Meta - Theory of Sequent - Style Calculi in CoqA
نویسنده
چکیده
We describe a formalisation of proof theory about sequent-style calculi, based on informal work in DP96]. The formalisation uses de Bruijn nameless dummy variables (also called de Bruijn indices) dB72], and is performed within the proof assistant Coq BB + 96]. We also present a description of some of the other possible approaches to formal meta-theory, particularly an abstract named syntax and higher order abstract syntax.
منابع مشابه
Machine - Assisted Meta - Theory of Sequent - StyleCalculi
A formalisation of the implicational fragments of two sequent calculi and a sequent-style presentation of natural deduction in Coq is presented. The systems presented are all typed lambda calculi. Based on this formalisation, some general comments on the feasibility of performing meta-theoretic proofs about typed lambda calculi in a proof assistant based on higher-order type theory are made. Co...
متن کاملPrincipal-Centric Reasoning in Constructive Authorization Logic
We present an authorization logic that is quite similar to constructive modal S4. The logic assumes that principals are conceited in their beliefs. We describe the sequent calculus, Hilbert-style axiomatization, and Kripke semantics of the logic. A distinguishing characteristic of the sequent calculus is that hypothetical reasoning is relativized to beliefs of principals. We prove several meta-...
متن کاملFormalized Meta-Theory of Sequent Calculi for Substructural Logics
When studying sequent calculi, proof theorists often have to prove properties about the systems, whether it is to show that they are “well-behaved”, amenable to automated proof search, complete with respect to another system, consistent, among other reasons. These proofs usually involve many very similar cases, which leads to authors rarely writing them in full detail, only pointing to one or t...
متن کاملImplementing Dependent Types Using Sequent Calculi
A critical issue concerning programming languages and proof assistants based on dependent type theory is the efficient implementation of reduction on open terms, where meta-variables can appear: this question is important not only for the execution of dependently typed programs, but already in the typechecker implementing the validation of such programs, through the use of the conversion rule. ...
متن کاملApplications of Proof Theory to Isabelle
Isabelle [3, 4] is a generic theorem prover. It suppports interactive proof in several formal systems, including first-order logic (intuitionistic and classical), higher-order logic, Martin-Löf type theory, and Zermelo-Fraenkel set theory. New logics can be introduced by specifying their syntax and rules of inference. Both natural deduction and sequent calculi are allowed. Isabelle’s approach i...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 1997