/* 0.28.0 */
/**
 * A primitive type is a simple type that represents a concrete value.
 *
 * - `any`: the top type
 *    - `expression`
 *    - `error`: an invalid value, such as `["Error", "missing"]`
 *    - `nothing`: the type of the `Nothing` symbol, the unit type
 *    - `never`: the bottom type
 *    - `unknown`: a value whose type is not known
 *
 * - `expression`:
 *    - a symbolic expression, such as `["Add", "x", 1]`
 *    - `<value>`
 *    - `symbol`: a symbol, such as `x`.
 *    - `function`: a function expression
 *      such as `["Function", ["Add", "x", 1], "x"]`.
 *
 * - `value`
 *    - `scalar`
 *      - `<number>`
 *      - `boolean`: a boolean value: `True` or `False`.
 *      - `string`: a string of characters.
 *    - `collection`
 *       - `list`: a collection of expressions, possibly recursive,
 *          with optional dimensions, e.g. `[number]`, `[boolean^32]`,
 *          `[number^(2x3)]`. Used to represent a vector, a matrix or a
 *          tensor when the type of its elements is a number
 *       - `set`: a collection of unique expressions, e.g. `set<string>`.
 *       - `tuple`: a fixed-size collection of named or unnamed elements, e.g.
 *          `tuple<number, boolean>`, `tuple<x: number, y: boolean>`.
 *       - `map`: a set key-value pairs, e.g. `map<x: number, y: boolean>`.
 *
 *
 *
 */
export type PrimitiveType = NumericType | 'collection' | 'list' | 'set' | 'map' | 'tuple' | 'value' | 'scalar' | 'function' | 'symbol' | 'boolean' | 'string' | 'expression' | 'unknown' | 'error' | 'nothing' | 'never' | 'any';
/**
 * - `number`: any numeric value = `complex` + `real` plus `NaN`
 * - `complex`: a number with non-zero real and imaginary parts = `finite_complex` plus `ComplexInfinity`
 * - `finite_complex`: a finite complex number = `imaginary` + `finite_real`
 * - `imaginary`: a complex number with a real part of 0 (pure imaginary)
 * - `finite_number`: a finite numeric value = `finite_complex`
 * - `finite_real`: a finite real number = `finite_rational` + `finite_integer`
 * - `finite_rational`: a pure rational number
 * - `finite_integer`: a whole number
 * - `real`: a complex number with an imaginary part of 0 = `finite_real` + `non_finite_number`
 * - `non_finite_number`: `PositiveInfinity`, `NegativeInfinity`
 * - `integer`: a whole number = `finite_integer` + `non_finite_number`
 * - `rational`: a pure rational number (not an integer) = `finite_rational` + `non_finite_number`
 *
 */
export type NumericType = 'number' | 'finite_number' | 'complex' | 'finite_complex' | 'imaginary' | 'real' | 'finite_real' | 'rational' | 'finite_rational' | 'integer' | 'finite_integer' | 'non_finite_number';
export type NamedElement = {
    name?: string;
    type: Type;
};
export type FunctionSignature = {
    kind: 'signature';
    args?: NamedElement[];
    optArgs?: NamedElement[];
    restArg?: NamedElement;
    result: Type;
};
export type AlgebraicType = {
    kind: 'union' | 'intersection';
    types: Type[];
};
export type NegationType = {
    kind: 'negation';
    type: Type;
};
export type ValueType = {
    kind: 'value';
    value: any;
};
/** Map is a non-indexable collection of key/value pairs.
 * An element of a map whose type is a subtype of `nothing` is optional.
 * For example, in `{x: number, y: boolean | nothing}` the element `y` is optional.
 */
export type MapType = {
    kind: 'map';
    elements: Record<string, Type>;
};
/** Collection, List, Set, Tuple and Map are collections.
 *
 * `CollectionType` is a generic collection of elements of a certain type.
 */
export type CollectionType = {
    kind: 'collection';
    elements: Type;
};
/**
 * The elements of a list are ordered.
 *
 * All elements of a list have the same type, but it can be a broad type,
 * up to `any`.
 *
 * The same element can be present in the list more than once.
 *
 * A list can be multi-dimensional. For example, a list of integers with
 * dimensions 2x3x4 is a 3D tensor with 2 layers, 3 rows and 4 columns.
 *
 */
export type ListType = {
    kind: 'list';
    elements: Type;
    dimensions?: number[];
};
/** Each element of a set is unique (is not present in the set more than once).
 * The elements of a set are not ordered.
 */
export type SetType = {
    kind: 'set';
    elements: Type;
};
export type TupleType = {
    kind: 'tuple';
    elements: NamedElement[];
};
/** Nominal typing */
export type TypeReference = {
    kind: 'reference';
    ref: string;
};
export type Type = PrimitiveType | AlgebraicType | NegationType | CollectionType | ListType | SetType | MapType | TupleType | FunctionSignature | ValueType | TypeReference;
/**
 * The type of a boxed expression indicates the kind of expression it is and
 * the value it represents.
 *
 * The type is represented either by a primitive type (e.g. number, complex, collection, etc.), or a compound type (e.g. tuple, function signature, etc.).
 *
 * Types are described using the following BNF grammar:
 *
 * ```bnf
 * <type> ::= <union_type> | "(" <type> ")"
 *
 * <union_type> ::= <intersection_type> (" | " <intersection_type>)*
 *
 * <intersection_type> ::= <primary_type> (" & " <primary_type>)*
 *
 * <primary_type> ::=  <primitive>
 *                | <tuple_type>
 *                | <signature>
 *                | <list_type>
 *
 * <primitive> ::= "any" | "unknown" | <value-type> | <symbolic-type> | <numeric-type>
 *
 * <numeric-type> ::= "number" | "complex" | "imaginary" | "real" | "rational" | "integer"
 *
 * <value-type> ::= "value" | <numeric-type> | "collection" | "boolean" | "string"
 *
 * <symbolic-type> ::= "expression" | "function" | "symbol"
 *
 * <tuple_type> ::= "tuple<" (<name> <type> "," <named_tuple_elements>*) ">"
 *            | "tuple<" (<type> "," <unnamed_tuple_elements>*) ">" |
 *            | "tuple<" <tuple_elements> ">"
 *
 * <tuple_elements> ::= <unnamed_tuple_elements> | <named_tuple_elements>
 *
 * <unnamed_tuple_elements> ::= <type> ("," <type>)*
 *
 * <named_tuple_elements> ::= <name> <type> ("," <name> <type>)*
 *
 * <signature> ::=  <arguments> " -> " <type>
 *
 * <arguments> ::= "()"
 *            | <argument>
 *            | "(" <argument-list> ")"
 *
 * <argument> ::= <type>
 *            | <name> <type>
 *
 * <rest_argument> ::= "..." <type>
 *            | <name> "..." <type>
 *
 * <optional_argument> ::= <argument> "?"
 *
 * <optional_arguments> ::= <optional_argument> ("," <optional_argument>)*
 *
 * <required_arguments> ::= <argument> ("," <argument>)*
 *
 * <argument-list> ::= <required_arguments> ("," <rest_argument>)?
 *            | <required_arguments> <optional_arguments>?
 *            | <optional_arguments>?
 *            | <rest_argument>
 *
 * <list_type> ::= "list<" <type> <dimensions>? ">"
 *
 * <dimensions> ::= "^" <fixed_size>
 *            | "^(" <multi_dimensional_size> ")"
 *
 * <fixed_size> ::= <positive-integer_literal>
 *
 * <multi_dimensional_size> ::= <positive-integer_literal> "x" <positive-integer_literal> ("x" <positive-integer_literal>)*
 *
 * <map> ::= "map" | "map<" <map_elements> ">"
 *
 * <map_elements> ::= <name> <type> ("," <name> <type>)*
 *
 * <set> ::= "set<" <type> ">"
 *
 * <collection ::= "collection<" <type> ">"
 *
 * <name> ::= <identifier> ":"
 *
 * <identifier> ::= [a-zA-Z_][a-zA-Z0-9_]*
 *
 * <positive-integer_literal> ::= [1-9][0-9]*
 *```
 *
 * Examples of types strings:
 * - `"number"`    -- a simple type primitive
 * - `"(number, boolean)"` -- a tuple type
 * - `"(x: number, y:boolean)"` -- a named tuple/record type. Either all arguments are named, or none are
 * - `"collection<any>"` -- an arbitrary collection type, with no length or element type restrictions
 * - `"collection<integer>"` -- a collection type where all the elements are integers
 * - `"collection<(number, boolean)>"` -- a collection of tuples
 * - `"collection<(value:number, seen:boolean)>"` -- a collection of named tuples
 * - `"[boolean]^32"` -- a collection type with a fixed size of 32 elements
 * - `"[integer]^(2x3)"` -- an integer matrix of 2 columns and 3 rows
 * - `"[integer]^(2x3x4)"` -- a tensor of dimensions 2x3x4
 * - `"number -> number"` -- a signature with a single argument
 * - `"(x: number, number) -> number"` -- a signature with a named argument
 * - `"(number, y:number?) -> number"` -- a signature with an optional named argument (can have several optional arguments, at the end)
 * - `"(number, ...number) -> number"` -- a signature with a rest argument (can have only one, and no optional arguments if there is a rest argument).
 * - `"() -> number"` -- a signature with an empty argument list
 * - `"number | boolean"` -- a union type
 * - `"(x: number) & (y: number)"` -- an intersection type
 * - `"number | ((x: number) & (y: number))"` -- a union type with an intersection type
 * - `"(number -> number) | number"` -- a union type with a signature and a primitive type
 */
export type TypeString = string;
export type TypeCompatibility = 'covariant' | 'contravariant' | 'bivariant' | 'invariant';
export type TypeResolver = (name: string) => Type | undefined;