A Second Easter: A Celebration of Presence

sermon text; MS Word document

The Churchman's prayer manual : for use at prayer meetings, mission services, conventions, Bible classes, study circles and other occasions of united prayer, as well as for private use compiled by G. R. Bullock-Webster.

http://www.archive.org/details/churchmansprayer00bulluoft

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

The Encyclopaedia of missions : descriptive, historical, biographical, statistical : with a full assortment of maps, a complete bibliography, and lists of Bible versions, missionary societies, mission stations, and a general index / edited by Edwin Munsell Bliss.

http://www.archive.org/details/encyclopaediamis02unknuoft

Islam and missions : being papers read at the Second Missionary Conference on behalf of the Mohammedan World at Lucknow, January 23-28, 1911 / edited by E.M. Wherry, S.M. Zwemer, C.G. Mylrea.

http://www.archive.org/details/islamandmissions012033mbp

Bible work in Bible lands, or, Events in the history of the Syria mission / by Isaac Bird.

http://www.archive.org/details/bibleworkinbible00birduoft

Bible illustrations from the New Hebrides : with notices of the progress of the mission / by John Inglis.

http://www.archive.org/details/bibleillustratio00ingluoft

Second letter to nephew 05/16/1881

Second letter to nephew, Daniel Avery Whedon from Daniel D. Whedon dated May 16, 1881.

Typability and Type Checking in the Second-Order Λ-Calculus Are Equivalent and Undecidable (Preliminary Draft)

We consider the problems of typability[1] and type checking[2] in the Girard/Reynolds second-order polymorphic typed λ-calculus, for which we use the short name "System F" and which we use in the "Curry style" where types are assigned to pure λ -terms. These problems have been considered and proven to be decidable or undecidable for various restrictions and extensions of System F and other related systems, and lower-bound complexity results for System F have been achieved, but they have remained "embarrassing open problems"[3] for System F itself. We first prove that type checking in System F is undecidable by a reduction from semi-unification. We then prove typability in System F is undecidable by a reduction from type checking. Since the reverse reduction is already known, this implies the two problems are equivalent. The second reduction uses a novel method of constructing λ-terms such that in all type derivations, specific bound variables must always be assigned a specific type. Using this technique, we can require that specific subterms must be typable using a specific, fixed type assignment in order for the entire term to be typable at all. Any desired type assignment may be simulated. We develop this method, which we call "constants for free", for both the λK and λI calculi.

A Direct Algorithm for the Type Interference in the Rank 2 Fragment of the Second--Order λ-Calculus

We study the problem of type inference for a family of polymorphic type disciplines containing the power of Core-ML. This family comprises all levels of the stratification of the second-order lambda-calculus by "rank" of types. We show that typability is an undecidable problem at every rank k ≥ 3 of this stratification. While it was already known that typability is decidable at rank ≤ 2, no direct and easy-to-implement algorithm was available. To design such an algorithm, we develop a new notion of reduction and show how to use it to reduce the problem of typability at rank 2 to the problem of acyclic semi-unification. A by-product of our analysis is the publication of a simple solution procedure for acyclic semi-unification.

Reliable Cellular Automata with Self-Organization

In a probabilistic cellular automaton in which all local transitions have positive probability, the problem of keeping a bit of information for more than a constant number of steps is nontrivial, even in an infinite automaton. Still, there is a solution in 2 dimensions, and this solution can be used to construct a simple 3-dimensional discrete-time universal fault-tolerant cellular automaton. This technique does not help much to solve the following problems: remembering a bit of information in 1 dimension; computing in dimensions lower than 3; computing in any dimension with non-synchronized transitions. Our more complex technique organizes the cells in blocks that perform a reliable simulation of a second (generalized) cellular automaton. The cells of the latter automaton are also organized in blocks, simulating even more reliably a third automaton, etc. Since all this (a possibly infinite hierarchy) is organized in "software", it must be under repair all the time from damage caused by errors. A large part of the problem is essentially self-stabilization recovering from a mess of arbitrary-size and content caused by the faults. The present paper constructs an asynchronous one-dimensional fault-tolerant cellular automaton, with the further feature of "self-organization". The latter means that unless a large amount of input information must be given, the initial configuration can be chosen to be periodical with a small period.