= Expr
Expressions calculator
:authors: Celestino Amoroso
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:encoding: utf-8
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#TODO: Work in progress (last update on 2024/05/09, 07:17 am)#

== Expr
_Expr_ is a GO package capable of analysing, interpreting and calculating expressions.

=== `dev-expr` test tool
`dev-expr` is a simple program that can be used to evaluate expressions interactively. As its name suggests, it was created for testing purpose. In fact, beyond in additon to the automatic test suite based on the Go test framework, `dev-expr` provides an important aid for quickly testing of new features during their development.

It cat work as a REPL, *R*ead-*E*xecute-*P*rint-*L*oop, or it can process expression acquired from files or standard input.

The program in located in the _tools_ directory.
Here are some examples of execution.

.Run `dev-expr` in REPL mode and ask for help
[source,shell]
----
# Assume the expr source directory. Type 'exit' or Ctrl+D to quit the program.

[user]$ tools/expr -- Expressions calculator v1.7.0,2024/05/08 (celestino.amoroso@portale-stac.it)
	Type help to get the list of command.
	See also https://git.portale-stac.it/go-pkg/expr/src/branch/main/README.adoc

>>> help
--- REPL commands:
        base -- Set the integer output base: 2, 8, 10, or 16
        exit -- Exit the program
        help -- Show command list
          ml -- Enable/Disable multi-line output
        mods -- List builtin modules
      source -- Load a file as input
         tty -- Enable/Disable ansi output <1>

--- Command line options:
    -b <builtin>       Import builtin modules.
                       <builtin> can be a list of module names or a glob-pattern.
                       Use the special value 'all' or the pattern '*' to import all modules.
    -e <expression>    Evaluate <expression> instead of standard-input
    -i                 Force REPL operation when all -e occurences have been processed
    -h, --help, help   Show this help menu
    -m, --modules      List all builtin modules
    -p                 Print prefix form
    -t                 Print tree form <2>

>>> 
----

<1> Only available for single fraction values
<2> Work in progress

.REPL examples
[source,shell]
----
[user]$ tools/expr -- Expressions calculator v1.6.1,2024/05/06 (celestino.amoroso@portale-stac.it)
        Type help to get the list of command.
        See also https://git.portale-stac.it/go-pkg/expr/src/branch/main/README.adoc
>>> 2+3
5
>>> 2+3*(4-1.5)
9.5
>>> 0xFD + 0b1 + 0o1 <1>
255
>>> 1|2 + 2|3 <2>
7|6
>>> ml <3>
>>> 1|2 + 2|3
7
-
6
>>> 1+2 but 5|2+0.5 <4>
3
>>> 1+2; 5|2+0.5 <5>
3
>>>
----

<1> Number bases: 0x = hexadecimal, 0o = octal, 0b = binary.
<2> Fractions: numerator | denominator.
<3> Activate multi-line output of fractions.
<4> But operator, see <<_but_operator>>.
<5> Multi-expression: the same result of the previous single expression but this it is obtained with two separated calculations.

=== Concepts and terminology
#TODO#

image::expression-diagram.png[]

== Data types
_Expr_ supports numerical, string, relational, boolean expressions, and mixed-type lists.

=== Numbers
Numbers can be integers (GO int64) or float (GO float64). In mixed operations involving integers and floats, integers are automatically promoted to floats.

.Arithmetic operators
[cols="^1,^2,6,4"]
|===
| Symbol    | Operation     | Description               | Examples

| [blue]`+` / [blue]`-` | _change sign_ | Change the sign of values | [blue]`-1` _[-1]_ +
[blue]`-(+2)` _[-2]_

| [blue]`+` | _sum_ | Add two values | [blue]`-1 + 2` _[1]_ +
[blue]`4 + 0.5` _[4.5]_

| [blue]`-` | _subtraction_ | Subtract the right value from the left one | [blue]`3 - 1` _[2]_ +
[blue]`4 - 0.5` _[3.5]_

| [blue]`*` | _product_ | Multiply two values | `-1 * 2` _[-2]_ +
[blue]`4 * 0.5` _[2.0]_

| [blue]`/` | _Division_ | Divide the left value by the right one | [blue]`-1 / 2` _[0]_ +
[blue]`1.0 / 2` _[0.5]_

| [blue]`./` | _Float division_ | Force float division | [blue]`-1 ./ 2` _[-0.5]_

| [blue]`%` | _Modulo_ | Remainder of the integer division | [blue]`5 % 2` _[1]_

|=== 

=== Fractions
_Expr_ also suports fractions. Fraction literals are made with tow integers separated by a vertical bar `|`.

.Examples
// [source,go]
// ----
`>>>` [blue]`1 | 2` +
[green]`1|2` +
`>>>` [blue]`4|6` +
[green]`2|3` [gray]_Fractions are always reduced to theri lowest terms_ +
`>>>` [blue]`1|2 + 2|3` +
[green]`7|6` +
`>>>` [blue]`1|2 * 2|3` +
[green]`1|3` +
`>>>` [blue]`1|2 / 1|3` +
[green]`3|2` +
`>>>` [blue]`1|2 ./ 1|3` [gray]_Force decimal division_ +
[green]`1.5` +
`>>>` [blue]`-1|2` +
[green]`-1|2` +
`>>>` [blue]`1|-2` [gray]_Wrong sign specification_ +
[red]_Eval Error: [1:3] infix operator "|" requires two non-nil operands, got 1_ +
`>>>` [blue]`1|(-2)` +
[green]`-1|2`
// ----

Fractions can be used together with integers and floats in expressions.

`>>>` [blue]`1|2 + 5` +
[green]`11|2` +
`>>>` [blue]`4 - 1|2` +
[green]`7|2` +
`>>>` [blue]`1.0 + 1|2` +
[green]`1.5` +



=== Strings
Strings are character sequences enclosed between two double quote [blue]`"`. Example: [blue]`"I'm a string"`.

Some arithmetic operators can also be used with strings.

.String operators
[cols="^1,^2,6,4"]
|===
| Symbol    | Operation     | Description               | Examples

| [blue]`+` | _concatenation_ | Join two strings or two _stringable_ values | [blue]`"one" + "two"` _["onetwo"]_ +
[blue]`"one" + 2` _["one2"]_

| [blue]`*` | _repeat_ | Make _n_ copy of a string  | [blue]`"one" * 2` _["oneone"]_
|===


=== Boolean
Boolean data type has two values only: _true_ and _false_. Relational and Boolean expressions produce Boolean values.


.Relational operators
[cols="^1,^2,6,4"]
|===
| Symbol    | Operation     | Description               | Examples

| [blue]`==` | _Equal_ | True if the left value is equal to the right one | [blue]`5 == 2` _[false]_ +
[blue]`"a" == "a"` _[true]_
| [blue]`!=` | _Not Equal_ | True if the left value is NOT equal to the right one | [blue]`5 != 2` _[true]_ +
[blue]`"a" != "a"` _[false]_
| [blue]`<` | _Less_ | True if the left value is less than the right one | [blue]`5 < 2` _[false]_ +
[blue]`"a" < "b"` _[true]_
| [blue]`\<=` | _Less or Equal_ | True if the left value is less than or equal to the right one | [blue]`5 \<= 2` _[false]_ +
[blue]`"b" \<= "b"` _[true]_
| [blue]`>` | _Greater_ | True if the left value is greater than the right one | [blue]`5 > 2` _[true]_ +
[blue]`"a" < "b"` _[false]_
| [blue]`>=` | _Greater or Equal_ | True if the left value is greater than or equal to the right one | [blue]`5 >= 2` _[true]_ +
[blue]`"b" \<= "b"` _[true]_
|===


.Boolean operators
[cols="^2,^2,5,4"]
|===
| Symbol    | Operation     | Description               | Examples

| [blue]`NOT` | _Not_ | True if the right value is false | [blue]`NOT true` _[false]_ +
[blue]`NOT (2 < 1)` _[true]_

| [blue]`AND` / [blue]`&&` | _And_ | True if both left and right values are true  | [blue]`false && true` _[false]_ +
[blue]`"a" < "b" AND NOT (2 < 1)` _[true]_

| [blue]`OR` / [blue]`\|\|` | _Or_ | True if at least one of the left and right values integers true| [blue]`false or true` _[true]_ +
[blue]`"a" == "b" OR (2 == 1)` _[false]_
|===

[CAUTION]
====
Currently, boolean operations are evaluated using _short cut evaluation_. This means that, if the left expression of operators [blue]`and` and [blue]`or` is sufficient to establish the result of the whole operation, the right expression would not evaluated at all.

.Example
[source,go]
----
2 > (a=1) or (a=8) > 0; a // <1>
----
<1> This multi-expression returns _1_ because in the first expression the left value of [blue]`or` is _true_ and as a conseguence its right value is not computed. Therefore the _a_ variable only receives the integer _1_.
====

=== List
_Expr_ supports list of mixed-type values, also specified by normal expressions.

.List examples
[source,go]
----
[1, 2, 3]                   // List of integers
["one", "two", "three"]     // List of strings
["one", 2, false, 4.1]      // List of mixed-types
["one"+1, 2.0*(9-2)]        // List of expressions
[ [1,"one"], [2,"two"]]     // List of lists
----


.List operators
[cols="^2,^2,5,4"]
|===
| Symbol    | Operation     | Description               | Examples

| [blue]`+` | _Join_ | Joins two lists | [blue]`[1,2] + [3]` _[ [1,2,3] ]_

| [blue]`-` | _Difference_ | Left list without elements in the right list  | [blue]`[1,2,3] - [2]` _[ [1,3] ]_
|===

== Dictionaries
The _dictionary_ data-type is set of pairs _key/value_. It is also known as _map_ or _associative array_. Dictionary literals are sequences of pairs separated by comma `,`; sequences are enclosed between brace brackets.

.List examples
[source,go]
----
{1:"one", 2:"two"}
{"one":1, "two": 2}
{"sum":1+2+3, "prod":1*2*3}
----

WARNING: Support for dictionaries is still ongoing.

== Variables
A variable is an identifier with an assigned value. Variables are stored in the object that implements the _ExprContext_ interface.

.Examples
[source,go]
----
a=1
x = 5.2 * (9-3)
x = 1; y = 2*x
----

== Other operations

=== [blue]`;` operator
The semicolon operator [blue]`;` is an infixed pseudo-operator. It evaluates the left expression first and then the right expression. The latter is the final result.

IMPORTANT: Technically [blue]`;` is not treated as a real operator. It acts as a separator in lists of expressions.

TIP: [blue]`;` can be used to set some variables before the final calculation.

.Example
[source,go]
----
a=1; b=2; c=3; a+b+c    // returns 6
----

=== [blue]`but` operator
[blue]`but` is an infixed operator. Its operands can be expressions of any type. It evaluates the left expression first, then the right expression. The value of the right expression is the final result. Examples: [blue]`5 but 2` returns 2, [blue]`x=2*3 but x-1` returns 5.

[blue]`but` is very similar to [blue]`;`. The only difference is that [blue]`;` can't be used inside parenthesis [blue]`(` and [blue]`)`.

=== Assignment operator [blue]`=`
The assignment operator [blue]`=` is used to define variables in the evaluation context or to change their value (see _ExprContext_).
The value on the left side of [blue]`=` must be an identifier. The value on the right side can be any expression and it becomes the result of the assignment operation.

.Example
[source,go]
----
a=15+1    // returns 16
----

=== Selector operator [blue]`? : ::`
The _selector operator_ is very similar to the _switch/case/default_ statement available in many programming languages.

.Syntax
[source,bnf]
----
<selector-operator> ::= <select-expression> "?" <selector-case> { ":" <selector-case> } ["::" <default-multi-expression>]
<selector-case> ::= [<match-list>] <case-value>
<match-list> ::= "["<item>{","<items>}"]"
<item> ::= <expression
<case-multi-expression> ::= "{" <multi-expression> "}"
<multi-expression> ::= <expression> {";" <expression>}
----

In other words, the selector operator evaluates the expression (`<select-expression>`) on the left-hand side of the `?` symbol; it then compares the result obtained with the values listed in the `<match-list>`'s. If the comparision find a match with a value in a match-list, the associated  `<case-multi-expression>` is evaluted, and its result will be the final result of the selection operation.

The match lists are optional. In that case, the position, from left to right, of the `<selector-case>` is used as match-list. Of course, that only works if the select-expression results in an integer.

The `:` symbol (colon) is the separator of the selector-cases. Note that if the value of the select-expression does not match any match-list, an error will be issued. Therefore, it is strongly recommended to provide a default (multi-)expression introduced by the `::` symbol (double-colon). Also note that the default expression has no match-list.


.Examples
[source,go]
----
1 ? {"a"} : {"b"}                           // returns "b"
10 ? {"a"} : {"b"} :: {"c"}                 // returns "c"
10 ? {"a"} :[true, 2+8] {"b"} :: {"c"}      // returns "b"
10 ? {"a"} :[true, 2+8] {"b"} ::[10] {"c"}  // error:  "... case list in default clause"
10 ? {"a"} :[10] {x="b" but x} :: {"c"}     // returns "b"
10 ? {"a"} :[10] {x="b"; x} :: {"c"}        // returns "b"
10 ? {"a"} : {"b"}                          // error:  "... no case catches the value (10) of the selection expression
----

== Priorities of operators
The table below shows all supported operators by decreasing priorities.

.Operators priorities
[cols="^2,^2,^2,^5,^5"]
|===
| Priority | Operators     | Position | Operation | Operands and results

.1+|*ITEM*| [blue]`.` | _Infix_ | _Item_| _collection_ `"."` _key_ -> _any_
.2+|*INC*| [blue]`++` | _Postfix_ | _Post increment_| _integer-variable_ `"++"` -> _integer_
| [blue]`++` | _Postfix_ | _Next item_ | _iterator_ `"++"` -> _any_
.1+|*FACT*| [blue]`!` | _Postfix_ | _Factorial_| _integer_ `"!"` -> _integer_
.3+|*SIGN*| [blue]`+`, [blue]`-` | _Prefix_ | _Change-sign_| (`"+"`\|`"-"`) _number_ -> _number_
| [blue]`#` | _Prefix_ | _Lenght-of_ | `"#"` _collection_ -> _integer_
| [blue]`#` | _Prefix_ | _Size-of_ | `"#"` _iterator_ -> _integer_
.5+|*PROD*| [blue]`*` | _Infix_ | _Product_ | _number_ `"*"` _number_ -> _number_
| [blue]`*` | _Infix_ | _String-repeat_ | _string_ `"*"` _integer_ -> _string_
| [blue]`/` | _Infix_ | _Division_ | _number_ `"/"` _number_ -> _number_
| [blue]`./` | _Infix_ | _Float-division_ | __number__ `"./"` _number_ -> _float_
| [blue]`%` | _Infix_ | _Integer-remainder_ | _integer_ `"%"` _integer_ -> _integer_
.5+|*SUM*| [blue]`+` | _Infix_ | _Sum_ | _number_ `"+"` _number_ -> _number_
| [blue]`+` | _Infix_ |  _String-concat_ | (_string_\|_number_) `"+"` (_string_\|_number_) -> _string_
| [blue]`+` | _Infix_ |  _List-join_ | _list_ `"+"` _list_ -> _list_
| [blue]`-` | _Infix_ | _Subtraction_ | _number_ `"-"` _number_ -> _number_
| [blue]`-` | _Infix_ | _List-difference_ | _list_ `"-"` _list_ -> _list_
.6+|*RELATION*| [blue]`<` | _Infix_ | _less_ | _comparable_ `"<"` _comparable_ -> _boolean_
| [blue]`\<=` | _Infix_ |  _less-equal_ | _comparable_ `"\<="` _comparable_ -> _boolean_
| [blue]`>` | _Infix_ |  _greater_ | _comparable_ `">"` _comparable_ -> _boolean_
| [blue]`>=` | _Infix_ |  _greater-equal_ | _comparable_ `">="` _comparable_ -> _boolean_
| [blue]`==` | _Infix_ |  _equal_ | _comparable_ `"=="` _comparable_ -> _boolean_
| [blue]`!=` | _Infix_ |  _not-equal_ | _comparable_ `"!="` _comparable_ -> _boolean_
.1+|*NOT*| [blue]`not` | _Prefix_ | _not_ | `"not"` _boolean_ -> _boolean_
.2+|*AND*| [blue]`and` | _Infix_ | _and_ | _boolean_ `"and"` _boolean_ -> _boolean_
| [blue]`&&` | _Infix_ | _and_ | _boolean_ `"&&"` _boolean_ -> _boolean_
.2+|*OR*| [blue]`or` | _Infix_ | _or_ | _boolean_ `"or"` _boolean_ -> _boolean_
| [blue]`\|\|` | _Infix_ | _or_ | _boolean_ `"\|\|"` _boolean_ -> _boolean_
.1+|*ASSIGN*| [blue]`=` | _Infix_ | _assignment_ | _identifier_ "=" _any_ -> _any_
.1+|*BUT*| [blue]`but` | _Infix_ | _but_ | _any_ "but" _any_ -> _any_
|===

== Functions
Functions in _Expr_ are very similar to functions in many programming languages.

In _Expr_ functions compute values in a local context (scope) that do not make effects on the calling context. This is the normal behavior. Using the reference operator [blue]`@` it is possibile to export local definition to the calling context.

=== Function calls
#TODO: function calls operations#

=== Function definitions
#TODO: function definitions operations#

== Builtins
#TODO: builtins#

=== Builtin functions

=== [blue]_import()_
[blue]_import([grey]#<source-file>#)_ loads the multi-expression contained in the specified source and returns its value.