Predikérbarity

Predikérbarity refers to a property of certain programming languages and systems that allows for the automatic generation of proof assistants or theorem provers from a given program. The core idea is that the program itself contains enough information to construct a formal proof of its correctness. This means that if a program is deemed "predikérbar", it can be used to build a system that can verify that the program behaves as intended, according to its specifications.

This concept is closely related to the idea of realizability, where a proof of a statement is accompanied by a computational procedure that demonstrates the truth of the statement. In the context of predikérbarity, the program is the computational procedure, and the proof assistant generated from it serves to formally verify the program's properties. Languages that exhibit high predikérbarity often have strong typing systems and features that align closely with logical formalisms, such as dependent types.

The benefits of predikérbarity include enhanced software reliability and security, as it enables rigorous verification. By automating parts of the proof process, it can reduce the burden on human theorem provers and allow for more extensive checking of complex software. However, achieving high predikérbarity can require significant design effort in the programming language itself, and the resulting proof assistants can be complex to use. The term is most commonly encountered in theoretical computer science and formal methods research.