Computer Theorem Proving and HoTT

Theorem-proving is a one-player game. The history of computer programs being the players goes back to 1956 and the ‘LT’ LOGIC THEORY MACHINE of Newell, Shaw and Simon. In game-playing terms, the ‘initial position’ is the core set of axioms chosen for the particular logic and the ‘moves’ are the rules of inference. Now, the Univalent Foundations Program at IAS Princeton and the resulting ‘HoTT’ book on Homotopy Type Theory have demonstrated the success of a new kind of experimental mathematics using computer theorem proving.

Protocols between programs and proofs

In this paper we describe a new protocol that we call the Curry-Howard protocol between a theory and the programs extracted from it. This protocol leads to the expansion of the theory and the production of more powerful programs. The methodology we use for automatically extracting “correct” programs from proofs is a development of the well-known Curry-Howard process. Program extraction has been developed by many authors, but our presentation is ultimately aimed at a practical, usable system and has a number of novel features. These include 1. a very simple and natural mimicking of ordinary mathematical practice and likewise the use of established computer programs when we obtain programs from formal proofs, and 2. a conceptual distinction between programs on the one hand, and proofs of theorems that yield programs on the other. An implementation of our methodology is the Fred system. As an example of our protocol we describe a constructive proof of the well-known theorem that every graph of even parity can be decomposed into a list of disjoint cycles. Given such a graph as input, the extracted program produces a list of the (non-trivial) disjoint cycles as promised.

Tailored instructional methods for students with diverse levels of computer knowledge and skills

The purpose of this online course is to ensure new nursing graduate students know how to use computer technologies required to complete academic and research activities. Powerful computers, high speed internet, digitalized resources and databases are widely available in educational institutes. New renovation and updates are being released at faster pace than ever. All these developments are necessary for a student to utilize computer programs and synthesize large amount of data in a limited time for any given academic research project. [See PDF for complete abstract]

Computer analysis and design of concrete shell roofs

This paper is a preliminary version of Chapter 3 of a State-of-the-Art Report by the IASS Working Group 5: Concrete Shell Roofs. The intention of this chapter is to set forth for those who intend to design concrete shell roofs information and advice about the selection, verification and utilization of commercial computer tools for analysis and design tasks.The computer analysis and design steps for a concrete shell roof are described. Advice follows on the aspects to be considered in the application of commercial finite element (FE)computer programs to concrete shell analysis, starting with recommendations on how novices can gain confidence and competence in the use of software. To establish vocabulary and provide background references, brief surveys are presented of, first,element types and formulations for shells and, second, challenges presented by advanced analyses of shells. The final section of the chapter indicates what capabilities to seek in selecting commercial FE software for the analysis and design of concrete shell roofs. Brief concluding remarks summarize advice regarding judicious use of computer analysis in design practice.

Effects of acid precipitation on soil leachate quality : computer calculations /

Mode of access: Internet.

Computer cost models for potable water treatment plants /

Mode of access: Internet.

Increased fuel economy in transportation systems by use of energy management. Volume II - digital automotive propulsion simulator programs and description.

Transportation Department, Washington, D.C.

Increased fuel economy in transportation systems by use of energy management. Volume III. Real-time (hybrid computer) simulation program set.

Transportation Department, Washington, D.C.

OPTREG - an interactive computer program for optimization and regression. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Investigation of tire-pavement interaction during maneuvering. Volume II. Tire analysis program package computer program manual. Final report.

Federal Highway Administration, Washington, D.C.

A finite element head injury model. Volume II: computer program documentation. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Computer simulation of human thoracic skeletal response - volume II, THORAX programmer's and user's manual. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Revision of Simulation Model of Automobile Collisions (SMAC) computer program: investigation of new integration algorithm. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

Operational hybrid computer simulation for vehicle handling studies. Final report.

National Highway Traffic Safety Administration, Washington, D.C.

A user's manual for the CALINE-2 computer program. Interim report.

Mode of access: Internet.