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Constructing Recursion Operators in Intuitionistic Type Theory
 Journal of Symbolic Computation
, 1984
"... MartinLöf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of wellfounded relations is presented. Using primitive recursion over higher types, induction and recursion are formally ..."
Abstract

Cited by 22 (5 self)
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MartinLöf's Intuitionistic Theory of Types is becoming popular for formal reasoning about computer programs. To handle recursion schemes other than primitive recursion, a theory of wellfounded relations is presented. Using primitive recursion over higher types, induction and recursion are formally derived for a large class of wellfounded relations. Included are < on natural numbers, and relations formed by inverse images, addition, multiplication, and exponentiation of other relations. The constructions are given in full detail to allow their use in theorem provers for Type Theory, such as Nuprl. The theory is compared with work in the field of ordinal recursion over higher types.
TYPE THEORY AND FUNCTIONAL PROGRAMMING A WORK PROPOSAL Gustavo Betarte
"... We propose a series of work areas related to type theory and functional programming. By type theory we mean the formulation of MartinLof's set theory using the theory of types as logical framework, extended with record types and subtyping. The areas presented are: the implementation of an environme ..."
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We propose a series of work areas related to type theory and functional programming. By type theory we mean the formulation of MartinLof's set theory using the theory of types as logical framework, extended with record types and subtyping. The areas presented are: the implementation of an environment for carrying out constructions in type theory, the systematic development of programming in type theory as a formal discipline and the formalization in type theory of the theory of functional programming languages. We also give a succint introduction to a theory of specifications and programs in which programs and their correctness proofs are separated but still can be built up simultaneously; we propose the implementation of a programming system for this theory too. The group of people presenting this work proposal is defined by their common interest to work together in at least one of the areas proposed. There will be people working in each of these areas in the Plata region. 1. Introdu...
A Set Constructor for Inductive Sets in MartinLof's Type Theory
 In Category Theory and Computer Science
, 1989
"... this paper, we will define a set constructor that one could use for defining many inductive data types ..."
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this paper, we will define a set constructor that one could use for defining many inductive data types