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Intrinsic Currying for C++ Template Metaprograms

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Trends in Functional Programming (TFP 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 11457))

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Abstract

C++ template metaprogramming is a form of strict functional programming, with a notable absence of intrinsic support for elementary higher-order operations. We describe a variadic template metaprogramming library which offers a model of implicitly curried, left-associative metafunction application through juxtaposition; inspired by languages such as Haskell, OCaml and F\(^\sharp \). New and existing traits and metafunctions, constructed according to conventional idioms, seemlessly take advantage of the framework’s features. Furthermore, a distinctive versatility is exposed, allowing a user to define higher-order metafunction classes using an equational definition syntax; without recourse to elaborate nested metafunctions. The primary type expression evaluator of the library is derived from a single application of an elementary folding combinator for type lists. The definition of the fold’s binary operator argument is therefore a focal point; and constructed mindful that substitution failure of a template parameter’s deduced type produces no compilation error. Two distinctive features of C++ metafunctions require particular consideration: zero argument metafunctions; and variadic metafunctions. We conclude by demonstrating characteristics of the library’s main evaluation metafunction in conjunction with the universal property of an updated right-fold combinator, to compose a range of metafunctions including map, reverse, left-fold, and the Ackermann function.

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Notes

  1. 1.

    Often map is named after the standard C++ runtime function. A fold is more often named ; with provided as an alias.

  2. 2.

    This is a second, distinct usage of the keyword. The keyword is not permitted in this context; though is.

  3. 3.

    The disambiguator informs the compiler that a dependent name following the operator, refers to a type [37, p. 228].

  4. 4.

    is a keyword used to query the type of an expression.

  5. 5.

    The type expression will evaluate to a type; an instantiation of , and hence also of . The braces which follow this expression will aggregate-initialise a object before using its conversion operator member to provide an value as the multiplier, with the multiplicand.

  6. 6.

    Regarding a template parameter pack: note that its declaration is preceded by an ellipsis; while its expansion is followed by one [37, p. 188].

  7. 7.

    The disambiguator informs the compiler that a dependent name following a , , or operator, refers to a template [37, p. 230].

  8. 8.

    Discussion regarding the virtue of this restriction remains an active topic within the ISO C++ Standards Committee; identified as core issue 1430 [25].

  9. 9.

    The class template makes use of a powerful C++ feature wherein template substitution failure is not an error (SFINAE). Furthermore, is defined as “SFINAE-friendly”. For example, as and have no common type, neither , nor the equivalent , has a member. The failed instantiation of the specialisation with resolves to the primary template; leaving subsequent access to the absent member only a substitution error. The alternative is a hard error. C++17’s is an alias template helpful in such contexts; provided with zero or more valid type template arguments, the aggregate instantiates to [37, p. 420].

  10. 10.

    A variant, , accepting class template arguments, is defined in Appendix A.1.

  11. 11.

    A template parameter pack is used by rather than a type list; and hence it is not strictly isomorphic to the Haskell fold above; this is however only part of the implementation, not of the public API.

  12. 12.

    A would do, though the minimal class template shown is sufficient for compile-time calculations.

  13. 13.

    The Pointfree.io website is an excellent resource for producing such translations.

  14. 14.

    A Curtains definition of the Haskell combinator is provided in Appendix A.4.

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Authors and Affiliations

  1. University of the West of Scotland, Paisley, UK

    Paul Keir & Andrew Gozillon

  2. Université catholique de Louvain, Louvain-la-Neuve, Belgium

    Seyed Hossein Haeri

Authors
  1. Paul Keir
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  2. Andrew Gozillon
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  3. Seyed Hossein Haeri
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Correspondence to Paul Keir .

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Editors and Affiliations

  1. Chalmers University of Technology, Gothenburg, Sweden

    Michał Pałka

  2. Chalmers University of Technology, Gothenburg, Sweden

    Magnus Myreen

A Appendix A

A Appendix A

1.1 A.1 Quotation for a Class Template Argument

figure bi

1.2 A.2 Curry-Invoke with Arity

figure bj

1.3 A.3 Conditional Invoke with Arity

figure bk

1.4 A.4 Additional Utility Metafunctions

figure bl

1.5 A.5 A Sample Variadic Metafunction:

figure bm

1.6 A.6 Point-Free Reverse From a Right-Fold

figure bn

1.7 A.7 Point-Free Left-Fold From a Right-Fold

Implementation derived from Hutton [18]; with assistance from the Pointfree.io website; which provides: .

figure bo

1.8 A.8 The SKI Combinators

figure bp

1.9 A.9 Point-Free Ackermann Function from a Right-Fold

Here and are used in lieu of and , for the Applicative instance of . The implementation is derived from Hutton [18]; with assistance from the Pointfree.io website.

figure bq

1.10 A.10 Non-recursive Factorial for Use with the Fixpoint Combinator

figure br

1.11 A.11 Primitive Left-Fold from a C++17 Fold Expression

figure bs

1.12 A.12 Reduction Steps of a Sample Curtains Expression

figure bt

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Keir, P., Gozillon, A., Haeri, S.H. (2019). Intrinsic Currying for C++ Template Metaprograms. In: Pałka, M., Myreen, M. (eds) Trends in Functional Programming. TFP 2018. Lecture Notes in Computer Science(), vol 11457. Springer, Cham. https://doi.org/10.1007/978-3-030-18506-0_3

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