Guard Your Daggers and Traces: On The Equational Properties of Guarded (Co-)recursion

  title={Guard Your Daggers and Traces: On The Equational Properties of Guarded (Co-)recursion},
  author={Stefan Milius and Tadeusz Litak},
Motivated by the recent interest in models of guarded (co-)recursion we study its equational properties. We formulate axioms for guarded fixpoint operators generalizing the axioms of iteration theories of Bloom and Esik. Models of these axioms include both standard (e.g., cpo-based) models of iteration theories and models of guarded recursion such as complete metric spaces or the topos of trees studied by Birkedal et al. We show that the standard result on the satisfaction of all Conway axioms… 

Guard Your Daggers and Traces: Properties of Guarded (Co-)recursion

It is shown that the standard result on the satisfaction of all Conway axioms by a unique dagger operation generalizes to the guarded setting and it is proved that guarded trace and guarded fixpoint operators are in one-to-one correspondence.

Sequent Calculus in the Topos of Trees

A sound and cut-free complete sequent calculus for KM lin is given via a strategy that decomposes implication into its static and irreflexive components and yields decidability of the logic and the coNP-completeness of its validity problem.

Dual-context calculi for modal logic

  • G. A. Kavvos
  • Computer Science
    2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
  • 2017
The resulting systems are dual-context systems, in the style pioneered by Girard, Barber, Plotkin, Pfenning, Davies, and others, that derive natural deduction systems for the necessity fragment of various constructive modal logics by exploiting a pattern found in sequent calculi.

Iteration and Labelled Iteration

Multimodal Dependent Type Theory

The consistency of MTT is proved and canonicity is established through an extension of recent type-theoretic gluing techniques, which hold irrespective of the choice of mode theory, and thus apply to a wide variety of modal situations.

Constructive Modalities with Provability Smack

I overview the work of the Tbilisi school on intuitionistic modal logics of well-founded/scattered structures and its connections with contemporary Theoretical Computer Science. Fixed-point theorems



Intensional Type Theory with Guarded Recursive Types qua Fixed Points on Universes

It is found that the functor category Grpdωop from the preordered set of natural numbers to the category of groupoids is a model of intensional type theory with guarded recursive types.

First Steps in Synthetic Guarded Domain Theory: Step-Indexing in the Topos of Trees

It is proposed that the internal logic of S provides the right setting for the synthetic construction of abstract versions of step-indexed models of programming languages and program logics.

New Foundations for Fixpoint Computations: FIX-Hyperdoctrines and the FIX-Logic

Productive coprogramming with guarded recursion

The concept of clock variables that index Nakano's guarded recursion are introduced, which allow us to "close over" the generation of infinite data, and to make finite observations, something that is not possible with guarded recursions alone.

Canonized Rewriting and Ground AC Completion Modulo Shostak Theories : Design and Implementation

A modular extension of ground AC-completion for deciding formulas in the combination of the theory of equality with user-defined AC symbols, uninterpreted symbols and an arbitrary signature disjoint Shostak theory X, implemented to extend the core of the Alt-Ergo theorem prover.

Iteration Theories: The Equational Logic of Iterative Processes

Written both for graduate students and research scientists in theoretical computer science and mathematics, this book provides a detailed investigation of the properties of the fixed point or

A very modal model of a modern, major, general type system

A model of recursive and impredicatively quantified types with mutable references is presented, interpreting all of the type constructors needed for typed intermediate languages and typed assembly languages used for object-oriented and functional languages and establishing a soundness proof of the typing systems underlying these TILs and TALs---ensuring that every well-typed program is safe.

Models of Sharing Graphs

This work develops the models of sharing graphs in terms of both syntax and semantics, and demonstrates that this framework can accommodate Milner’s action calculi, a proposed framework for general interactive computation, by showing that the calculi are equivalent to the closed fragments ofaction calculi and their higher-order/reflexive extensions.