M. Hyland. A Simple Proof of the Church-Rosser
Theorem.
This typed manuscript was written in Oxford in 1973. It contains a direct proof of
the Finiteness of Developments Theorem and a deduction from it
of Church-Rosser.
This copy came to me from Roger Hindley. It seems he had it via
Henk Barendregt as the writing on it is Barendregt's. Roger Hindley told me
that the approach which I took is different from that taken by Schroer.
Untitled Letter to Dana Scott
This dates to 1973-74. It contains a proof that there is a
Scott Domain (here an Algebraic Lattice)
which is isomorphic both to its function space and to its product with
itself. This shows inter alia that there is a cartesian closed category
with exactly one (non-trivial) object aside from the terminal.
Later Scott found a more elegant indirect proof of the existence of
Domains of that kind. But Paul Taylor revisited my construction
in his PhD thesis.
Handwritten note Topological spaces, limit spaces and continuous lattices.
This was written 1974-75. I must have read Brian Day's famous Reflection Theorem
paper when I wrote this but probably not other relevant material. It is related
to material in my PhD thesis.
Handwritten note Cartesian closed co-reflective
subcategories of TOP.
This was written 1974-75. I knew the case treated in J. L. Kelley's General Topology
and simply generalised.
Detailed handwritten notes for a talk Meaning and the lambda
calculus given at a Symposium held in Rome 1975.
Handwritten note Extensionality of Morris's and Wadsworth's
relations.
I am not sure when this was written. Surely after 1976 else I should
have been able to check the copy of Wadsworth's thesis which Gandy had;
and before 2000 as I distinctly remember mentioning it to Christian Urban
as proofs in a mess which one might try to formalise.