Fsub with Recursive Types: \types-as-propositions" Interpretation in M. Rabin's S2s
نویسنده
چکیده
Subtyping judgments of the polymorphic second-order typed-calculus F extended by recursive types and diierent known inference rules for these types could be interpreted in S2S, M.Rabin's monadic second-order theory of two successor functions. On the one hand, this provides a comprehensible model of the parametric and inheritance polymorphisms over recursive types, on the other, proves that the corresponding subtyping theories are not essentially undecidable, i.e., possess consistent de-cidable extensions.
منابع مشابه
A Semantic Version of the Diller-Nahm Variant of Gödel’s Dialectica Interpretation
According to Gödel’s original Dialectica Interpretation from 1958 a proposition is a pair of types X and Y together with a decidable relation R ⊆ X×Y between them. For our purposes we assume that types are subsets of N and (constructive) functionals between them are total recursive functions between sets of natural numbers. Entailment between propositions (X, Y,R) and (U, V, S) is given by a pa...
متن کاملThe Least Must Speak with the Greatest
We extend a propositions-as-types correspondence between linear logic and session types to include recursive sessions. Our extension takes least and greatest fixed points as dual, an idea well-known to theorists, but which has not previously appeared in the treatment of recursive sessions. We preserve the freedom from races, deadlock, and livelock that is a hallmark of the propositions-as-types...
متن کاملP´olya Urn Models and Connections to Random Trees: A Review
This paper reviews P´olya urn models and their connection to random trees. Basic results are presented, together with proofs that underly the historical evolution of the accompanying thought process. Extensions and generalizations are given according to chronology: • P´olya-Eggenberger’s urn • Bernard Friedman’s urn • Generalized P´olya urns • Extended urn schemes • Invertible urn schemes ...
متن کاملCombining Recursive and Dynamic Types
A denotational semantics of simply typed lambda calculus with a basic type Dynamic, modelling values whose type is to be inspected at run-time, has been given by Abadi e.a..1]. We extend this interpretation to cover (formally contractive) recursive types as well. Soundness of typing rules and freeness of run-time type errors for well-typed programs hold. The interpretation works also for implic...
متن کاملThe Emptiness Problem for Automata on Infinite Trees
The purpose of this paper is to give an alternative proof to the decidability of the emptiness problem for tree automata, as shown in Rabin [4]. The proof reduces the emptiness problem for automata on infinite trees to that for automata on finite trees, by showing that any automata definable set of infinite trees must contain a finitelygenerable tree. Section 1: Introduction The analysis of fin...
متن کامل