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Erasure and Polymorphism in Pure Type Systems [chapter]

Nathan Mishra-Linger, Tim Sheard
Foundations of Software Science and Computational Structures  
We introduce Erasure Pure Type Systems, an extension to Pure Type Systems with an erasure semantics centered around a type constructor ∀ indicating parametric polymorphism.  ...  Because the execution model of EPTS generalizes the familiar notions of type erasure and parametric polymorphism, we believe functional programmers will find it quite natural to program in such a setting  ...  Erasure Pure Type Systems This section introduces Erasure Pure Type Systems (EPTS), an extension of Pure Type Systems (PTS) with annotations indicating erasable parts of a program.  ... 
doi:10.1007/978-3-540-78499-9_25 dblp:conf/fossacs/Mishra-LingerS08 fatcat:p4y2j2ui3bbo5gppznwadfynn4

Is Impredicativity Implicitly Implicit?

Stefan Monnier, Nathaniel Bos, Assia Mahboubi, Marc Bezem
2020 Types for Proofs and Programs  
More specifically, we revisit several famous type systems believed to be consistent and which do include some form of impredicativity, and show that they can be refined to equivalent systems where impredicative  ...  Of all the threats to the consistency of a type system, such as side effects and recursion, impredicativity is arguably the least understood.  ...  Erasable Pure Type Systems The calculi we use in this paper are erasable pure type systems (EPTS) [22] , which are pure type systems (PTS) [4] extended with a notion of erasability.  ... 
doi:10.4230/lipics.types.2019.9 dblp:conf/types/MonnierB19 fatcat:elcjyuestje6tkxh37diflg6nm

Page 8650 of Mathematical Reviews Vol. , Issue 2003k [page]

2003 Mathematical Reviews  
To date, languages that support intensional polymorphism have required a type-passing (as opposed to type-erasure) interpretation where types are constructed and passed to polymorphic functions at run  ...  In addition, our type system provides another improvement in expressiveness: It allows unknown types to be refined in place, thereby avoiding certain beta-expansions required by other frameworks.” 2003k  ... 

Compiling structural types on the JVM

Gilles Dubochet, Martin Odersky
2009 Proceedings of the 4th workshop on the Implementation, Compilation, Optimization of Object-Oriented Languages and Programming Systems - ICOOOLPS '09  
This article describes Scala's compilation technique of structural types for the JVM. The technique uses Java reflection and polymorphic inline caches.  ...  The article ends with a comparison of reflective and generative techniques for compiling structural types.  ...  Since reflective method lookup and application are purely dynamic, the JVM's type system won't be in the way.  ... 
doi:10.1145/1565824.1565829 dblp:conf/ecoop/DubochetO09 fatcat:b3zdc232qvb7jmuxgjpjusjtwu

From Exponential to Polynomial-Time Security Typing via Principal Types [chapter]

Sebastian Hunt, David Sands
2011 Lecture Notes in Computer Science  
Hunt and Sands (POPL'06) studied a flow sensitive type (FST) system for multi-level security, parametric in the choice of lattice of security levels.  ...  Later work by Hunt and Sands (ESOP'08) adapted the FST system to provide an erasure type system which determines whether some input is correctly erased at a designated time.  ...  Discussions with Tobias Gedell and Daniel Hedin in the early stages of this work provided valuable insights. Jens Krinke helped us navigate the related work on program slicing.  ... 
doi:10.1007/978-3-642-19718-5_16 fatcat:qpiqc2pdozg4dibjm5ji6fc6ji

Explicit Effect Subtyping [chapter]

Amr Hany Saleh, Georgios Karachalias, Matija Pretnar, Tom Schrijvers
2018 Lecture Notes in Computer Science  
To remedy this, we present an explicitly-typed polymorphic core calculus for algebraic effect handlers with a subtyping-based type-and-effect system.  ...  It reifies appeals to subtyping in explicit casts with coercions that witness the subtyping proof, quickly exposing typing bugs in program transformations.  ...  We would like to thank the anonymous reviewers for careful reading and insightful comments. Part of this work is funded by the Flemish Fund for Scientific Research (FWO).  ... 
doi:10.1007/978-3-319-89884-1_12 fatcat:3oyq4seri5btflslc6whehp7gu

Lightweight scalable components

Tetsuo Kamina, Tetsuo Tamai
2007 Proceedings of the 6th international conference on Generative programming and component engineering - GPCE '07  
The only one language construct we propose in this paper is type parameter members, which allows type parameters to be referred from the outside of class declarations.  ...  To investigate properties of type parameter members in the real programming language settings, we develop a programming language Scalable Java (SJ), an extension of Java generics with type parameter members  ...  Furthermore, programs written in the pure family polymorphism approaches tend to be less verbose than ours, where we need to provide type bounds to type parameter members and define fixed point classes  ... 
doi:10.1145/1289971.1289996 dblp:conf/gpce/KaminaT07 fatcat:7kfe2lalkbepxpthybrbh7yg2i

Generic derivation of induction for impredicative encodings in Cedille

Denis Firsov, Aaron Stump
2018 Proceedings of the 7th ACM SIGPLAN International Conference on Certified Programs and Proofs - CPP 2018  
All data erase to pure lambda terms, and there is no built-in notion of datatype.  ...  Cedille is a pure type theory extending the Curry-style Calculus of Constructions with implicit products, primitive heterogeneous equality, and dependent intersections.  ...  Ghani et al. described the derivation of induction principle for inductive types in fibrational setting [6] .  ... 
doi:10.1145/3176245.3167087 fatcat:yoq7hshp6zhpvh2z4iie66hgx4

Explicit Effect Subtyping [article]

Georgios Karachalias, Matija Pretnar, Amr Hany Saleh, Stien Vanderhallen, Tom Schrijvers
2020 arXiv   pre-print
To remedy this, we present an explicitly-typed polymorphic core calculus for algebraic effect handlers with a subtyping-based type-and-effect system.  ...  It reifies appeals to subtyping in explicit casts with coercions that witness the subtyping proof, quickly exposing typing bugs in program transformations.  ...  ,Žiga Lukšič, Leonidas Lampropoulos, Klara Mardirosian, Ruben Pieters, Alexander Vandenbroucke, Nicolas Wu, andŽiga Zupančič for all their helpful comments and suggestions.  ... 
arXiv:2005.13814v1 fatcat:gaubphgk2vailof4wj5exd5du4

Coq Coq correct! verification of type checking and erasure for Coq, in Coq

Matthieu Sozeau, Simon Boulier, Yannick Forster, Nicolas Tabareau, Théo Winterhalter
2019 Proceedings of the ACM on Programming Languages (PACMPL)  
This paper presents the first implementation of a type checker for the kernel of Coq (without the module system and template polymorphism), which is proven correct in Coq with respect to its formal specification  ...  We present a verified version of this subtle type-and-proof erasure step, therefore enabling the verified extraction of a safe type-checker for Coq.  ...  , a Pure Type System with an infinite hiearchy of universes Type i and an impredicative sort Prop, extended with inductive and co-inductive type families.  ... 
doi:10.1145/3371076 fatcat:sdm7suzouzexpdey3o4o5wzkce

A calculus with polymorphic and polyvariant flow types

2002 Journal of functional programming  
Flow types can guide a compiler in generating customized data representations in a strongly typed setting.  ...  These flow types can encode polyvariant control and data flow information within a polymorphically typed program representation.  ...  Functions that are type polymorphic in the type system of the source language may become type monomorphic in a representation type system.  ... 
doi:10.1017/s0956796801004245 fatcat:cmb2ybnjijbo3ampb6f5u57dxy

Two Ways to Bake Your Pizza — Translating Parameterised Types into Java [chapter]

Martin Odersky, Enno Runne, Philip Wadler
2000 Lecture Notes in Computer Science  
We have identified in previous work two translations for parametrically typed extensions of Java.  ...  This paper describes both translations in detail, compares their time and space requirements and discusses how each affects the Java security model. † This work was completed while at the University of  ...  Acknowledgments This work was supported by Sun Laboratories Academic Collaboration Grant "Measuring the Cost of Parameterised Types in Java."  ... 
doi:10.1007/3-540-39953-4_10 fatcat:mkhgeogjlncl7k6lbb3cjri72i

More On Implicit Syntax [chapter]

Marko Luther
2001 Lecture Notes in Computer Science  
Experiences with the implementation in Typelab proved them both efficient and practical.  ...  Proof assistants based on type theories, such as Coq and Lego, allow users to omit subterms on input that can be inferred automatically.  ...  Acknowledgments I thank Martin Strecker for developing large parts of the Typelab system.  ... 
doi:10.1007/3-540-45744-5_31 fatcat:6rowrhx6mjdcbeqquu7ttkx5ly

Mechanized metatheory for a $$\lambda $$ λ -calculus with trust types

Rodrigo Ribeiro, Lucília Figueiredo, Carlos Camarão
2013 Journal of the Brazilian Computer Society  
We give formal proofs of type soundness, erasure and simulation theorems and also prove decidability of the typing problem. As a result of our formalisation a certified type checker is derived.  ...  In this work, we use the Coq proof assistant to formalise a λ-calculus with trust types, originally formulated by Ørbaek and Palsberg.  ...  Their type system relies on polymorphism, thus allowing that commands and expression types depend on the context in which they occur.  ... 
doi:10.1007/s13173-013-0119-5 fatcat:jfdmzpfurfa3dblcubtlxootpu

A Notion of Classical Pure Type System (Preliminary version)

Gilles Barthe, John Hatcliff, Morten Heine Sørensen
1997 Electronical Notes in Theoretical Computer Science  
We present a notion of classical pure type system, which extends the formalism of pure type system with a double negation operator. c 1997 Published by Elsevier Science B. V.  ...  in a generic way standard notions from higher-order rewrite systems and type theories.  ...  The second convention applies also to domain-free classical pure type systems and to pure type systems and domain-free pure type systems when working in a context of the form ?  ... 
doi:10.1016/s1571-0661(05)80170-7 fatcat:kugibpuzfvgcjkiasxdqeadsu4
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