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Finitely stratified polymorphism

Daniel Leivant
1991 Information and Computation  
STRATIFIED POLYMORPHISM WITH TYPE RECURSION 5.1, Recursive Types  ...  In the final Section 5 we consider stratified polymorphism with recursive types.  ... 
doi:10.1016/0890-5401(91)90053-5 fatcat:nr2cayee5zgthi3dhsa2g4r6z4

Page 7328 of Mathematical Reviews Vol. , Issue 2000j [page]

2000 Mathematical Reviews  
Ying Jiang (Beijing) 2000j:68023 68N18 03B40 03B70 Danner, Norman (1-IN; Bloomington, IN); Leivant, Daniel (1-IN; Bloomington, IN) Stratified polymorphism and primitive recursion.  ...  Thus, the nu- meric functions definable in our calculus are precisely the primitive recursive functions.” 2000j:68024 68N18 03B40 03F52 Guerrini, Stefano (I-ROME-IS; Rome) A general theory of sharing graphs  ... 

Strong normalization for applied lambda calculi

Ulrich Berger, Martín Escardó
2005 Logical Methods in Computer Science  
We consider the untyped lambda calculus with constructors and recursively defined constants.  ...  We apply this result to extensions of G\"odel's system T and system F extended by various forms of bar recursion for which strong normalisation was hitherto unknown.  ...  As our running example we discuss a few primitive recursive constants and rewrite rules for modified bar recursion.  ... 
doi:10.2168/lmcs-1(2:3)2005 fatcat:62yvbhp6ong2pncufiltflnocm

Page 2858 of Mathematical Reviews Vol. , Issue 94e [page]

1994 Mathematical Reviews  
“The interpretation works also for implicitly polymorphic lan- guages such as ML with dynamic and recursive types, and for explicitly polymorphic languages under the types-as-ideals inter- pretation.”  ...  In this paper, we present a necessary and sufficient condition for the consistency of the com- pleted database and use it to prove the consistency of the completed database for definite, locally stratified  ... 

Page 6278 of Mathematical Reviews Vol. , Issue 2003h [page]

2003 Mathematical Reviews  
primitive in the polymorphic setting, concluding that polymorphic query languages need to be carefully designed.  ...  It follows that transitive-closure, least, and stratified fixed-point logic are equivalent with respect to this benchmark.”  ... 

Parameter-free polymorphic types

Klaus Aehlig
2008 Annals of Pure and Applied Logic  
Consider the following restriction of the polymorphically typed lambda calculus ("System F"). All quantifications are parameter free.  ...  function built by primitive recursion from g and h, and f s = g(h 1 s) . . .  ...  Theorem 31 (Aehlig [1] ) Let n and k be a natural number and R(·, ·) a primitive recursive relation.  ... 
doi:10.1016/j.apal.2008.06.002 fatcat:6urbuzeq4nednpa65hv2hxelga

Index-Stratified Types

Rohan Jacob-Rao, Brigitte Pientka, David Thibodeau, Michael Wagner
2018 International Conference on Rewriting Techniques and Applications  
The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build new types.  ...  We prove the soundness of Tores as a programming and proof language via the key theorems of subject reduction and termination.  ...  There is no positivity condition on recursive types, as the typing rules for Mendler-recursion enforce termination without it. A stratified type is defined by primitive recursion on an index term.  ... 
doi:10.4230/lipics.fscd.2018.19 dblp:conf/rta/Jacob-RaoPT18 fatcat:qoiz4aejl5fgdhhr2u6hrvs7uq

Object type constructors

Dominic Duggan
2002 Acta Informatica  
Object type constructors solve the difficulties with combining container objects with type inference and parametric polymorphism, the latter of which are used very successfully in functional languages  ...  such as ML and Haskell.  ...  Thanks to Martin Abadi, Peter Canning, Luca Cardelli, Jens Palsberg, Didier Rémy and John Reppy for helpful comments.  ... 
doi:10.1007/s002360100076 fatcat:zt2bjywwczb2nj5z4lapuiabfm

Index-Stratified Types (Extended Version) [article]

Rohan Jacob-Rao, Brigitte Pientka, David Thibodeau
2018 arXiv   pre-print
The novel features we introduce are well-founded Mendler-style (co)recursion over indexed data types and a form of recursion over objects in the index language to build new types.  ...  The latter, which we call index-stratified types, are analogue to the concept of large elimination in dependently typed languages.  ...  There is no positivity condition on recursive types, as the typing rules for Mendler-recursion enforce termination without it. A stratified type is defined by primitive recursion on an index term.  ... 
arXiv:1805.00401v1 fatcat:eeaduhaj5zcitfsw6rxmq7teua

A Simple Semantics for Polymorphic Recursion [chapter]

William L. Harrison
2005 Lecture Notes in Computer Science  
Polymorphic recursion is a useful extension of Hindley-Milner typing and has been incorporated in the functional programming language Haskell.  ...  However, polymorphic recursion is, perhaps, not as broadly understood as it could be and this, in part, motivates the denotational semantics presented here.  ...  Acknowledgements The author wishes to thank Dick Kieburtz, Brian Dunphy, and Mark Jones for their encouragement and for numerous discussions on aspects of polymorphic recursion, its relationship to the  ... 
doi:10.1007/11575467_4 fatcat:px3c3sa7v5axfpahgrjgcqe6wi

FreeST: Context-free Session Types in a Functional Language

Bernardo Almeida, Andreia Mordido, Vasco T. Vasconcelos
2019 Electronic Proceedings in Theoretical Computer Science  
Based on a core linear functional programming language, it features primitives to fork new threads, and for channel creation and communication.  ...  This abstract provides a gentle introduction to the language and discusses the validation process and runtime system.  ...  in Science and Technology).  ... 
doi:10.4204/eptcs.291.2 fatcat:tuhptsvb3rhu7pq4ibcjg3tlua

Refinement types for Haskell

Niki Vazou, Eric L. Seidel, Ranjit Jhala, Dimitrios Vytiniotis, Simon Peyton-Jones
2014 Proceedings of the 19th ACM SIGPLAN international conference on Functional programming - ICFP '14  
We present a stratified type system that labels binders as potentially diverging or not, and that (circularly) uses refinement types to verify the labeling.  ...  We show that LIQUIDHASKELL is able to prove 96% of all recursive functions terminating, while requiring a modest 1.7 lines of termination-annotations per 100 lines of code.  ...  McMillan, Andrey Rybalchenko, Philip Wadler, and the reviewers for their excellent suggestions and feedback about earlier versions of this paper.  ... 
doi:10.1145/2628136.2628161 dblp:conf/icfp/VazouSJVJ14 fatcat:k4x3nousrze5rfqyrcdn32awfa

Refinement types for Haskell

Ranjit Jhala
2014 Proceedings of the ACM SIGPLAN 2014 Workshop on Programming Languages meets Program Verification - PLPV '14  
We present a stratified type system that labels binders as potentially diverging or not, and that (circularly) uses refinement types to verify the labeling.  ...  We show that LIQUIDHASKELL is able to prove 96% of all recursive functions terminating, while requiring a modest 1.7 lines of termination-annotations per 100 lines of code.  ...  McMillan, Andrey Rybalchenko, Philip Wadler, and the reviewers for their excellent suggestions and feedback about earlier versions of this paper.  ... 
doi:10.1145/2541568.2541569 dblp:conf/plpv/Jhala14 fatcat:7md5gsdqqbhlzlrvypu3ulyqte

Refinement types for Haskell

Niki Vazou, Eric L. Seidel, Ranjit Jhala, Dimitrios Vytiniotis, Simon Peyton-Jones
2014 SIGPLAN notices  
We present a stratified type system that labels binders as potentially diverging or not, and that (circularly) uses refinement types to verify the labeling.  ...  We show that LIQUIDHASKELL is able to prove 96% of all recursive functions terminating, while requiring a modest 1.7 lines of termination-annotations per 100 lines of code.  ...  McMillan, Andrey Rybalchenko, Philip Wadler, and the reviewers for their excellent suggestions and feedback about earlier versions of this paper.  ... 
doi:10.1145/2692915.2628161 fatcat:g3rt2hu3azafhfrni5jy4ziixu

A Semantics for : a Calculus with Overloading and Late-binding

T. Studer
2001 Journal of Logic and Computation  
In this paper we provide a new semantics for a stratified version of Castagna's λ {} , a λ-calculus combining overloading with late-binding.  ...  We will prove the soundness of our model with respect to subtyping, type-checking and reductions.  ...  We would like to thank Giorgio Ghelli, Gerhard Jäger and Thomas Strahm for many helpful comments on earlier versions of this paper.  ... 
doi:10.1093/logcom/11.4.527 fatcat:6wnqyvktnbeknhlq6y7taob7v4
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