Nominal Unification from a Higher-Order Perspective

Nominal Logic is a version of first-order logic with equality, name-binding, renaming via name-swapping and freshness of names. Contrarily to higher-order logic, bindable names, called atoms, and instantiable variables are considered as distinct entities. Moreover, atoms are capturable by instantiations, breaking a fundamental principle of lambda-calculus. Despite these differences, nominal unification can be seen from a higher-order perspective. From this view, we show that nominal unification can be reduced to a particular fragment of higher-order unification problems: Higher-Order Pattern Unification. This reduction proves that nominal unification can be decided in quadratic deterministic time, using the linear algorithm for Higher-Order Pattern Unification. We also prove that the translation preserves most generality of unifiers

Nominal Unification of Higher Order Expressions with Recursive Let

A sound and complete algorithm for nominal unification of higher-order expressions with a recursive let is described, and shown to run in non-deterministic polynomial time. We also explore specializations like nominal letrec-matching for plain expressions and for DAGs and determine the complexity of corresponding unification problems.Comment: Pre-proceedings paper presented at the 26th International Symposium on Logic-Based Program Synthesis and Transformation (LOPSTR 2016), Edinburgh, Scotland UK, 6-8 September 2016 (arXiv:1608.02534

Closed nominal rewriting and efficiently computable nominal algebra equality

We analyse the relationship between nominal algebra and nominal rewriting, giving a new and concise presentation of equational deduction in nominal theories. With some new results, we characterise a subclass of equational theories for which nominal rewriting provides a complete procedure to check nominal algebra equality. This subclass includes specifications of the lambda-calculus and first-order logic.Comment: In Proceedings LFMTP 2010, arXiv:1009.218

From nominal sets binding to functions and lambda-abstraction: connecting the logic of permutation models with the logic of functions

Permissive-Nominal Logic (PNL) extends first-order predicate logic with term-formers that can bind names in their arguments. It takes a semantics in (permissive-)nominal sets. In PNL, the forall-quantifier or lambda-binder are just term-formers satisfying axioms, and their denotation is functions on nominal atoms-abstraction. Then we have higher-order logic (HOL) and its models in ordinary (i.e. Zermelo-Fraenkel) sets; the denotation of forall or lambda is functions on full or partial function spaces. This raises the following question: how are these two models of binding connected? What translation is possible between PNL and HOL, and between nominal sets and functions? We exhibit a translation of PNL into HOL, and from models of PNL to certain models of HOL. It is natural, but also partial: we translate a restricted subsystem of full PNL to HOL. The extra part which does not translate is the symmetry properties of nominal sets with respect to permutations. To use a little nominal jargon: we can translate names and binding, but not their nominal equivariance properties. This seems reasonable since HOL---and ordinary sets---are not equivariant. Thus viewed through this translation, PNL and HOL and their models do different things, but they enjoy non-trivial and rich subsystems which are isomorphic

Relating Nominal and Higher-order Abstract Syntax Specifications

Nominal abstract syntax and higher-order abstract syntax provide a means for describing binding structure which is higher-level than traditional techniques. These approaches have spawned two different communities which have developed along similar lines but with subtle differences that make them difficult to relate. The nominal abstract syntax community has devices like names, freshness, name-abstractions with variable capture, and the new-quantifier, whereas the higher-order abstract syntax community has devices like lambda-binders, lambda-conversion, raising, and the nabla-quantifier. This paper aims to unify these communities and provide a concrete correspondence between their different devices. In particular, we develop a semantics-preserving translation from alpha-Prolog, a nominal abstract syntax based logic programming language, to G-, a higher-order abstract syntax based logic programming language. We also discuss higher-order judgments, a common and powerful tool for specifications with higher-order abstract syntax, and we show how these can be incorporated into G-. This establishes G- as a language with the power of higher-order abstract syntax, the fine-grained variable control of nominal specifications, and the desirable properties of higher-order judgments.Comment: To appear in PPDP 201

The unification bonus (malus) in postwall Eastern Germany

This paper presents estimates of the unification bonus for East Germans over the period 1991 to 1998. The unification bonus is defined as the discounted value of the difference between a person?s actual income and his or her counterfactual real income stream forecast for a hypothetical continuation of economic life in a static GDR. The two main issues tackled in this study are the construction of valid deflators for a comparison of real incomes during the transition from a centralized to a market economy and the estimation of plausible counterfactual income streams. Our central result is that 19 percent of East Germans received a present value malus and so can be regarded as unification losers but that the aggregate bonus is ten times the size of the aggregate malus of the sample. --Real income comparison,income distribution and mobility,economies in transition

Wages and Wage-Bargaining Institutions in the Emu : A Survey of the Issues

A perceived need to increase nominal wage flexibility as a substitute for domestic monetary policy and a tendency to less wage moderation are likely to promote bargaining co-ordination and social pacts in the EMU. But such co-ordination is not likely to be sustainable in the long run, as it conflicts with other forces working in the direction of decentralization and deunionisation. Although monetary unification will strengthen the incentives for higher-level transnational co-ordination of wage bargaining, such a development is improbable because of the co-ordination costs involved. If transnational co-ordination develops, it is most likely to occur within multinational firms.Wage bargaining, co-ordination, monetary union

Germany's Slump Explaining the Unemployment Crisis of the 1990s

According to a widespread view, Germany's unemployment crisis is caused by rigid labour markets, low profitability and increasing international competition. We argue that this view does not provide a convincing explanation for the dramatic rise in Germany's unemployment rate since 1989, first because no distinction is drawn between the situation in the Eastern part of Germany and that in the Western part of Germany, and second because supply-side conditions in the Western part of Germany have not generally deteriorated. We argue that Germany's slump is the result of a series of adverse supply and demand shocks since unification. Supply shocks dominated in the East, demand shocks in the West. These shocks were mainly policy-induced. The adoption of an extremely overvalued exchange rate and rapid wage increases in East Germany magnified the general problems of transition, resulting in a loss of employment of more than a third and a sustained structural weakness of its economy. The wage explosion was made possible by the government's failure to create a proper institutional framework for wage negotiations. The unification shock to the East added at least 2.5 percentage points to Germany's overall unemployment rate, as measured by the OECD definition. We attribute some 1.5 to 2.5 percentage points of the present unemployment rate to the weak economic growth of the last several years and the impact of the increasing tax wedge on the wage level. Weak growth has been largely the consequence of uncoordinated, contradictory and procyclical macroeconomic policies that have been adopted since unification, while the increasing tax wedge has been mostly driven by the decision of the government to finance unification partly through the social security system. Econometric evidence suggests a structural break in aggregate wage-setting in West Germany, with increased nominal flexibility in recent years and insignificant persistent effects since the 1980s. Hence, aggregate wage setting in the Western part of Germany is highly responsive to unemployment, while in the Eastern part, it is not.German economy 1989-97, unemployment, unification

"On the 'Burden' of German Unification The Economic Consequences of Messrs. Waigel and Tietmeyer"

This paper investigates the causes of western Germany's remarkably poor performance since 1992. The paper challenges the view that the poor record of the nineties, particularly the marked deterioration in public finances since unification, might be largely attributable to unification. Instead, the analysis highlights the role of ill-timed and overly ambitious fiscal consolidation in conjunction with tight monetary policies of an exceptional length and degree. The issue of fiscal sustainability and Germany's fiscal and monetary policies are assessed both in the light of economic theory and in comparison to the best practices of other more successful countries. The analysis concludes that Germany's dismal record of the nineties must not be seen as a direct and apparently inevitable result of unification. Rather, the record arose as a perfectly unnecessary consequence of unsound macro demand policies conducted under the Bundesbank's dictate in response to it, policies that caused the severe and protracted de-stabilization of western Germany in the first place.

On the 'Burden' of German Unification: The Economic Consequences of Messrs. Waigel and Tietmeyer

This paper investigates the causes of western Germany's remarkably poor performance since 1992. The paper challenges the view that the poor record of the nineties, particularly the marked deterioration in public finances since unification, might be largely attributable to unification. Instead, the analysis highlights the role of ill-timed and overly ambitious fiscal consolidation in conjunction with tight monetary policies of an exceptional length and degree. The issue of fiscal sustainability and Germany's fiscal and monetary policies are assessed both in the light of economic theory and in comparison to the best practices of other more successful countries. The analysis concludes that Germany's dismal record of the nineties must not be seen as a direct and apparently inevitable result of unification. Rather, the record arose as a perfectly unnecessary consequence of unsound macro demand policies conducted under the Bundesbank's dictate in response to it, policies that caused the severe and protracted de-stabilization of western Germany in the first place.