Thierry Coquand and Peter Dybjer. Normalization algorithms, mechanical normalization and intuitionistic model constructions. In Proceedings of El Vintermote, number 73 in Programming Methodology Group Reports. Chalmers University, Goteborg, 1993. Home/Search Document Not in Database Summary Related Articles Check |
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Constructions, Inductive Types and Strong Normalization - Altenkirch (1993) (Correct)
.... then we define using the material presented in appendix A: Tree = N (f(A; fg) ffl; fBg)g) We have the following derived rules: Gamma Tree : Set (Tree Form) 4 e.g. the type theoretic presentation of negative domain equations [Hof93b] the simple minded consistency arguments as presented in [CD93] and the universe constructions presented in [Dyb92b] essentially rely on this or a comparable mechanism. Chapter 4. Inductive types 79 Gamma leaf = C 0 Tree : A Tree Gamma sup = C 1 Tree : B Tree) Tree (Tree intro) Gamma:Tree oe Gamma R oe Tree : Pia : A:oe[leafa] ....
....Theory is useful for verification We have given some support for this slogan this by implementing the proof for the strong normalization of System F in LEGO. It should be noted that the structure of this proof was still very much influenced by the conventional formulation in predicate logic. In [CD93] it is shown how type theoretic systems can be analyzed in a typetheoretic way. I will close by mentioning some areas which deserve further attention: 1. In this thesis we followed the traditional approach to show strong normalization and to derive further metatheoretic properties (like ....
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Thierry Coquand and Peter Dybjer. Normalization algorithms, mechanical normalization and intuitionistic model constructions. In Proceedings of El Vintermote, number 73 in Programming Methodology Group Reports. Chalmers University, Goteborg, 1993.
Consistency in ALF - Altenkirch (1994) (1 citation) (Correct)
....give a set theoretic semantics for all consistent theories, extending the semantics proposed by Dybjer, thus showing relative consistency w.r.t. set theory. 4. To formally show that type checking and equality is decidable. This could be done by extending Dybjer s and Coquand s glueing construction [CD93]. 2 Examples of inconsistent theories We list here four examples of inconsistent theories which can be constructed with the current ALF system. These examples are typical for the possibilities to introduce inconsistencies. Here we understand an inconsistent theorie as one in which we can ....
Thierry Coquand and Peter Dybjer. Normalization algorithms, mechanical normalization and intuitionistic model constructions. In Proceedings of El Vintermote, number 73 in Programming Methodology Group Reports. Chalmers University, Goteborg, 1993.
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