A Negishi Approach to Recursive Contracts

Even in statically typed languages it is useful to have certain invariants checked dynamically. Findler and Felleisen gave an algorithm for dynamically checking expressive higher-order types called contracts. They did not, however, give a semantics of contracts. The lack of a semantics makes it impossible to define and prove soundness and completeness of the checking algorithm. (Given a semantics, a sound checker never reports violations that do not exist under that semantics; a complete checker is – in principle – able to find violations when violations exist.) Ideally, a semantics should capture what programmers intuitively feel is the meaning of a contract or otherwise clearly point out where intuition does not match reality. In this paper we give an interpretation of contracts for which we prove the Findler-Felleisen algorithm sound and (under reasonable assumptions) complete. While our semantics mostly matches intuition, it also exposes a problem with predicate contracts where an arguably more intuitive interpretation than ours would render the checking algorithm unsound. In our semantics we have to make use of a notion of safety (which we define in the paper) to avoid unsoundness. We are able to eliminate the “leakage” of safety into the semantics by changing the language, replacing the original version of unrestricted predicate contracts with a restricted form. The corresponding loss in expressive power can be recovered by making safety explicit as a contract. This can be done either in ad-hoc fashion or by including general recursive contracts. The addition of recursive contracts has far-reaching implications, deeply affecting the formulation of our model and requiring different techniques for proving soundness.

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Recursive contracts, firm longevity, and rat races: An experimental analysis

European Economic Review ◽

10.1016/j.euroecorev.2013.03.009 ◽

2013 ◽

Vol 61 ◽

pp. 217-231 ◽

Cited By ~ 1

Author(s):

Peter Bardsley ◽

Nisvan Erkal ◽

Nikos Nikiforakis ◽

Tom Wilkening

Keyword(s):

Experimental Analysis ◽

Recursive Contracts

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Recursive Contracts

Econometrica ◽

10.3982/ecta9902 ◽

2019 ◽

Vol 87 (5) ◽

pp. 1589-1631 ◽

Cited By ~ 9

Author(s):

Albert Marcet ◽

Ramon Marimon

Keyword(s):

Bellman Equation ◽

Dynamic Models ◽

Optimization Problems ◽

Dynamic Contracting ◽

Economic Dynamic ◽

Recursive Formulation ◽

Recursive Solution ◽

Continuation Problem ◽

Recursive Contracts

We obtain a recursive formulation for a general class of optimization problems with forward‐looking constraints which often arise in economic dynamic models, for example, in contracting problems with incentive constraints or in models of optimal policy. In this case, the solution does not satisfy the Bellman equation. Our approach consists of studying a recursive Lagrangian. Under standard general conditions, there is a recursive saddle‐point functional equation (analogous to a Bellman equation) that characterizes a recursive solution to the planner's problem. The recursive formulation is obtained after adding a co‐state variable μ t summarizing previous commitments reflected in past Lagrange multipliers. The continuation problem is obtained with μ t playing the role of weights in the objective function. Our approach is applicable to characterizing and computing solutions to a large class of dynamic contracting problems.

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