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A General Formulation of Simultaneous InductiveRecursive Definitions in Type Theory
 Journal of Symbolic Logic
, 1998
"... The first example of a simultaneous inductiverecursive definition in intuitionistic type theory is MartinLöf's universe à la Tarski. A set U0 of codes for small sets is generated inductively at the same time as a function T0 , which maps a code to the corresponding small set, is defined by recursi ..."
Abstract

Cited by 65 (10 self)
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The first example of a simultaneous inductiverecursive definition in intuitionistic type theory is MartinLöf's universe à la Tarski. A set U0 of codes for small sets is generated inductively at the same time as a function T0 , which maps a code to the corresponding small set, is defined by recursion on the way the elements of U0 are generated. In this paper we argue that there is an underlying general notion of simultaneous inductiverecursive definition which is implicit in MartinLöf's intuitionistic type theory. We extend previously given schematic formulations of inductive definitions in type theory to encompass a general notion of simultaneous inductionrecursion. This enables us to give a unified treatment of several interesting constructions including various universe constructions by Palmgren, Griffor, Rathjen, and Setzer and a constructive version of Aczel's Frege structures. Consistency of a restricted version of the extension is shown by constructing a realisability model ...
A Machine Assisted Formalization of Pointfree Topology in Type Theory
, 1994
"... We will present a formalization of pointfree topology in MartinLöf's type theory. A notion of point will be introduced and we will show that the points of a Scott topology form a Scott domain. This work follows closely the intuitionistic approach to pointfree topology and domain theory, developed m ..."
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Cited by 6 (2 self)
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We will present a formalization of pointfree topology in MartinLöf's type theory. A notion of point will be introduced and we will show that the points of a Scott topology form a Scott domain. This work follows closely the intuitionistic approach to pointfree topology and domain theory, developed mainly by MartinLöf and Sambin. The important difference is that the definitions and proofs are machine checked by the proof assistant ALF.