System F with Constraint Types

System F is a type system that can be seen as both a proof system for second-order propositional logic and as a polymorphic programming language. In this work we explore several extensions of System F by types which express subtyping constraints. These systems include terms which represent proofs of subtyping relationships between types. Given a proof that one type is a subtype of another, one may use a coercion term constructor to coerce terms from the first type to the second. The ability to manipulate type constraints as first-class entities gives these systems a lot of expressive power, including the ability to encode generalized algebraic data types and intensional type analysis. The main contributions of this work are in the formulation of constraint types and a proof of strong normalization for an extension of System F with constraint types

On the legitimacy of coercion for the nancing of public goods

The literature on public goods has shown that e?cient outcomes are impossible if participation constraints have to be respected. This paper addresses the question whether they should be imposed. It asks under what conditions e?ciency considerations justify that individuals are forced to pay for public goods that they do not value. It is shown that participation constraints are desirable if public goods are provided by a malevolent Leviathan. By contrast, with a Pigouvian planner, e?ciency can be achieved. Finally, the paper studies the delegation of public goods provision to a pro?t-maximizing ?rm. This also makes participation constraints desirable

A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions

The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm is in charge of giving a meaning to the terms, types and proof terms directly written by the user or generated by using tactics, decision procedures or general automation. The terms are written in an "external syntax" meant to be user friendly that allows omission of information, untyped binders and a certain liberal use of user defined sub-typing. The refiner modifies the terms to obtain related well typed terms in the internal syntax understood by the kernel of the ITP. In particular, it acts as a type inference algorithm when all the binders are untyped. The proposed algorithm is bi-directional: given a term in external syntax and a type expected for the term, it propagates as much typing information as possible towards the leaves of the term. Traditional mono-directional algorithms, instead, proceed in a bottom-up way by inferring the type of a sub-term and comparing (unifying) it with the type expected by its context only at the end. We propose some novel bi-directional rules for CIC that are particularly effective. Among the benefits of bi-directionality we have better error message reporting and better inference of dependent types. Moreover, thanks to bi-directionality, the coercion system for sub-typing is more effective and type inference generates simpler unification problems that are more likely to be solved by the inherently incomplete higher order unification algorithms implemented. Finally we introduce in the external syntax the notion of vector of placeholders that enables to omit at once an arbitrary number of arguments. Vectors of placeholders allow a trivial implementation of implicit arguments and greatly simplify the implementation of primitive and simple tactics

Social Welfare and Coercion in Public Finance

This paper develops an expanded framework for social planning in which the existence of coercion is explicitly acknowledged. Key issues concern the precise definition of coercion for individuals and in the aggregate, its difference from redistribution, and its incorporation into normative analysis. We explore modifications to traditional rules for optimal fiscal policy in the presence of coercion constraints and determine the degree of coercion implied by traditional social planning. The paper maps the trade-off between social welfare and aggregate coercion and explores its implications for normative policy and the comparative evaluation of institutions, including competitive democracy.coercion, redistribution, social planning, optimal fiscal policy, marginal cost of funds, public goods, collective choice

The Difference Prevention Makes: Regulating Preventive Justice

Since the terrorist attacks of September 11, 2001, the United States and many other countries have adopted a ‘‘paradigm of prevention,’’ employing a range of measures in an attempt to prevent future terrorist attacks. This includes the use of pre textual charges for preventive detention, the expansion of criminal liability to prohibit conduct that precedes terrorism, and expansion of surveillance at home and abroad. Politicians and government officials often speak of prevention as if it is an unqualified good. Everyone wants to prevent the next terrorist attack, after all. And many preventive initiatives, especially where they are not coercive and do not intrude on liberty, are welcome. But the move to a ‘‘preventive justice’’ model also creates potential for significant abuse. These risks suggest that we should be cautious about adopting preventive approaches, especially where they involve coercion. In part I of this essay, I articulate why preventive coercion is a problem. I respond, in particular, to a recent essay by Fred Schauer, ‘‘The Ubiquity of Prevention,’’ which argued that ‘‘it is a mistake to assume that preventive justice is a problem in itself [because] preventive justice is all around us, and it is hard to imagine a functioning society that could avoid it.’’ In part II, I outline the formal constitutional and other constraints that are implicated by preventive measures in the United States, and I demonstrate that these constraints play a relatively small role in the actual operation of preventive measures. In part III, I maintain that informal constraints may actually play a more significant operational role in checking the abuses of prevention

Applying Block Chain Technologies to Digital Voting Algorithms

Voting is a fundamental aspect to democracy. Many countries have advanced voting systems in place, but many of these systems have issues behind them such as not being anonymous or verifiable. Additionally, most voting systems currently have a central authority in charge of counting votes, which can be prone to corruption. We propose a voting system which mitigates many of these issues. Our voting system attempts to provide decentralization, pseudoanonymity, and verifiability. For our system, we have identified the requirements, implemented the backbone of the system, recognized some of its shortcomings, and proposed areas of future work on this voting system

International Coercion, Emulation and Policy Diffusion: Market-Oriented Infrastructure Reforms, 1977-1999

Why do some countries adopt market-oriented reforms such as deregulation, privatization and liberalization of competition in their infrastructure industries while others do not? Why did the pace of adoption accelerate in the 1990s? Building on neo-institutional theory in sociology, we argue that the domestic adoption of market-oriented reforms is strongly influenced by international pressures of coercion and emulation. We find robust support for these arguments with an event-history analysis of the determinants of reform in the telecommunications and electricity sectors of as many as 205 countries and territories between 1977 and 1999. Our results also suggest that the coercive effect of multilateral lending from the IMF, the World Bank or Regional Development Banks is increasing over time, a finding that is consistent with anecdotal evidence that multilateral organizations have broadened the scope of the “conditionality” terms specifying market-oriented reforms imposed on borrowing countries. We discuss the possibility that, by pressuring countries into policy reform, cross-national coercion and emulation may not produce ideal outcomes.http://deepblue.lib.umich.edu/bitstream/2027.42/40099/3/wp713.pd

Elaboration in Dependent Type Theory

To be usable in practice, interactive theorem provers need to provide convenient and efficient means of writing expressions, definitions, and proofs. This involves inferring information that is often left implicit in an ordinary mathematical text, and resolving ambiguities in mathematical expressions. We refer to the process of passing from a quasi-formal and partially-specified expression to a completely precise formal one as elaboration. We describe an elaboration algorithm for dependent type theory that has been implemented in the Lean theorem prover. Lean's elaborator supports higher-order unification, type class inference, ad hoc overloading, insertion of coercions, the use of tactics, and the computational reduction of terms. The interactions between these components are subtle and complex, and the elaboration algorithm has been carefully designed to balance efficiency and usability. We describe the central design goals, and the means by which they are achieved