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The study of polarity in computation has revealed that an “ideal” programming language combines both call-by-value and call-by-name evaluation; the two calling conventions are each ideal for half the types in a programming language. But this binary choice leaves out call-by-need which is used in practice to implement lazy-by-default languages like Haskell. We show how the notion of polarity can be extended beyond the value/name dichotomy to include call-by-need by only adding a mechanism for sharing and the extra polarity shifts to connect them, which is enough to compile a Haskell-like functional language with user-defined types.
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Uniform Strong Normalization for Multi-discipline Calculi
Modern programming languages have effects and mix multiple calling conventions, and their core calculi should too. We characterize calling conventions by their “substitution discipline” that says what variables stand for, and design calculi for mixing disciplines in a single program. Building on variations of the reducibility candidates method, including biorthogonality and symmetric candidates which are both specialized for one discipline, we develop a single uniform framework for strong normalization encompassing call-by-name, call-by-value, call-by-need, call-by-push-value, non-deterministic disciplines, and any others satisfying some simple criteria. We explicate commonalities of previous methods and show they are special cases of the uniform framework and they extend to multi-discipline programs.
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- Award ID(s):
- 1719158
- PAR ID:
- 10173524
- Date Published:
- Journal Name:
- Rewriting Logic and Its Applications. WRLA 2018.
- Volume:
- 11152
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Conference Paper:
- https://doi.org/10.1007/978-3-319-99840-4_12
