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  1. Proceedings of the Fourth International Workshop on Logical Frameworks and Meta-Languages (LFMTP '09)
  2. Theory support for weak higher order abstract syntax in Isabelle/HOL
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Higher-order abstract syntax in classical higher-order logic
A syntactic account of singleton types via hereditary substitution
Formalizing a strong normalization proof for Moggi's computational metalanguage: a case study in Isabelle/HOL-nominal
How can we prove that a proof search method is not an instance of another?
Theory support for weak higher order abstract syntax in Isabelle/HOL
Coercive subtyping in lambda-free logical frameworks
Universal algebra over lambda-terms and nominal terms: the connection in logic between nominal techniques and higher-order variables
A practical module system for LF
The calculus of nominal inductive constructions: an intensional approach to encoding name-bindings
Higher-order constraint simplification in dependent type theory

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Theory support for weak higher order abstract syntax in Isabelle/HOL

Content Provider ACM Digital Library
Author Gunter, Elsa L. Osborn, Christopher J. Popescu, Andrei
Abstract We describe the theoretical underpinnings to support the construction of an extension to the Isabelle/HOL theorem prover to support the creation of datatypes for weak higher-order abstract syntax, and give an example of its application. This theoretical basis is centered around the concept of variable types (i.e. types whose elements are variables), and the concept of two terms in a given type having the "same structure" up to a given set of substitutions (the difference set) of one variable for another as allowed by that set. We provide an axiomatization of types for which the notion of having the same structure is well-behaved with the axiomatic class of same_struct_thy. We show that being a same_struct_thy is preserved by products, sums and certain function spaces. Within a same_struct_thy, not all terms necessarily have the same structure as anything, including themselves. Those terms having the same structure as themselves relative to the empty difference set are said to be proper. A proper function from variables to terms corresponds to an abstraction of a variable in a term and also corresponds to substitution of variables for that variable in the term. Proper functions form the basis for a formalization of weak higher-order abstract syntax.
Starting Page 12
Ending Page 20
Page Count 9
File Format PDF
ISBN 9781605585291
DOI 10.1145/1577824.1577827
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2009-08-02
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Axiomatic classes Isabelle/hol Syntax with bindings Proper functions Weak hoas
Content Type Text
Resource Type Article
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