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We study superdevelopments in the weak lambda calculus of Cagman and Hindley,a confluent variant of the standard weak lambda calculus in which reductionbelow lambdas is forbidden. In contrast to developments, a superdevelopmentfrom a term M allows not only residuals of redexes in M to be reduced but alsosome newly created ones. In the lambda calculus there are three ways newredexes may be created; in the weak lambda calculus a new form of redexcreation is possible. We present labeled and simultaneous reductionformulations of superdevelopments for the weak lambda calculus and prove themequivalent.

Superdevelopments for Weak Reduction