Year: 2015
Type: dissertation
Abstract: In this thesis we describe two new systems for reasoning about deductive\nsystems: HybridLF and Canonical HybridLF.\nHybridLF brings together the Hybrid approach (due to Ambler, Crole\nand Momigliano [15]) to higher-order abstract syntax (HOAS) in Isabelle/HOL\nwith the logical framework LF, a dependently-typed system for proving theorems\nabout logical systems. Hybrid provides a version of HOAS in the form of\nthe lambda calculus, in which Isabelle functions are automatically converted\nto a nameless de Bruijn represenation. Hybrid allows untyped expressions to\nbe entered as human-readable functions, which are then translated into the\nmachine-friendly de Bruijn form. HybridLF uses and updates these techniques\nfor variable representation in the context of the dependent type theory\nLF, providing a version of HOAS in the form of LF.\nCanonical HybridLF unites the variable representation techniques of\nHybrid with Canonical LF, in which all terms are in canonical form and definitional\nequality is reduced to syntactic equality. We extend the Hybrid approach\nto HOAS to functions with multiple variables by introducing a family\nof abstraction functions, and use the Isabelle option type to denote errors instead\nof including an ERR element in the Canonical HybridLF expression\ntype.\nIn both systems we employ the meta-logic M2 to prove theorems about\ndeductive systems. M2 [28] is a first-order logic in which quantifiers range\nover the objects and types generated by an LF signature (that encodes a\ndeductive system). As part of the implementation of M2 we explore higher-order\nunification in LF, adapting existing approaches to work in our setting.
Author: Amy Elizabeth Furniss
Language: English
Subfield: Software
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W2240654589