Truly Modular (Co)datatypes for Isabelle/HOL

نویسندگان

  • Jasmin Christian Blanchette
  • Johannes Hölzl
  • Andreas Lochbihler
  • Lorenz Panny
  • Andrei Popescu
  • Dmitriy Traytel
چکیده

We extended Isabelle/HOL with a pair of definitional commands for datatypes and codatatypes. They support mutual and nested (co)recursion through well-behaved type constructors, including mixed recursion–corecursion, and are complemented by syntaxes for introducing primitive (co)recursive functions and by a general proof method for reasoning coinductively. As a case study, we ported Isabelle’s Coinductive library to use the new commands, eliminating the need for tedious ad hoc constructions.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Nonfree Datatypes in Isabelle/HOL - Animating a Many-Sorted Metatheory

Datatypes freely generated by their constructors are well supported in mainstream proof assistants. Algebraic specification languages offer more expressive datatypes on axiomatic means: nonfree datatypes generated from constructors modulo equations. We have implemented an Isabelle/HOL package for nonfree datatypes, without compromising foundations. The use of the package, and its nonfree iterat...

متن کامل

Primitively (Co)recursive Definitions for Isabelle/HOL

Isabelle/HOL has recently been enriched with a definitional package for datatypes and codatatypes. The package introduces the specified types and derives auxiliary constants and characteristic theorems, notably (co)recursors and (co)induction principles. We now introduce support for high-level specifications of (co)recursive functions, in the form of three commands: primrec, primcorec, and prim...

متن کامل

Nitpick: A Counterexample Generator for Isabelle/HOL Based on the Relational Model Finder Kodkod (System Description)∗

Nitpick is a counterexample generator for Isabelle/HOL that builds on Kodkod, a SAT-based firstorder relational model finder. Nitpick supports unbounded quantification, (co)inductive predicates and datatypes, and (co)recursive functions. Fundamentally a finite model finder, it approximates infinite types by finite subsets. Our experimental results on Isabelle theories and the TPTP library indic...

متن کامل

Inductive Datatypes in HOL - Lessons Learned in Formal-Logic Engineering

Isabelle/HOL has recently acquired new versions of definitional packages for inductive datatypes and primitive recursive functions. In contrast to its predecessors and most other implementations, Isabelle/HOL datatypes may be mutually and indirect recursive, even infinitely branching. We also support inverted datatype definitions for characterizing existing types as being inductive ones later. ...

متن کامل

Foundational (Co)datatypes and (Co)recursion for Higher-Order Logic

We describe a line of work that started in 2011 towards enriching Isabelle/HOL’s language with coinductive datatypes, which allow infinite values, and with a more expressive notion of inductive datatype than previously supported by any system based on higher-order logic. These (co)datatypes are complemented by definitional principles for (co)recursive functions and reasoning principles for (co)...

متن کامل

ذخیره 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 2014