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  1. Proceedings of the 2015 ACM SIGPLAN Symposium on Haskell (Haskell '15)
  2. Functional pearl: getting a quick fix on comonads
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Improving Haskell types with SMT
Reasoning with the HERMIT: tool support for equational reasoning on GHC core programs
Bridging the GUI gap with reactive values and relations
Variations on variants
Freer monads, more extensible effects
Injective type families for Haskell
Déjà Fu: a concurrency testing library for Haskell
Practical probabilistic programming with monads
Guilt free ivory
A typechecker plugin for units of measure: domain-specific constraint solving in GHC Haskell
Formally proving a compiler transformation safe
The remote monad design pattern
Modular reifiable matching: a list-of-functors approach to two-level types
Functional pearl: getting a quick fix on comonads
Type families with class, type classes with family
Improving implicit parallelism
Embedding a full linear Lambda calculus in Haskell
Type-safe runtime code generation: accelerate to LLVM

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Functional pearl: getting a quick fix on comonads

Content Provider ACM Digital Library
Author Foner, Kenneth
Abstract A piece of functional programming folklore due to Piponi provides Löb's theorem from modal provability logic with a computational interpretation as an unusual fixed point. Interpreting modal necessity as an arbitrary Functor in Haskell, the "type" of Löb's theorem is inhabited by a fixed point function allowing each part of a structure to refer to the whole. However, Functor's logical interpretation may be used to prove Löb's theorem only by relying on its implicit functorial strength, an axiom not available in the provability modality. As a result, the well known loeb fixed point "cheats" by using functorial strength to implement its recursion. Rather than Functor, a closer Curry analogue to modal logic's Howard inspiration is a closed (semi-)comonad, of which Haskell's ComonadApply typeclass provides analogous structure. Its computational interpretation permits the definition of a novel fixed point function allowing each part of a structure to refer to its own context within the whole. This construction further guarantees maximal sharing and asymptotic efficiency superior to loeb for locally contextual computations upon a large class of structures. With the addition of a distributive law, closed comonads may be composed into spaces of arbitrary dimensionality while preserving the performance guarantees of this new fixed point. From these elements, we construct a small embedded domain-specific language to elegantly express and evaluate multidimensional "spreadsheet-like" recurrences for a variety of cellular automata. .
Starting Page 106
Ending Page 117
Page Count 12
File Format PDF
ISBN 9781450338080
DOI 10.1145/2804302.2804310
Language English
Publisher Association for Computing Machinery (ACM)
Publisher Date 2015-08-30
Publisher Place New York
Access Restriction Subscribed
Subject Keyword Spreadsheets Haskell Modal logic Closed comonads
Content Type Text
Resource Type Article
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