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A Predicative Analysis of Structural Recursion
, 1999
"... We introduce a language based upon lambda calculus with products, coproducts and strictly positive inductive types that allows the definition of recursive terms. We present the implementation (foetus) of a syntactical check that ensures that all such terms are structurally recursive, i.e., recursive ..."
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Cited by 41 (20 self)
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We introduce a language based upon lambda calculus with products, coproducts and strictly positive inductive types that allows the definition of recursive terms. We present the implementation (foetus) of a syntactical check that ensures that all such terms are structurally recursive, i.e., recursive calls appear only with arguments structurally smaller than the input parameters of terms considered. To ensure the correctness of the termination checker, we show that all structurally recursive terms are normalizing with respect to a given operational semantics. To this end, we define a semantics on all types and a structural ordering on the values in this semantics and prove that all values are accessible with regard to this ordering. Finally, we point out how to do this proof predicatively using set based operators.
A predicative strong normalisation proof for a λcalculus with interleaving inductive types
 TYPES FOR PROOF AND PROGRAMS, INTER40 A. ABEL AND T. ALTENKIRCH NATIONAL WORKSHOP, TYPES '99, SELECTED PAPERS. LECTURE NOTES IN COMPUTER SCIENCE
, 1999
"... We present a new strong normalisation proof for a λcalculus with interleaving strictly positive inductive types λ^µ which avoids the use of impredicative reasoning, i.e., the theorem of KnasterTarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metaleve ..."
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Cited by 8 (5 self)
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We present a new strong normalisation proof for a λcalculus with interleaving strictly positive inductive types λ^µ which avoids the use of impredicative reasoning, i.e., the theorem of KnasterTarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel. To achieve this we show that every strictly positive operator on types gives rise to an operator on saturated sets which is not only monotone but also (deterministically) set based  a concept introduced by Peter Aczel in the context of intuitionistic set theory. We also extend this to coinductive types using greatest fixpoints of strictly monotone
A Predicative Strong Normalisation Proof for a lambdaCalculus with Interleaving Inductive Types
, 2000
"... We present a new strong normalisation proof for a calculus with interleaving strictly positive inductive types which avoids the use of impredicative reasoning, i.e., the theorem of KnasterTarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel ..."
Abstract

Cited by 4 (0 self)
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We present a new strong normalisation proof for a calculus with interleaving strictly positive inductive types which avoids the use of impredicative reasoning, i.e., the theorem of KnasterTarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel. To achieve this we show that every strictly positive operator on types gives rise to an operator on saturated sets which is not only monotone but also (deterministically) set based  a concept introduced by Peter Aczel in the context of intuitionistic set theory. We also extend this to coinductive types using greatest fixpoints of strictly monotone operators on the metalevel. 1
A Predicative Strong Normalisation Proof for a
"... We present a new strong normalisation proof for a calculus with interleaving strictly positive inductive types which avoids the use of impredicative reasoning, i.e., the theorem of KnasterTarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel ..."
Abstract
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We present a new strong normalisation proof for a calculus with interleaving strictly positive inductive types which avoids the use of impredicative reasoning, i.e., the theorem of KnasterTarski. Instead it only uses predicative, i.e., strictly positive inductive definitions on the metalevel. To achieve this we show that every strictly positive operator on types gives rise to an operator on saturated sets which is not only monotone but also (deterministically) set based  a concept introduced by Peter Aczel in the context of intuitionistic set theory. We also extend this to coinductive types using greatest fixpoints of strictly monotone operators on the metalevel.