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This doctoral thesis addresses one major difficulty in formal proof: removing obstructions to intuition which hamper the proof endeavour. We investigate this in the context of formally verifying geometric algorithms using the theorem prover Isabelle, by first proving the Graham’s Scan algorithm for finding convex hulls, then using the challenges we encountered as motivations for the design of a general, modular framework for combining mathematical tools. We introduce our integration framework — the Prover’s Palette, describing in detail the guiding principles from software engineering and the key differentiator of our approach — emphasising the role of the user. Two integrations are described, using the framework to extend Eclipse Proof General so that the computer algebra systems QEPCAD and Maple are directly available in an Isabelle proof context, capable of running either fully automated or with user customisation. The versatility of the approach is illustrated by showing a variety of ways that these tools can be used to streamline the theorem proving process, enriching the user’s intuition rather than disrupting it. The usefulness of our approach is then demonstrated through the formal verification of an algorithm for computing Delaunay triangulations in the Prover’s Palette.

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International Telemetering Conference Proceedings / October 28-31, 1996 / Town and Country Hotel and Convention Center, San Diego, California / This paper discusses the telemetry processing and data verification performed by the SBV Processing, Operations and Control Center (SPOCC) located at MIT Lincoln Laboratory (MIT LL). The SPOCC is unique among the Midcourse Space Experiment (MSX) Data Processing Centers because it supports operational demonstrations of the SBV sensor for Space-Based Space Surveillance applications. The surveillance experiment objectives focus on tracking of resident space objects (RSOs), including acquisition of newly launched satellites. Since Space Surveillance operations have fundamentally short timelines, the SPOCC must be deeply involved in the mission planning for the series of observations and must receive and process the resulting data quickly. In order to achieve these objectives, the MSX Concept of Operations (CONOPS) has been developed to include the SPOCC in the operations planning process. The SPOCC is responsible for generating all MSX spacecraft command information required to execute space surveillance events using the MSX. This operating agreement and a highly automated planning system at the SPOCC allow the planning timeline objectives to be met. In addition, the Space Surveillance experiment scenarios call for active use of the 1 Mbps real-time link to transmit processed targets tracks from the SBV to the SPOCC for processing and for short time-line response of the SPOCC to process the track of the new object and produce new commands for the MSX spacecraft, or other space surveillance sensors, to re-acquire the object. To accomplish this, surveillance data processed and stored onboard the SBV is transmitted to the APL Mission Processing Center via 1 Mbps contacts with the dedicated Applied Physics Laboratory (APL) station, or via one of the AFSCN RTS locations, which forwards the telemetry in real-time to APL. The Mission Processing facility at APL automatically processes the MSX telemetry to extract the SBV allocation and forwards the data via file transfer over a dedicated fractional T1 link to the SPOCC. The data arriving at the SPOCC is automatically identified and processed to yield calibrated metric observations of RSOs. These results are then fed forward into the mission planning process for follow-up observations. In addition to the experiment support discussed above, the SPOCC monitors and stores SBV housekeeping data, monitors payload health and status, and supports diagnosis and correction. There are also software tools which support the assessment of the results of surveillance experiments and to produce a number of products used by the SBV instrument team to assess the overall performance characteristics of the SBV instrument.

published_or_final_version / Electrical and Electronic Engineering / Doctoral / Doctor of Philosophy

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