Basics

• Data is given and as-is. Indices into other elements beyond the data are just indices.
• Data is finite. Otherwise we are talking about streams/processes/delayed computations/promises etc.
• Data is either atomic or composite.
  • The choice of atoms and composites varies with the domain.

Information

• Meaning and information are only provided by context.
  • Context refers to the fact that lots of data is in textual form and literal reading of text misses the bigger picture.
• Data is only a representation of objects in some abstract domain. The domain includes constraints and invariants.

Abstract data and representation

• Abstract data types allow to capture the invariants and constraints of the domain.
• Construction of abstract data may fail.
• Representation of abstract data is an injection in the structural side and always succeeds.
• Roundtripping from ADT -> Representation -> ADT never fails.

Shape

• The structure of raw data in informatics is linear (and via grammars) can be represented as a tree. This is serialisation and deserialisation.
• Non-informatic physical data may have a 3d-structure. Example: 2d grid on paper. But in informatics everything is just 1d.
• Data already inside some domain may contain already complex invariants and multi-dimensional or hypergraph structures.
• Going from linearised data to the domain may involve jumps through several domains (e.g.: lex to tokens -> parser to AST, DTO <-> domain data, digits -> number -> currency amount).

Immutability

• Data is always implemented immutably.
• But there may be immutable “objects” implemented by non-data.
  • Classic example: a read-only database replica. Is not data, because the connection/data retrival may fail.
  • Function references.
  • Immutable references in high-level languages. May be implemented by different pointers due to a moving garbage collector.
  • An immutable datastructure with a caching/memoizing/amortising element.
  • Indices between several immutable data elements.

Implementation

• A type system can track not only data, but also abstract data.
• The runtime of a system may track a subset of data via known implementation atoms, construction-only composities and deep freezing of objects.
  • This can be a bit in the object header, set upon construction or freezing.