Foundational extensible corecursion: a proof assistant perspective
نویسندگان
چکیده
منابع مشابه
Foundational Extensible Corecursion
This paper presents a theoretical framework for defining corecursive functions safely in a total setting, based on corecursion up-to and relational parametricity. The end product is a general corecursor that allows corecursive (and even recursive) calls under wellbehaved operations, including constructors. Corecursive functions that are well behaved can be registered as such, thereby increasing...
متن کاملFriends with Benefits - Implementing Corecursion in Foundational Proof Assistants
We introduce AmiCo, a tool that extends a proof assistant, Isabelle/ HOL, with flexible function definitions well beyond primitive corecursion. All definitions are certified by the assistant’s inference kernel to guard against inconsistencies. A central notion is that of friends: functions that preserve the productivity of their arguments and that are allowed in corecursive call contexts. As ne...
متن کاملCrafting a Proof Assistant
Proof assistants are complex applications whose development has never been properly systematized or documented. This work is a contribution in this direction, based on our experience with the development of Matita: a new interactive theorem prover based—as Coq—on the Calculus of Inductive Constructions (CIC). In particular, we analyze its architecture focusing on the dependencies of its compone...
متن کاملGrowing a Proof Assistant
Theoreticians often use sophisticated notation to communicate and reason about key ideas in their theories and models. Notation is often domain-specific or even invented on-the-fly when creating a new theory or model. Proof assistants aid theoreticians by rigorously checking formal models, but have poor support for allowing users to conveniently define and use sophisticated notation. For exampl...
متن کاملFoundational Proof Certificates
Consider a world where exporting proof evidence into a well defined, universal, and permanent format is taken as “feature zero” for computational logic systems. In such a world, provers will communicate and share theorems and proofs; libraries will archive and organize proofs; and marketplaces of proofs would be open to any prover that admits checkable proof objects. In that world, proof checke...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: ACM SIGPLAN Notices
سال: 2015
ISSN: 0362-1340,1558-1160
DOI: 10.1145/2858949.2784732