We provide a coinductive definition of strongly convergent reductions between infinite lambda terms. This approach avoids the notions of ordinals and metric convergence which have appeared in the… (More)

As observed by Intrigila [16], there are hardly techniques available in the λ-calculus to prove that two λ-terms are not β-convertible. Techniques employing the usual Böhm Trees are inadequate when… (More)

We present a coinductive framework for defining infinitary analogues of equational reasoning and rewriting in a uniform way. We define the relation =, a notion of infinitary equational reasoning, and… (More)

We present a coinductive framework for defining and reasoning about the infinitary analogues of equational logic and term rewriting in a uniform way. We define ∞ =, the infinitary extension of a… (More)

We present a coinductive treatment of infinitary term rewriting with reductions of arbitrary ordinal length. Our framework allows the following succinct definition of the infinitary rewrite relation… (More)

We propose a natural syntactic account of extensional equality in type theory. Starting from the classical definition of extensional equality by induction on type structure, we show how the logical… (More)

We prove an extensionality theorem for the “type-in-type” dependent type theory with Σ-types. We suggest that the extensional equality type be identified with the logical equivalence relation on the… (More)

Working in the untyped lambda calculus, we study Morris’s λ-theory H+. Introduced in 1968, this is the original extensional theory of contextual equivalence. On the syntactic side, we show that this… (More)