A predicative analysis of structural recursion
A Abel, T Altenkirch - Journal of functional programming, 2002 - cambridge.org
Journal of functional programming, 2002•cambridge.org
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, ie 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 …
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, ie 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 …
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.

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