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» Logical Relations and Inductive Coinductive Types
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JAR
2007
123views more  JAR 2007»
13 years 5 months ago
Reasoning about Object-based Calculi in (Co)Inductive Type Theory and the Theory of Contexts
Abstract. We illustrate a methodology for formalizing and reasoning about Abadi and Cardelli’s object-based calculi, in (co)inductive type theory, such as the Calculus of (Co)Ind...
Alberto Ciaffaglione, Luigi Liquori, Marino Micula...
CALCO
2011
Springer
214views Mathematics» more  CALCO 2011»
12 years 5 months ago
Indexed Induction and Coinduction, Fibrationally
This paper extends the fibrational approach to induction and coinduction pioneered by Hermida and Jacobs, and developed by the current authors, in two key directions. First, we pr...
Clément Fumex, Neil Ghani, Patricia Johann
TLCA
1993
Springer
13 years 9 months ago
A Logic for Parametric Polymorphism
In this paper we introduce a logic for parametric polymorphism. Just as LCF is a logic for the simply-typed λ-calculus with recursion and arithmetic, our logic is a logic for Sys...
Gordon D. Plotkin, Martín Abadi
CORR
2012
Springer
212views Education» more  CORR 2012»
12 years 29 days ago
A Bi-Directional Refinement Algorithm for the Calculus of (Co)Inductive Constructions
The paper describes the refinement algorithm for the Calculus of (Co)Inductive Constructions (CIC) implemented in the interactive theorem prover Matita. The refinement algorithm ...
Andrea Asperti, Wilmer Ricciotti, Claudio Sacerdot...