Construct Value

This section explores the concepts of value, value constructor, type and kind in PureScript.

Intro

Value

A value refers to a concrete runtime expression — something that the program evaluates, stores, or passes around. We can construct values by value/data constructor (custom) and literals (built-in). Value has a type, and we can examine with :type or :t in REPL.

Type

Type describes what kind of data something is. Type has a kind, and we can use :kind or :k to examine in REPL. There is a special kind called Type which represents the kind of all types which have values, like Number and String.

Type constructor

Type constructor takes type argument and construct type.

data Maybe a = Nothing | Just a

• Maybe a: a type
• Maybe: a type constructor, which takes a type parameter, and creates a type (Maybe a)
• Just a: a value
• Just: a value constructor, which takes a parameter, and create a value (Just a) of type Maybe a;

List is an example of a type constructor. Values do not have the type List directly, but rather List a for some type a. That is, List takes a type argument a and constructs a new type List a.

Note that just like function application, type constructors are applied to other types simply by juxtaposition: the type List Entry is, in fact, the type constructor List applied to the type Entry – it represents a list of entries. There are also kinds for type constructors. For example, the kind Type -> Type represents a function from types to types, just like List.

Value Constructor

Constructor makes values of that type. A value constructor (also known as a data constructor) is a function that constructs a value of a data type. Value constructors are just functions that take the fields as parameters and return a value of some type (like Shape) as a result.

Examples

The following are examples for these concepts.

Some values

Expression	Is it a Value?	Type	Notes
7	✅ Yes	Int	A number literal
"hello"	✅ Yes	String	A string literal
true	✅ Yes	Boolean	A boolean literal
Circle 0.0 0.0 5.0	✅ Yes	Shape	A value constructed using a data constructor
Just 5	✅ Yes	Maybe Int	Value using a built-in algebraic data type
add 1 2	✅ Yes	Int	Result of a function application
\x -> x + 1	✅ Yes	Int -> Int	A function value (lambda expression)

Some types and type definition

Thing	What it is	Kind	Why it's not a value
Int	A type	Type	Describes values like 7, but isn’t a value
Shape	A type name	Type	A category of values, not a value itself
data Shape = ...	Type declaration	(not applicable)	Defines a type and its constructors, not a value
add :: Int -> Int -> Int	Type annotation	(not applicable)	Describes the type of a value, not the value itself

Value, Type and Constructor

Value	Type	Constructor?	Notes
7	Int	❌ None	Literal for a primitive type
true	Boolean	❌ None	Same
Circle	Shape	✅ Circle	User-defined data constructor
Just 5	Maybe	✅ Just	Built-in algebraic data type

Code example:

data Shape = Circle Number Number Number
         | Rectangle Number Number Number Number

This defines a type named Shape, and two data constructors.

Literal

In PureScript (and many programming languages), the term "literal" refers to syntax that allows you to directly write a value of a specific type in your code, without needing to construct it through functions or other runtime operations.

A string literal is text written directly between double quotes ("..."):

-- A string literal representing the value "hello"
str :: String
str = "hello"

An array literal is a list of values written between square brackets ([ ... ]):

-- An array literal with the values 1, 2, 3
arr :: Array Int
arr = [1, 2, 3]

Contrast with Non-Literal Constructs:

-- Non-literal (constructed at runtime):
dynamicArray = Array.cons 1 (Array.cons 2 (Array.cons 3 []))
dynamicString = String.fromCharArray ['h', 'e', 'l', 'l', 'o']

Why "Literal" Matters:

• Compile-Time Known: Literals are fixed values embedded in the source code.
• No Runtime Overhead: They don’t require functions like Array.from or new Object().
• Pattern Matching: Can be used directly in patterns:

Summary

Concept	Role	Example
Type	Category of values	Shape
Constructor	Function to create values	Circle 1.0 1.0 5.0
Value	Actual instance of a type	myShape = Circle 1.0 1.0 5.0
Pattern match	Use constructors to handle data	case shape of Circle x y r -> ...