A Formalisation of Nominal α-equivalence with A and AC Function Symbols
نویسندگان
چکیده
A formalisation of soundness of the notion of α-equivalence in nominal abstract syntax modulo associative (A) and associative-commutative (AC) equational theories is described. Initially, the notion of α-equivalence is specified based on a so called “weak” nominal relation as suggested by Urban in his nominal development in Isabelle/HOL. Then, it is formalised in Coq that this equality is indeed an equivalence relation. After that, general α-equivalence with A and AC function symbols is specified and formally proved to be an equivalence relation. As corollaries, the soundness α-equivalence modulo A and modulo AC is obtained. Finally, an algorithm for checking α-equivalence modulo A and AC is proposed. General α-equivalence problems are log-linearly solved while AC and the combination of A and AC α-equivalence problems have the same complexity as standard first-order approaches. This development is a first step towards verification of nominal matching, unification and narrowing algorithms modulo equational theories in general.
منابع مشابه
Extensions of nominal terms
This thesis studies two major extensions of nominal terms. In particular, we study an extension with λ-abstraction over nominal unknowns and atoms, and an extension with an arguably better theory of freshness and α-equivalence. Nominal terms possess two levels of variable: atoms a represent variable symbols, and unknowns X are ‘real’ variables. As a syntax, they are designed to facilitate metap...
متن کاملFormalisation of Stoughton's Substitution for Lambda Calculus in Constructive Type Theory
In [7], Allen Stoughton proposed a notion of substitution for the Lambda calculus formulated in its original syntax with only one sort of symbols (names) for variables and without identifying α-convertible terms. According to such formulation, the action of substitution on terms is de ned by simple structural recursion and an interesting theory arises concerning e.g. α conversion. In this paper...
متن کاملGentle Formalisation of Stoughton’s Lambda Calculus Substitution
In [5], Allen Stoughton proposed a notion of substitution for the Lambda calculus formulated in its original syntax with only one sort of symbols (names) for variables –without identifying α-convertible terms. According to such formulation, the action of substitution on terms is defined by simple structural recursion and an interesting theory arises concerning e.g. α conversion. In this paper w...
متن کاملFormalising in Nominal Isabelle Crary's Completeness Proof for Equivalence Checking
In the book on Advanced Topics in Types and Programming Languages, Crary illustrates the reasoning technique of logical relations in a case study about equivalence checking. He presents a type-driven equivalence checking algorithm and verifies its completeness with respect to a definitional characterisation of equivalence. We present in this paper a formalisation of Crary’s proof using Isabelle...
متن کاملThe graph of equivalence classes and Isoclinism of groups
Let $G$ be a non-abelian group and let $Gamma(G)$ be the non-commuting graph of $G$. In this paper we define an equivalence relation $sim$ on the set of $V(Gamma(G))=Gsetminus Z(G)$ by taking $xsim y$ if and only if $N(x)=N(y)$, where $ N(x)={uin G | x textrm{ and } u textrm{ are adjacent in }Gamma(G)}$ is the open neighborhood of $x$ in $Gamma(G)$. We introduce a new graph determined ...
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:
- Electr. Notes Theor. Comput. Sci.
دوره 332 شماره
صفحات -
تاریخ انتشار 2017