name: hinze-streams version: 1.0 license: BSD3 license-file: LICENSE author: Ralf Hinze maintainer: Don Stewart homepage: http://code.haskell.org/~dons/code/hinze-streams category: Data synopsis: Streams and Unique Fixed Points description: Numeric instances for infinite streams. An implementation of: . /Functional Pearl: Streams and Unique Fixed Points/, Ralf Hinze, University of Oxford . Streams, infinite sequences of elements, live in a coworld: they are given by a coinductive data type, operations on streams are implemented by corecursive programs, and proofs are conducted using coinduction. But there is more to it: suitably restricted, stream equations possess unique solutions, a fact that is not very widely appreciated. We show that this property gives rise to a simple and attractive proof technique essentially bringing equational reasoning to the coworld. In fact, we redevelop the theory of recurrences, finite calculus and generating functions using streams and stream operators building on the cornerstone of unique solutions. The development is constructive: streams and stream operators are implemented in Haskell, usually by one-liners. The resulting calculus or library, if you wish, is elegant and fun to use. Finally, we rephrase the proof of uniqueness using generalised algebraic data types. . Along with the usual instances for infinite streams, this provides: Num, Enum, Real, Fractional, as well as recurrences on streams, finite calculus, generators . build-type: Simple stability: experimental cabal-version: >= 1.2 library build-depends: base, haskell98, Stream exposed-modules: Data.Stream.Hinze.Idiom Data.Stream.Hinze.Memo Data.Stream.Hinze.NumExt Data.Stream.Hinze.Stream extensions: MultiParamTypeClasses, FlexibleInstances