Decidability Extracted: Synthesizing “correct-by-construction” Decision Procedures from Constructive Proofs

The topic of this thesis is the extraction of eecient and readable programs from formal constructive proofs of decidability. The proof methods employed to generate the eecient code are new and result in clean and readable Nuprl extracts for two non-trivial programs. They are based on the use of Nuprl's set type and techniques for extracting ecient programs from induction principles. The constructive formal theories required to express the decidability theorems are of independent interest. They formally circumscribe the mathematical knowledge needed to understand the derived algorithms. The formal theories express concepts that are taught at the senior college level. The decidability proofs themselves, depending on this material, are of interest and are presented in some detail. The proof of decidability of classical propositional logic is relative to a semantics based on Kleene's strong three-valued logic. The constructive proof of intuitionis-tic decidability presented here is the rst machine formalization of this proof. The exposition reveals aspects of the Nuprl tactic collection relevant to the creation of readable proofss clear extracts and eecient code are illustrated in the discussion of the proofs. The earliest manifestation of the impulse to create something permanent occurred about 1961 when he discovered a bag of concrete mix in the woodsand, dragging it to a nearby stream, tore it open, and added water, building his rst site sculpture. To his own amazement, the sculpture was still extant in 1962. He graduated from Clarkstown High School in New City, New York in 1974 and attended the State University of New York Cortland, studying painting with Jim Thorpe. In 1976, on the recommendation of his mentors, Caldwell moved to New York City to study in the Empire State College studio art program run by Irving Kriesberg at Westbeth 1. He met Penelope Potter in the Westbeth studioo building her a wall and then crossing the Brooklyn bridge with her on foot. Together they moved to Boston, to continue studies at the Boston Museum School of Fine Arts, living in Back Bay at rst, and later behind a painting in a Congress Street loft. In 1978 they were married and moved to Second Street in NYC. Their daughter Clea Caldwell was born in NYC. Taxi driving, cabinetry work in SoHo lofts, and picture framing supported the Caldwell family. In 1979 he was hired and trained as a draftsman on a an early computer aided drafting system, beginning his computer …