacity of 10x10 real numbers: R
new m := [0.00](10,10);
** 3d matrix with capacity of 10x10x10 reals: R = 0.00
new m := [0.00](10,10,10);
** data set of 4 integers: Z
new s := {1,2,3,4};
** hash map of (Integer: String)
new c := {1:"storage",2:"string"};
** object with two attributes: name ∈ S, age ∈ Z
new b := {name:"Goliath", age:30};
When we define parameters we can use type inference only for optional parameters. Mandatory parameters must have type declaration using ∈ symbol. If default value is not specified the parameter will have defailt zero initial value.
Optional Parameters:
** in rule foo, parameters a, b are optional.
rule foo(a: 0 ∈ Z, b: 0 ∈ Z) => (r ∈ Z):
let r := a + b;
rule;
rule main:
print foo(); -- 0
print foo(1); -- 1
print foo(1,2); -- 3
return;
Multiple parameters:
** parameters: a, b are mandatory, c is optional.
rule foo(a, b, c:0 ∈ Z) => (r ∈ Z):
let r := a + b + c;
return;
rule main:
print foo(1,2); -- 3
print foo(1,2,3); -- 6
print foo(1); -- Error: expected 2 arguments
return;
Pass arguments by name:
We can use parameter name and pair-up symbol ":" for argument value.
** rule with optional parameter (c)
rule bar(a, b, c:0 ∈ Z) => (result ∈ Z):
let result := a+b+c;
return;
** observe we use pair-up ":" to give value for each argument
rule main:
print bar( 1, 1 ); -- print 2 because c = 0
print bar( a:1, b:1, c:1 ); -- print 3 because c = 1
return;
In mathematics rational number is any number that can be expressed as the fraction p/q of two integer numbers: numerator "p" of type integer and a non-zero denominator "q" of type natural> 0.
Since "q" may be equal to 1, every binary integer is also a rational number.
Note: Q numbers are approximated numbers.
Other precision constants:
Literal Notation: p\q
It can be used with type inference to create Q numbers:
new x: 0 ∈ Q; -- 0
new a: 1\2 ∈ Q; -- 0.5
new b: 1\4 ∈ Q; -- 0.25
new c: 1\8 ∈ Q; -- 0.125
new d: 1\16 ∈ Q; -- 0.062
new e: 1\32 ∈ Q; -- 0.031
Qm.n is m+n+1 bit signed integer container with n fractional bits.
Qm is a m+1 bit signed integer containing 0 fractional bits.
number of bits = m+n+1
precision is 2⁻ⁿ
range is [-(2ᵐ)..(2ᵐ-2⁻ⁿ)]
For example: Number format "Q5.2" can store in range (-32.00..31.75) on 8 bits.
new v ∈ Q5.2;
let v := -32; -- minim value
let v := 31.75; -- maxim value
See also: wikipedia
Next I have predefined some numbers for orientation.
rezolution -> | 1\4 ≈ | 1\8 ≈ | 1\16 ≈ | 1\32 ≈ | 1\64 ≈ |
---|---|---|---|---|---|
↓ memory space | ±0.25 | ±0.125 | ±0.062 | ±0.031 | ±0.015 |
8 bytes | Q(5.2 ) | Q(4.3 ) | Q(3.4 ) | Q(2.5 ) | Q(1.6 ) |
16 bytes | Q(13.2 ) | Q(12.3 ) | Q(11.4 ) | Q(10.5 ) | Q(9.6 ) |
32 bytes | Q(29.2 ) | Q(28.3 ) | Q(27.4 ) | Q(26.5 ) | Q(25.6 ) |
64 bytes | Q(61.2 ) | Q(60.3 ) | Q(59.4 ) | Q(58.5 ) | Q(56.6 ) |
128 bytes | Q(125.2) | Q(124.3) | Q(123.4) | Q(122.5) | Q(121.6) |
Note: r ≈ is the approximate resolution.
A very large number with high resolution on 64 bit:
Q(50.12)
A number on 32 bit with resolution = 0.0005:
Q(20.11)
Q(14.17)
Bee is using default Q type for type inference, when precision is not specified. Default Q number has precision 10⁻⁵ = 2⁻¹⁷ ≈ 0.00001 and occupy 32 bit. It's a relative small number. For larger numbers you must specify the resolution and capacity.
Rational numbers and other numbers can be compared using "≈" instead of "=". Bee can be used to make aproximative computations and logic expressions based on precision.
In next example b = 0.33(3), delta = (b - a) = 0.083
** override default precision
set $precision := 0.01;
rule main:
new a := 0.25; -- real
new b := 1\3; -- rational O.33(3)
** using specified precision 0.01
print (a ≈ b); -- 0B0: (False, 0.033 - 0.25 = 0.08 )
** using specified precision:
print (a ≈ b ± 0.01); -- 0b0 (False)
print (a ≈ b ± 0.05); -- 0b0 (False)
print (a ≈ b ± 0.10); -- 0b1 (True)
return
Rational numbers are similar to complex numbers. The calculation of rational number is postponed until is necesary in expressions and it can produce different results depending on the precision.
** execute conversion
rule main:
new a := 0.25; -- real
new b := 1\4; -- rational
** explicit conversion R :> Q
expect a ≠ b; -- not equal, type mismatch
expect a ≈ b; -- values match, aproximation
expect a ≡ b; -- implicit conversion, match
** explicit conversion R :> Q
new c := a :> Q;
expect c = b; -- type & value match
expect c ≡ b; -- type & value match
** implicit conversion Q :> R
new r := c ∈ R;
expect c = 0.25;
return
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