Results 1 
2 of
2
TypeBased Termination of Recursive Definitions
, 2002
"... This article The purpose of this paper is to introduce b, a simply typed calculus that supports typebased recursive definitions. Although heavily inspired from previous work by Giménez (Giménez 1998) and closely related to recent work by Amadio and Coupet (Amadio and CoupetGrimal 1998), the techn ..."
Abstract

Cited by 39 (3 self)
 Add to MetaCart
This article The purpose of this paper is to introduce b, a simply typed calculus that supports typebased recursive definitions. Although heavily inspired from previous work by Giménez (Giménez 1998) and closely related to recent work by Amadio and Coupet (Amadio and CoupetGrimal 1998), the technical machinery behind our system puts a slightly different emphasis on the interpretation of types. More precisely, we formalize the notion of typebased termination using a restricted form of type dependency (a.k.a. indexed types), as popularized by (Xi and Pfenning 1998; Xi and Pfenning 1999). This leads to a simple and intuitive system which is robust under several extensions, such as mutually inductive datatypes and mutually recursive function definitions; however, such extensions are not treated in the paper
OrderSorted Inductive Types
, 1999
"... System F ! is an extension of system F ! with subtyping and bounded quantification. Ordersorted algebra is an extension of manysorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higherorder typed calculus with subtyping, bounded quantification a ..."
Abstract

Cited by 4 (3 self)
 Add to MetaCart
System F ! is an extension of system F ! with subtyping and bounded quantification. Ordersorted algebra is an extension of manysorted algebra with overloading and subtyping. We combine both formalisms to obtain IF ! , a higherorder typed calculus with subtyping, bounded quantification and ordersorted inductive types, i.e. data types with builtin subtyping and overloading. Moreover we show that IF ! enjoys important metatheoretic properties, including confluence, strong normalization, subject reduction and decidability of typechecking. 1 Introduction Typed functional programming languages such as Haskell and ML and typetheory based proofdevelopment systems such as Coq and Lego support the introduction of inductively defined types such as natural numbers or booleans, parameterized inductively defined types such as lists and even parameterized mutual inductively defined types such as trees and forests. In addition, those languages support the definition of functions ...