Isabelle, Isar - a versatile environment for human readable formal proof documents

The basic motivation of this work is to make formal theory developments with machine-checked proofs accessible to a broader audience. Our particular approach is centered around the Isar formal proof language that is intended to support adequate composition of proof documents that are suitable for human consumption. Such primary proofs written in Isar may be both checked by the machine and read by human-beings; final presentation merely involves trivial pretty printing of the sources. Sound logical foundations of Isar are achieved by interpretation within the generic Natural Deduction framework of Isabelle, reducing all high-level reasoning steps to primitive inferences. The resulting Isabelle/Isar system is generic with respect to object-logics and proof tools, just as pure Isabelle itself. The full Isar language emerges from a small core by means of several derived elements, which may be combined freely with existing ones. This results in a very rich space of expressions of formal reasoning, supporting many viable proof techniques. The general paradigms of Natural Deduction and Calculational Reasoning are both covered particularly well. Concrete examples from logic, mathematics, and computer-science demonstrate that the Isar concepts are indeed sufficiently versatile to cover a broad range of applications.