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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 for ..."
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Cited by 23 (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.
DRAFT
, 2008
"... This book about typed lambda terms comes in two volumes: the present one about lambda terms typed using simple, recursive and intersection types and a planned second volume about higher order, dependent and inductive types. In some sense this book is a sequel to Barendregt [1984]. That book is about ..."
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This book about typed lambda terms comes in two volumes: the present one about lambda terms typed using simple, recursive and intersection types and a planned second volume about higher order, dependent and inductive types. In some sense this book is a sequel to Barendregt [1984]. That book is about untyped lambda calculus. Types give the untyped terms more structure: function applications are allowed only in some cases. In this way one can single out untyped terms having special properties. But there is more to it. The extra structure makes the theory of typed terms quite different from the untyped ones. The emphasis of the book is on syntax. Models are introduced only in so far they give useful information about terms and types or if the theory can be applied to them. The writing of the book has been different from that about the untyped lambda calculus. First of all, since many researchers are working on typed lambda calculus, we were aiming at a moving target. Also there was a wealth of material to work with. For these reasons the book has been written by several
From Heyting's arithmetic to verified programs
, 1998
"... We discuss higher type constructions inherent to intuitionistic proofs. As an example we consider Gentzen's proof of transnite induction up to the ordinal 0 . From the constructive content of this proof we derive higher type algorithms for some ordinal recursive hierarchies of number theoretic ..."
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We discuss higher type constructions inherent to intuitionistic proofs. As an example we consider Gentzen's proof of transnite induction up to the ordinal 0 . From the constructive content of this proof we derive higher type algorithms for some ordinal recursive hierarchies of number theoretic functions.