3 research outputs found
Data Types as Quotients of Polynomial Functors
A broad class of data types, including arbitrary nestings of inductive types, coinductive types, and quotients, can be represented as quotients of polynomial functors. This provides perspicuous ways of constructing them and reasoning about them in an interactive theorem prover
Quotients of Bounded Natural Functors
The functorial structure of type constructors is the foundation for many
definition and proof principles in higher-order logic (HOL). For example,
inductive and coinductive datatypes can be built modularly from bounded natural
functors (BNFs), a class of well-behaved type constructors. Composition,
fixpoints, and, under certain conditions, subtypes are known to preserve the
BNF structure. In this article, we tackle the preservation question for
quotients, the last important principle for introducing new types in HOL. We
identify sufficient conditions under which a quotient inherits the BNF
structure from its underlying type. Surprisingly, lifting the structure in the
obvious manner fails for some quotients, a problem that also affects the
quotients of polynomial functors used in the Lean proof assistant. We provide a
strictly more general lifting scheme that supports such problematic quotients.
We extend the Isabelle/HOL proof assistant with a command that automates the
registration of a quotient type as a BNF, reducing the proof burden on the user
from the full set of BNF axioms to our inheritance conditions. We demonstrate
the command's usefulness through several case studies.Comment: Extended version of homonymous IJCAR 2020 pape
Automated Deduction – CADE 28
This open access book constitutes the proceeding of the 28th International Conference on Automated Deduction, CADE 28, held virtually in July 2021. The 29 full papers and 7 system descriptions presented together with 2 invited papers were carefully reviewed and selected from 76 submissions. CADE is the major forum for the presentation of research in all aspects of automated deduction, including foundations, applications, implementations, and practical experience. The papers are organized in the following topics: Logical foundations; theory and principles; implementation and application; ATP and AI; and system descriptions