Parametricity for Haskell with Imprecise Error Semantics

Stenger, Florian; Voigtländer, Janis

doi:10.1007/978-3-642-02273-9_22

Cited by 8 publications

(4 citation statements)

References 6 publications

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“…There is not as much reuse as one might want, different simplification heuristics have to be used for different language settings, there is no really deterministic algorithm but instead some search involved, and sometimes the only "simplification" that seems to work is to unfold all definitions and leave it at that. Moreover, if one were to move on and consider automatic generation of free theorems for further language settings, like imprecise error semantics [13], then the story would repeat itself. There would be yet another set of changes to the basic definitions for relations and relational actions, new things to take care of during simplification of candidate free theorems, etc.…”

Section: Typical Complicationsmentioning

confidence: 99%

“…Both a) and b) are the case in all languages and ∆-definitions we are aware of. This does not just mean partiality and seq in Haskell, but also for example the setting with imprecise error semantics as studied in [13]. Even in work on parametricity and free theorems for a functional-logic language [10], where the definition of ∆, including the case R 1 → R 2 , turns out somewhat differently (since having to deal with nondeterminism and thus with power domain types), the statement of the parametricity theorem and the definition of R 1 → R 2 are such that the conjuring lemma holds.…”

Section: The Conjuring Lemma Of Parametricitymentioning

confidence: 99%

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Free Theorems Simply, via Dinaturality

Voigtländer¹

2019

Preprint

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Free theorems are a popular tool in reasoning about parametrically polymorphic code. They are also of instructive use in teaching. Their derivation, though, can be tedious, as it involves unfolding a lot of definitions, then hoping to be able to simplify the resulting logical formula to something nice and short. Even in a mechanised generator it is not easy to get the right heuristics in place to achieve good outcomes. Dinaturality is a categorical abstraction that captures many instances of free theorems. Arguably, its origins are more conceptually involved to explain, though, and generating useful statements from it also has its pitfalls. We present a simple approach for obtaining dinaturality-related free theorems from the standard formulation of relational parametricity in a rather direct way. It is conceptually appealing and easy to control and implement, as the provided Haskell code shows.

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Section: Typical Complicationsmentioning

confidence: 99%

Section: The Conjuring Lemma Of Parametricitymentioning

confidence: 99%

Free Theorems Simply, via Dinaturality

Voigtländer¹

2019

Preprint

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“…So far, free theorems have been considered a qualitative tool only. That is, statements like (1) have been established as extensional equivalences or semantic approximations in a definedness order, and in fact a lot of research has gone into what definedness and/or strictness conditions are needed on the involved functions in various language settings and into extending the approach to richer type systems (Launchbury and Paterson 1996;Johann and Voigtländer 2004;Stenger and Voigtländer 2009;Voigtländer 2009b;Christiansen et al 2010;Bernardy et al 2010b). It is natural, though, to ask about the quantitative content of free theorems in terms of program efficiency.…”

Section: Introductionmentioning

confidence: 99%

Improvements for Free

Seidel¹,

Voigtländer²

2011

Electron. Proc. Theor. Comput. Sci.

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"Theorems for Free!" (Wadler, FPCA 1989) is a slogan for a technique that allows to derive statements about functions just from their types. So far, the statements considered have always had a purely extensional flavor: statements relating the value semantics of program expressions, but not statements relating their runtime (or other) cost. Here we study an extension of the technique that allows precisely statements of the latter flavor, by deriving quantitative theorems for free. After developing the theory, we walk through a number of example derivations. Probably none of the statements derived in those simple examples will be particularly surprising to most readers, but what is maybe surprising, and at the very least novel, is that there is a general technique for obtaining such results on a quantitative level in a principled way. Moreover, there is good potential to bring that technique to bear on more complex examples as well. We turn our attention to short-cut fusion (Gill et al., FPCA 1993) in particular

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“…This is not an overly theoretical paper. Also on purpose, we do not consider Haskell intricacies, like those studied by Johann and Voigtländer (2004) and Stenger and Voigtländer (2009), that do affect relational parametricity but in a way orthogonal to what is of interest here. Instead, we stay with Reynolds' and Wadler's simple model (but consider the extension to general recursion in Appendix C).…”

Section: Introductionmentioning

confidence: 99%

Free theorems involving type constructor classes

Voigtländer

2009

Proceedings of the 14th ACM SIGPLAN International Conference on Functional Programming

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Free theorems are a charm, allowing the derivation of useful statements about programs from their (polymorphic) types alone. We show how to reap such theorems not only from polymorphism over ordinary types, but also from polymorphism over type constructors restricted by class constraints. Our prime application area is that of monads, which form the probably most popular type constructor class of Haskell. To demonstrate the broader scope, we also deal with a transparent way of introducing difference lists into a program, endowed with a neat and general correctness proof.

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Parametricity for Haskell with Imprecise Error Semantics

Cited by 8 publications

References 6 publications

Free Theorems Simply, via Dinaturality

Free Theorems Simply, via Dinaturality

Improvements for Free

Free theorems involving type constructor classes

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