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The Gentle Art of Levitation
"... We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arises by interpreting its description—a firstclass value in a datatype of descriptions. Moreover, the latter itself has a de ..."
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Cited by 20 (4 self)
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We present a closed dependent type theory whose inductive types are given not by a scheme for generative declarations, but by encoding in a universe. Each inductive datatype arises by interpreting its description—a firstclass value in a datatype of descriptions. Moreover, the latter itself has a description. Datatypegeneric programming thus becomes ordinary programming. We show some of the resulting generic operations and deploy them in particular, useful ways on the datatype of datatype descriptions itself. Surprisingly this apparently selfsupporting setup is achievable without paradox or infinite regress. 1.
Why dependent types matter
 In preparation, http://www.epig.org/downloads/ydtm.pdf
, 2005
"... We exhibit the rationale behind the design of Epigram, a dependently typed programming language and interactive program development system, using refinements of a well known program—merge sort—as a running example. We discuss its relationship with other proposals to introduce aspects of dependent ty ..."
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Cited by 9 (2 self)
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We exhibit the rationale behind the design of Epigram, a dependently typed programming language and interactive program development system, using refinements of a well known program—merge sort—as a running example. We discuss its relationship with other proposals to introduce aspects of dependent types into functional programming languages and sketch some topics for further work in this area. 1.
Computer Theorem Proving in Math
"... We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context. ..."
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We give an overview of issues surrounding computerverified theorem proving in the standard puremathematical context.
unknown title
, 2004
"... Abstract: We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical settheoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be removed in revision, and also contains as a tara ..."
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Abstract: We give a brief discussion of some of the issues which have arisen in the course of formalizing some classical settheoretical mathematics in the Coq system. This sprouts from, expands and replaces a chapter of math.HO/0311260 which will be removed in revision, and also contains as a tarattachment to the source file the revised and expanded version of the proof development which had been attached to math.HO/0311260.