A First Step in the Translation of Alloy to Coq

International audienceAlloy is both a formal language and a tool for software mod-eling. The language is basically first order relational logic. The analyzer is based on instance finding: it tries to refute assertions and if it succeeds it reports a counterexample. It works by translating Alloy models and instance finding into SAT problems. If no instance is found it does not mean the assertion is satisfied. Alloy relies on the small scope hypothesis: examining all small cases is likely to produce interesting counterexamples. This is very valuable when developing a system. However, Alloy cannot show their absence. In this paper, we propose an approach where Alloy can be used as a first step, and then using a tool we develop, Alloy models can be translated to Coq code to be proved correct interactively

GARP, SEPARABILITY, AND THE REPRESENTATIVE AGENT

We examine whether annual,quarterly, and monthly U.S. aggregateconsumption data could have beengenerated by a utility-maximizingrepresentative agent withintertemporally separable utility. Themodel appears inapplicable over the fulltime periods covered by the NIPA data,which are the sample periods often usedin the literature. The model doesappear applicable, however, over longsubsamples. The data also areinconsistent with separabilityassumptions routinely made in theliterature. In particular, the maincategories of consumption (nondurables,services, and durables) are not mutuallyseparable. We consider the implicationsof our results for inference aboutconsumption based on the representative-agent model.

SEPARABILITY, AGGREGATION, AND EULER EQUATION ESTIMATION

We derive a seminonparametric utility function containing theconstant relative risk aversion (CRRA) function as a special case,and we estimate the associated Euler equations with U.S. consumptiondata. There is strong evidence that the CRRA function ismisspecified. The correctly specified function includes laggedeffects of durable goods and perhaps nondurable goods, is bounded asrequired by Arrow s Utility Boundedness Theorem, and has a positiverate of time preference. Constraining sample periods and separabilitystructure to be consistent with the generalized axiom of revealedpreference affects estimation results substantially. Using Divisiaaggregates instead of the NIPA aggregates also affects results.