What do you call these? [array][string][int]

Don Cruickshank’s helpful answer provides one piece of the puzzle, but let me try give a comprehensive overview:

By itself, a [<fullTypeNameOrTypeAccelerator>] expression is a type literal, i.e. a reference to a .NET type in the form of a System.Reflection.TypeInfo instance, which is rich source of reflection on the type it represents.

<fullTypeNameOrTypeAccelerator> can be the full name of a .NET type (e.g., [System.Text.RegularExpressions.Regex] – optionally with the System. prefix omitted ([Text.RegularExpressions.Regex]) or the name of a PowerShell type accelerator (e.g, [regex])

---

Type literals by themselves are used:

• Typically, to access static members (typically methods) via ::, the static member-access operator; e.g.:

  # Call the static 'Match' method of the [regex]
  # (System.Text.RegularExpressions.Regex) type.
  # -> '10'
  [regex]::Match('A10', '\d+').Value
  

• Less frequently, to reflect on the given type by calling the instance methods of the TypeInfo instance that every type literal is; e.g.:

  # Get the names of all .NET interfaces that the [regex]
  # (System.Text.RegularExpressions.Regex) implements.
  # -> 'ISerializable'
  [regex].GetInterfaces().Name
  

---

Type literals are also used in the following constructs:

• As casts, to convert (coerce) the (RHS^[1]) operand to the specified type or to construct an instance, if possible:

  # Convert a string to [datetime] (System.DateTime).
  # Equivalent to the following call:
  #    [datetime]::Parse('1970-01-01', [cultureinfo]::InvariantCulture)
  [datetime] '1970-01-01'
  
  # Construct a [regex] instance.
  # The same as the following constructor call:
  #     [regex]::new('\d+')
  $re = [regex] '\d+'
  

  • The examples show that PowerShell casts are much more flexible than in C#, for instance, and instance construction and type conversions frequently happen implicitly – see this answer for more information. The same rules apply to all the other uses listed below.

• As type constraints:

  • To specify the type of a parameter variable in a function or script:

    function foo { param([datetime] $d) $d.Year }; foo '1970-01-01'
    

  • To lock in the type of a regular variable for all future assignments:^[2]

    [datetime] $foo = '1970-01-01'
    # ...
    $foo = '2021-01-01' # the string is now implicitly forced to [datetime] 
    

• As the RHS of the -is and -as operators, for type tests and conditional conversions:

  • -is tests not only for the exact type, but also for derived types as well as interface implementations:

    # Exact type match (the `Get-Date` cmdlet outputs instances of [datetime])
    (Get-Date) -is [datetime]  # $true
    
    # Match via a *derived* type:
    # `Get-Item /` outputs an instance of type [System.IO.DirectoryInfo],
    # which derives from [System.IO.FileSystemInfo]
    (Get-Item /) -is [System.IO.FileSystemInfo] # $true
    
    # Match via an *interface* implementation:
    # Arrays implement the [System.Collections.IEnumerable] interface.
    1..3 -is [System.Collections.IEnumerable] # true
    

  • -as converts the LHS instance to an instance of the RHS type if possible, and returns $null otherwise:

    '42' -as [int] # 42
    
    'foo' -as [int] # $null
    

• [PowerShell v7.3+ only] As the type arguments in generic method calls:

  • E.g, the following calls the Enumerable.OfType<TResult>(IEnumerable) LINQ method with [int] as its type argument (thereby requesting that only enumerable elements that are of that type be returned):

    # -> 2, 4
    [System.Linq.Enumerable]::OfType[int](@('one', 2, 'three', 4))
    

  • See about_Calling_Generic_Methods.

---

^{[1] In the context of operators and mathematical equations, the initialisms LHS and RHS are commonly used, referring to the left-hand side and right-hand side operands, respectively.}

^{[2] Technically, there is no real difference between a parameter and a regular variable: the type constraints functions the same way in both cases, but parameter variables, after having been bound (assigned to) automatically on invocation, aren’t usually assigned to again.}