Unsolvable terms in typed lambda calculus with fix-point operators: Extended abstract
We consider the finitely typed lambda calculus with "fixed-point" combinators Yσ 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.
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