Unsolvable terms in typed lambda calculus with fix-point operators: Extended abstract

Abstract

We consider the finitely typed lambda calculus with "fixed-point" combinators Y_σ of each type (σ→σ)→σ satisfying the equation Y=λf:σ→σ.f(Yf). (1) This formal system models computations with recursively defined equations. The decision problem for equality of terms of this calculus is open. We present a procedure for deciding when a λ-Y-term is "unsolvable"; this implies decidability of equations between λ-Y-terms and λ-terms without Y's. We also give tight characterizations of unsolvable terms under certain syntactic constraints.

Irina Bercovici died tragically on February 17, 1985. following childbirth. She left detailed notes for planned revisions and future improvements of the extended abstract she had submitted to the program committee. We hope to eventually carry to completion the improvements she planned, but we felt it appropriate to present here the available record of her written results at the time of her death. The present paper is the extended abstract submitted to the program committee, somewhat revised by us according to Irina's notes. — A. Meyer and V. Breazu-Tannen, MIT Laboratory for Computer Science.