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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 ..."
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Cited by 39 (3 self)
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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
Termination Checking with Types
, 1999
"... The paradigm of typebased termination is explored for functional programming with recursive data types. The article introduces , a lambdacalculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types ..."
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Cited by 28 (6 self)
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The paradigm of typebased termination is explored for functional programming with recursive data types. The article introduces , a lambdacalculus with recursion, inductive types, subtyping and bounded quanti cation. Decorated type variables representing approximations of inductive types are used to track the size of function arguments and return values. The system is shown to be type safe and strongly normalizing. The main novelty is a bidirectional type checking algorithm whose soundness is established formally.
Termination of Mutually Recursive Functions
, 2000
"... Introduction 2. The foetus Project 3. Mutually Recursive Functions with One Argument 4. Mutually Recursive Functions with Several Arguments Slide 2 Recursion over Inductive Types ffl Functional programming languages and logical frameworks base upon calculus enriched with inductive types. Examples ..."
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Introduction 2. The foetus Project 3. Mutually Recursive Functions with One Argument 4. Mutually Recursive Functions with Several Arguments Slide 2 Recursion over Inductive Types ffl Functional programming languages and logical frameworks base upon calculus enriched with inductive types. Examples: ML, LEGO ffl Definition of functions/constants by recursion over inductive type possible. ffl Standard means: recursor/elimination. Ensures totality. Example: half' = R N (x B : 0) (x N f B!N : R B (f true) (1 + (f false))) half = n N : half' n false Drawback: Misses intuition, readability, usability. 1 Slide 3 Pattern Matching ffl Alternative: "fr