A Kripke-Style Model for the Admissibility of Structural Rules

This paper demonstrates the admissibility of the basic structural rules of dependent type theory, such as weakening, substitution and splitting lemmas, through a Kripke-style term model.

[1]  Mark-Jan Nederhof,et al.  Modular proof of strong normalization for the calculus of constructions , 1991, Journal of Functional Programming.

[2]  Martin Hofmann,et al.  On the Interpretation of Type Theory in Locally Cartesian Closed Categories , 1994, CSL.

[3]  Gordon D. Plotkin,et al.  Abstract syntax and variable binding , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[4]  Healfdene Goguen.  Typed Operational Semantics , 1995, TLCA.

[5]  Andrew M. Pitts,et al.  A new approach to abstract syntax involving binders , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[6]  Zhaohui Luo,et al.  ECC, an extended calculus of constructions , 1989, [1989] Proceedings. Fourth Annual Symposium on Logic in Computer Science.

[7]  Bengt Nordström,et al.  Programming in Martin-Lo¨f's type theory: an introduction , 1990 .

[8]  Joëlle Despeyroux,et al.  Metatheoretic Results for a Modal lambda-Calculus , 2000, J. Funct. Log. Program..

[9]  Thomas Streicher,et al.  Semantics of type theory - correctness, completeness and independence results , 1991, Progress in theoretical computer science.

[10]  Martin Hofmann.  Semantical analysis of higher-order abstract syntax , 1999, Proceedings. 14th Symposium on Logic in Computer Science (Cat. No. PR00158).

[11]  J. Gallier,et al.  A Proof of Strong Normalization for the Theor y of Constructions Using a Kripke-like Interpretation , 1990 .

[12]  James McKinna,et al.  Pure Type Systems Formalized , 1993, TLCA.

[13]  Furio Honsell,et al.  A framework for defining logics , 1993, JACM.

[14]  Zhaohui Luo,et al.  Some Algorithmic and Proof-Theoretical Aspects of Coercive Subtyping , 1996, TYPES.

[15]  Healfdene Goguen.  A typed operational semantics for type theory , 1994 .

[16]  Amy P. Felty,et al.  Higher-Order Abstract Syntax in Coq , 1995, TLCA.