H. Pfeifer and H. Rue. Polytypic proof construction. In Y. Bertot, editor, Proc. TPHOLs'99, volume 1690 of LNCS, pages 55--72. Springer-Verlag, 1999. Home/Search Document Details and Download
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Recursive Families of Inductive Types - Capretta (2000) (2 citations) (Correct)
....example, 10] It is less intuitive but simpler for theoretical purposes, so we adopt it. Every strictly positive operator X : X ] has a functorial extension, which, for X;Y : maps every f : X Y to a function [f ] X ] Y ] preserving identities and composition (see [9] and [20]) This condition is su cient to formulate the rules for inductive types (Matthes [16] gives an extension of system F in which this is the only condition required for inductive types) In the next sections we consider extensions of the positivity condition that still have the functorial property. ....
.... iteration principle: T : z : I T ] u : T ( rec [z]u) I T and T : z : T ] u : T ( it [z]u) I T : It is well known that the recursion and iteration principles are equivalent, whereas the full induction principle is a proper extension of them (see, for example, 11] or [20]) The types of natural numbers, binary trees, and lists over a type A can be de ned as N : X (N 1 X) where N 1 is the type with only one element 0 1 ; T : X (N 1 X X) and List(A) N 1 A X , respectively. Their constructors can be de ned in terms of the single constructor intro: 0 ....
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Holger Pfeifer and Harals Rue. Polytypic proof construction. In Yves Bertot, Gilleds Dowek, Andre Hirschowits, Christine Paulin, and Laurent Thery, editors, Theorem Proving in Higher Order Logics, 12th International Conference, TPHOLs '99, volume 1690 of LNCS, pages 54-72. Springer-Verlag, 1999.
Universes for Generic Programs and Proofs in Dependent Type .. - Benke, Dybjer, Jansson (2003) (1 citation) (Correct)
No context found.
H. Pfeifer and H. Rue. Polytypic proof construction. In Y. Bertot, editor, Proc. TPHOLs'99, volume 1690 of LNCS, pages 55--72. Springer-Verlag, 1999.
Indexed Induction-Recursion - Dybjer, Setzer (2004) (Correct)
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H. Pfeifer and H. Rue. Polytypic proof construction. In Y. Bertot, editor, Proc. TPHOLs'99, volume 1690 of LNCS, pages 55--72. Springer-Verlag, 1999.
Indexed Induction-Recursion - Peter Dybjer And (2001) (Correct)
No context found.
H. Pfeifer and H. Rue. Polytypic proof construction. In Y. Bertot, editor, Proc. TPHOLs'99, volume 1690 of LNCS, pages 55-72. Springer-Verlag, 1999.
Universes for Generic Programs and Proofs in Dependent Type .. - Benke, Dybjer, Jansson (2003) (1 citation) (Correct)
No context found.
H. Pfeifer and H. Rue. Polytypic proof construction. In Y. Bertot, editor, Proc. TPHOLs'99, volume 1690 of LNCS, pages 55-72. Springer-Verlag, 1999.
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