Information and Computation - Semantics of Data Types
Formal Aspects of Computing
Inductive Definitions in the system Coq - Rules and Properties
TLCA '93 Proceedings of the International Conference on Typed Lambda Calculi and Applications
A Simple Model for Quotient Types
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
Extensions of Pure Type Systems
TLCA '95 Proceedings of the Second International Conference on Typed Lambda Calculi and Applications
The Calculus of algebraic Constructions
RtA '99 Proceedings of the 10th International Conference on Rewriting Techniques and Applications
CSL '95 Selected Papers from the9th International Workshop on Computer Science Logic
COLOG '88 Proceedings of the International Conference on Computer Logic
Automata-driven automated induction
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
Quotient Types: A Modular Approach
TPHOLs '02 Proceedings of the 15th International Conference on Theorem Proving in Higher Order Logics
CSL'10/EACSL'10 Proceedings of the 24th international conference/19th annual conference on Computer science logic
On the strength of proof-irrelevant type theories
IJCAR'06 Proceedings of the Third international joint conference on Automated Reasoning
A semi-reflexive tactic for (sub-)equational reasoning
TYPES'04 Proceedings of the 2004 international conference on Types for Proofs and Programs
Pragmatic quotient types in coq
ITP'13 Proceedings of the 4th international conference on Interactive Theorem Proving
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We present a new method to specify a certain class of quotient in intentional type theory, and in the calculus of inductive constructions in particular. We define the notion of "normalized types". The main idea is to associate a normalization function to a type, instead of the usual relation. This function allows to compute on a particular element for each equivalence class, avoiding the difficult task of computing on equivalence classes themselves. We restrict ourselves to quotients that allow the construction of such a function, i.e. quotient having a canonical member for each equivalence class. This method is described as an extension of the calculus of constructions allowing normalized types. We prove that this calculus has the properties of strong normalization, subject reduction, decidability of typing. In order to show the example of the definition of Z by a normalized type, we finally present a pseudo Coq session.