Developments in Formal Proofs
نویسنده
چکیده
A proof assistant is interactive computer software that humans use to prepare scripts of mathematical proofs. These proof scripts can be parsed and verified directly from the fundamental rules of logic and the foundational axioms of mathematics. The technology underlying proof assistants and formal proofs has been under development for decades and grew out of efforts in the early twentieth century to place mathematics on solid foundations. Proof assistants have been built upon various mathematical foundations, including Zermelo-Fraenkel set theory (Mizar), Higher Order Logic (HOL), and dependent type theory (Coq) [50], [37], [14]. A formal proof is one that has been verified from first principles (generally by computer).
منابع مشابه
Towards Animation of Proofs {testing proofs by examples{
In this paper, we introduce the notion of proof animation. It is a new application of the principle of \Curry-Howard isomorphism" to formal proof developments. Logically, proof animation is merely a contrapositive of \proofs as programs," which is an application of Curry-Howard isomorphism to formal program developments. Nonetheless, the new viewpoint totally changes the scene. The motivation, ...
متن کاملSupporting Reuse of Event-B Developments through Generic Instantiation
It is believed that reusability in formal development should reduce the time and cost of formal modelling within a production environment. Along with the ability to reuse formal models, it is desirable to avoid unnecessary re-proof when reusing models. Event-B is a formal method that allows modelling and refinement of systems. Event-B supports generic developments through the context construct....
متن کاملLattice Properties
This formalization introduces and collects some algebraic structures based on lattices and complete lattices for use in other developments. The structures introduced are modular, and lattice ordered groups. In addition to the results proved for the new lattices, this formalization also introduces theorems about latices and complete lattices in general.
متن کاملTowards Formal Proof Metrics
Recent years have seen increasing success in building large formal proof developments using interactive theorem provers (ITPs). Some proofs have involved many authors, years of effort, and resulted in large, complex interdependent sets of proof “source code” files. Developing these in the first place, and maintaining and extending them afterwards, is a considerable challenge. It has prompted th...
متن کاملThe Twelvefold Way
This entry provides all cardinality theorems of the Twelvefold Way. The Twelvefold Way [1, 5, 6] systematically classifies twelve related combinatorial problems concerning two finite sets, which include counting permutations, combinations, multisets, set partitions and number partitions. This development builds upon the existing formal developments [2, 3, 4] with cardinality theorems for those ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1408.6474 شماره
صفحات -
تاریخ انتشار 2014