Abstract

this paper, we sketch the definition theory for a nonstrict positive free logic in which there is exactly one error object err to which all terms without existential import can refer. Having exactly one error object identifies nontermination and all run-time errors. This is most natural in languages such as Miranda and haskell in which execution is aborted immediately when an error is raised [16]. By using a free logic, we are able to state the axioms of a mathematical theory without cluttering the axiomatization with error conditions, as would be required using restricted quantification in standard logic. For example, Peano's axiom:

Citations