Sage-Code Laboratory

EVE Data Types

The purpose of any programming language is to manipulate data. On the lowest level, data is basicly 0 and 1 signals. EVE is a high level language so our idea of data type is more complex. EVE has a gradual-typing system that will be explaine below.

Let's describe the basic types:


Primitive Types

Class Name Description Minim Maxim
Integer Signed on 64 bit -2⁶³ 2⁶³-1
Natural Unsigned on 64 bit 0 2⁶⁴-1
Decimal Float precision number on 8 bytes 0 1.8 × 10³⁰⁸
Unicode Single Unicode symbol UTF-32 4 bytes 0 2³²-1
Ordinal Enumeration of symbols, Short 16 bit 0 2¹⁶-1
Date Calendar date 01/01/0001 01/01/9999
Time Time of the day (24h) 0 8.64e+7ms
Logic Is a Ordinal subtype having values: False = 0, True = 1 0 1
Note: Primitive types get zero initial values automatically an can not be Null. This is a major thing in EVE. No null primitive-types!

Numeric Types

In EVE we can have two categories of numbers:

Category EVE Types
Discrete Ordinal, Integer, Natural, Range
Continuous Single, Double, Decimal, Domain

Discrete numbers:

type Chars Bytes min max maximum number
Integer 20 8 -2⁶³ 2⁶³-1 ≤ 9,223,372,036,854,775,807
Natural 20 8 0 2⁶⁴-1 ≤ 18,446,744,073,709,551,615

For conversion into characters:

Continuous numbers

The type Double is represented using floating precision numbers.
Floating decimal numbers are most simply described by 3 Integers:

The numerical value of a finite number is −1ˢ × c × 2ⁿ Using this formula EVE define two floating point types.

Single: is single-precision 32-bit IEEE 754:
Double is double-precision 64-bit IEEE 754:

type Digits Bytes maximum number
Single 7 4 ≤ 3.4 × 10³⁸
Double 16 8 ≤ 1.8 × 10³⁰⁸

Precision is variable depending on the size of the number. The number of digits represents the largest number that can be converted from string format into a Double and back without loosing any digit. Think of it like a digital display from a packet calculator.

Numeric literals

Example Description
0 Integer zero
123 Integer number using symbols: {0,1,2,3,4,5,6,7,8,9}
1/2 Single number use symbols: {.,0,1,2,3,4,5,6,7,8,9}
0.5 Double number use symbols: {.,0,1,2,3,4,5,6,7,8,9}


#numeric literals
routine main:
    Integer i; // Initial value = 0
    Natural n; // Initial value = 0
    Double  r; // Initial value = 0.00
    i := 9223372036854775807;  //  maximum
    n := 18446744073709551615; //  maximum
    r := 1/2; //  0.5

See also: scientific notation

Composite Types

Composite data types are unions of data elements. A composite variable that is not initialized can have Null value that is similar to zero but different. Some of these types are going to be explained later. We enumerate them all here to grasp the idea.

Class Name Description
Range Integer range of numbers equaly distanced (x..y:ratio)
Domain Decimal range of numbers equaly distanced [x..y:ratio]
String Limited capacity string: ('single quoted')
Text Unlimited capacity string: ("double quoted")
List Dynamic unsorted enumeration of values or objects of same type
Map Enumeration of (key:value) pairs unique sorted by key
Set Enumeration of unique elements of the same type sorted by value
Object Base class for creation of plain simple objects
Exception Composite type derived from Object base class


A range is a notation that can create a sub-set of integer numbers.


range ::= (min..max:ratio);



Numeric ranges:

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)
  expect( 32667 in (0..+)); //will pass
  expect(-32668 in (-..0)); //will pass


Symbol ranges:

** using symbol ranges
routine main:
  print ('0'..'5') // ('0','1','2','3','4','5')

  ** following statements should pass
  expect ('0' in ('0'..'9'));  //will pass   
  expect ('X' in ('A'..'Z'));  //will pass


Domains are similar to ranges, except they cover continuous numbers. Domains are decimal numbers not integers. So you can not print an entire domain. If you try, an infitinet loop may trigger. To prevent it we use $loop_limit constant.


domain ::= [min..max:ratio]  <: Super_Type


** sub-type declarations
routine main:
    print [0..1:0.25]; // 0.00, 0.25, 0.50, 0.75, 1.00


Data Coercion

In computer science coercion is used to implicitly or explicitly change an entity of one data type into another of different type. This is ready to take advantage of type hierarchies and type representations. If not designed properly the coercion can be a fatal mistake. EVE is a safe language so we do only safe coercion.

Implicit coercion In EVE the arithmetic operators are polymorphic. Numeric operators can do implicit data conversion to accommodate the data types and return an accurate result. Automatic conversion is possible only when there is no risk of loosing data precision. If there is a loss of precision we can end-up with a run-time error. To prevent this EVE will implement a safe compile-time check.


#example of implicit conversion
routine main:
  Integer a = 2;
  Double  b = 1.5; 
  b := a;       //  this implicit cast is possible b = 2.0
  b := a + 3.5; //  add 3.5 then assign result to b = 5.5
  a := b;       //  error: can not assign Double to  Integer
  a := 1.5;     //  error: can not assign Double to  Integer

Explicit coercion Explicit coercion is a forced conversion. Can be used to convert backwards from higher data range to lower data range or from continuous numbers to discrete numbers. This however can cause a data or precision loss. Explicit coercion is using a function.

Examples of explicit coercion:

# explicit coercion in EVE
routine main:
  Integer a = 0;
  Double  b = 1.5;
**explicit coercion lose (0.5)
  a := floor(b);
  write  a; //will print: 1
**explicit coercion add (0.5)
  a := ceiling(b); 
  print  a; //will print: 2

**explicit coercion rounding:  
  a := round(b);
  print  a; //  will print: 2

Number to a string

  String  s; 
  Integer v = 1000;
  s := format(v); //  explicit coercion s = '1000'
end local;

String to a number

This can be ready using the casting function parse(), only if the string contains a number. Otherwise the conversion fail and will rise and exception.

  Integer  v; 
  Double   b;
  String   s = '1000';
  String   r = '200.02';
  v := parse(s); //  make v = 1000
  v := parse(r); //  make v = 200 and decimal .02 is lost
  b := parse(r); //  make b = 200.02 and decimal .02 is preserved
end local;

Note: Build-in functions that are located in EVE default library: { parse(), format(), ceiling(), floor() round()}. This module is one of the standard modules that are automatically included in any EVE program.

Type inference

This is a logical deduction of data type from constant literals.


** Define a list of 10 elements using type inference
routine main:
  List ls = [0,1,2,3,4,5,6,7,8,9]; //  initialized list of Integer
  print  ls.type(); //  List[Integer]
  expect (ls is List[Integer]);

Default types

Literals are representations of specific particular data type in source code.

Basic types Next notation use "9" to show any digit in range [0..9].

Literal Type
9 Integer
-9 Integer
0x9ABCDEF Natural
0b1010101 Binary
9.9 Double
U+0001 Word

Zero literals

Literal Type
[] List
{} Set/Map
() List
"" Text
'' String
0 Integer
0.0 Double

Collection literals

Literal Type
{a:0, b, c} Ordinal
{x:'b',y:'d'} Object
[1, 2, 3] List[Byte]
['a','b','c'] List[Symbol]
["a","b","c"] List[Text]

Type Inference

Sometimes the type is partially specified to simplify type declaration:

  ** member type is inferred later from first member
  List a := [];

Type verification

We can verify the type using "is" operator:

routine main:
  Object r = {name:"test", age:"24"}; 
  Map    t = {('key1':"value1"),('ley2':"value2")};
  ** check variable types using introspection
  expect  is Text;
  expect r.age   is Text;
  expect t.key   is String;
  expect t.value is Text;

Printing type()

For type introspection we can use type() built-in function:

routine main:
  Double i = 1.5;
  expect i is Double;
  write "type of i is \s" ? type(i);

Polymorphic operators

In mathematics there are very few operators: {+, -, / , * } that can operate with any kind of numbers: negative, positive, rational or real. Operators are not bound to specific data types. Therefore these operators are called "polymorphic".

Some languages define different operators for Integers and Floating decimal numbers. For example in OCaml the operator "/" can divide Integers while "/." can divide Floating point decimal numbers. This is unexpected for a mathematician who is expecting to use one single operator for division.

In EVE, operators are mapped to functions. To design polymorphic operators we overload the function signature using type dispatch. The dispatch is using left side operand first, this is the leading operand. For unary operators there is only right side operand so this becomes the leading operand.

Logical type

In Latin the "falsus" and "verum" are translated in English to "false" and "true".

name value binary
False Logic.False 00000000 00000000
True Logic.True 00000000 00000001


  Logic: name = False; // explicit initialization

Internal design

Probably best to define Logic type is Ordinal:

type Logic = { .False , .True } <: Ordinal;

Logical expressions

A logical expression is a demonstration or logical deduction having result T or F. The order of operations can be controlled using operator precedence and parentheses ().

Operator precedence:{not, and, or, xor}

Result of logical expressions can be used into a conditional statement to make a decision. Also results of logical expressions can be stored in logical variables to be used later in other conditions.

Gradual typing

Gradual typing is a type system in which some variables may be given types and the correctness of the typing is checked at compile-time (which is static typing) and some variables may be left un-typed and eventual type errors are reported at run-time (which is dynamic typing). To declare gradual types we use a polymorphic type called "@variant".

Variant Types

A Variant is a polymorphic variable that can have multiple types but only one at a time:

type Name = {Type | Type | ... } <: Variant;

  Name: v = value; //  declare single variable (with initial value)

Variant Properties

Making a null-able type

For this we use a special type Null


type Number = {Integer | Double | Null} <: Variant;

  Number: x; // default value is Null


A variant can establish its data type at runtime:


routine main:
  Double | Integer v, x ,t;
  ** positive example
  v := 1;     //  v is  Integer
  x := 1.5;   //  x is Double    
  t := 1 / 2; //  make t Double
  ** safe conversion
  t := 12; //  t is Double
  ** negative examples
  v := x;  //  ERROR: v is  Integer 

A variant is a way to create a generic routine.

# variant parameter in routines
routine swap(Integer | Double x, y):
  Integer | Double i
  expect type(x) = type(y);
  i := x; //  intermediate reference
  x := y; //  first  swap
  y := x; //  second swap

routine main:
  Integer y;   // default zero
  Double a, b; // default zero
  ** invert two  Integer numbers
  x := 10;
  y := 20;  
  swap(x, y);
  expect (x == 20) and (y == 10);
  ** invert two Double numbers
  a := 1.5;
  b := 2.5;
  swap(a, b);
  expect (a == 2.5) and (b == 1.5);

Single symbol

Symbols are Unicode UTF32. That is using 32 bit Integer

Value NUL = U+0000. This is also the default value.

Calendar date

In EVE we represent calendar date.

Date storage

Date literals

When can create a date literal using 3 format functions:

Note: A reversible function is overloaded.

#overloaded function
routine main:
  Date: date := "2019/01/30" as YDM
  print date as YDM; //  2019/01/30
  print date as DMY; //  30/01/2019
  print date as MDY; //  01/30/2019

Time Duration

Time data type can be used to represent duration.

Representation Time is represented as a number on 8 bytes.


Time format is created using two reversible functions: t12() and t24()

ss: can be 0..60 seconds
xx: can be: (am/pm)


# time demo
routine main:
  Time: (time1, time2, time3) = "00:00";
  time1 := "23:63" as T24;
  time2 := "23:63:59,99" as T24;
  time3 := "11:63:59pm,99ms" as T12;
** example of collection iteration
routine test():
  List this = ["a","b","c","d","e"];
  Integer i = 0;
  Symbol:  e;
  while i < this.length() loop
    e := this[i];
    i := i + 1;
    if e  >= "c" then
      write e + (e == this.tail ? '' : ',')
    end if;
    write ('i = ' + i);
  end loop;

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