A Sermon on the occasion of the death of Mrs. Mary Chapman Halsey

Memorial Sermon

In southern India : a visit to some of the chief mission stations in the Madras presidency / by Mrs. Murray Mitchell.

http://www.archive.org/details/insouthernindivi00mitcuoft

The child in the midst : a comparative study of child welfare in Christian and non-Christian lands / by Mary Schauffler Labaree.

http://www.archive.org/details/childinthemidst028451mbp

Historical sketch of the Flathead Indian nation from the year 1813 to 1890 : embracing the history of the establishment of St. Mary's Indian Mission in the Bitter Root Valley, Mont. : with sketches of the missionary life of Father Ravalli and other early missionaries : wars of the Blackfeet and Flatheads and sketches of history, trapping and trading in the early days / by Peter Ronan.

http://www.canadiana.org/ECO/mtq?doc=16974 View document online

Mary and I. Forty years with the Sioux.

http://www.archive.org/details/maryandifortyyea00riggrich

The Missionary pioneer, or, A brief memoir of the life, labours, and death of John Stewart, (man of colour) founder, under God of the mission among the Wyandotts at Upper Sandusky, Ohio / Published by Joseph Mitchell.

http://www.archive.org/details/missionarypionee00stewrich

The Undecidability of Mitchell's Subtyping Relationship

Mitchell defined and axiomatized a subtyping relationship (also known as containment, coercibility, or subsumption) over the types of System F (with "→" and "∀"). This subtyping relationship is quite simple and does not involve bounded quantification. Tiuryn and Urzyczyn quite recently proved this subtyping relationship to be undecidable. This paper supplies a new undecidability proof for this subtyping relationship. First, a new syntax-directed axiomatization of the subtyping relationship is defined. Then, this axiomatization is used to prove a reduction from the undecidable problem of semi-unification to subtyping. The undecidability of subtyping implies the undecidability of type checking for System F extended with Mitchell's subtyping, also known as "F plus eta".