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Examples

Term x + (y + 0).

• Domain "natural numbers".
  • Object constant 0 interpreted as "zero".
  • Binary function constant + interpreted as addition.
  • Assignment [x |-> "one", y |-> "two"]. gives natural number "three" as meaning.
  • Assignment [x |-> "one", y |-> "zero"] gives natural number "one" as meaning.
• Domain "character strings".
  • Object constant 0 interpreted as "empty string".
  • Binary function constant + interpreted as string concatenation.
  • Assignment [x |-> "hi, ", y |-> "babe"] gives string "hi, babe" as meaning.

Semantics of a term depends on domain and variable assignment.