# Value Types

A *value* in Penrose can have any of the following categories:

- Numbers (type
`FloatV`

), constructed as either a numerical value or`?`

signifying the unknown value to be determined during optimization (see here). - Booleans (type
`BoolV`

), constructed as either`true`

or`false`

. - Strings (type
`StrV`

), constructed as text written in between double-quotes (like`"hello world"`

), and concatenations (like`"\text{" + x.label + "}"`

) - Path data (type
`PathDataV`

), constructed as in here. - List of points (type
`PtListV`

), constructed as a matrix or a list of lists. - Colors (type
`ColorV`

), constructed as in here. - List of numbers (type
`ListV`

), constructed as comma-separated numbers surrounded between square brackets, like`[1, 2, ?, 4, 5]`

. - Vectors (type
`VectorV`

), constructed as comma-separated numbers surrounded by parentheses, like`(1, 2, 3, ?, 5)`

. - Matrices (type
`MatrixV`

), constructed as vectors of vectors, like`((1, 2, 3), (4, 5, 6), (7, 8, 9))`

. - Tuples (type
`TupV`

), constructed as a pair of two numbers surrounded by brackets, like`{1, ?}`

. - List of lists (type
`LListV`

), constructed like`[[1, 2, 3], [4, 5, 6], [7, 8, 9]]`

. - List of shapes (type
`ShapeListV`

), constructed as a list of paths to previously-defined shapes. For example,`[t.shape1, t.shape2, t.shape3]`

where`t.shape1`

,`t.shape2`

, and`t.shape3`

are all previously-defined.

Many of the value types can also be results of computations among other types and shapes (see details).

As of now, Penrose's types are not strictly enforced, except when they act as shape parameters (see details).