name: introduce lambda-match (explicit match failure and fall-through) summary: Haskell 98 provides *two different translations* of lambda abstractions involving pattern matching, only one of which is directly accessible (Section 3.3 - the other is embedded in the translation of do-notation, see "ok" in Section 3.14). providing explicit source notation for the second translation, substantially simplifies programmability of pattern-match fall-through by reification of pattern-match failure, two central language features that are so far only available through the built-in, non-composable case construct. what: in Section 3.3, the translation for conventional lambda abstractions with patterns is given as [| \p1 .. pn-> e |] = \x1 .. xn-> case (x1,..,xn) of (p1,..,pn) -> e with xi fresh identifiers, and pattern-match failure resulting in _|_. the latter is unfortunate, and results in partial functions the coverage of which cannot be combined, but it is forced by translation into conventional lambda calculus. since computational lambda calculus (\-M) has become a central part of Haskell programming practice, there shall be an alternative form of lambda abstraction, dubbed here lambda-match, with associated translation into \-M: [| |p1 .. pn-> e |] = \x1 .. xn-> case (x1,..,xn) of { (p1,..,pn) -> return e; _ -> fail "no match" } [note1: this is the translation in principle - in practice, to enable composition of lambda-matches without further language extensions, a slight modification is needed, wrapping the right-hand sides of the case in a Match constructor, see library and patch] a library for composing these lambda-matches shall provide for composition of alternative lambda-matches (+++), match failure (nomatch) and embedding of the explicit match monad into pure expressions (splice, where "splice |p1..pn->e = \p1..pn->e"). [note2: an alternative translation would use do-notation instead of case as the target: [| |p1 .. pn-> e |] = \x1 .. xn-> do { (p1,..,pn) <- return (x1,..,xn); return e } both translations easily accomodate guards and pattern guards as well, the former by building on existing support for these two features in case constructs, the latter without requiring any previous implementation of pattern guards, by lifting (pattern) guards into the match monad] implementation impact: minimal - limited to an extension in parser/desugarer, employing previously inaccessible syntax for lambda-match, and a slight variation of the existing lambda translation; also adds a small library to support composition of matches. [note3: a first draft of the composition library and a patch for GHC (about a dozen new lines in the parser) are provided as attachments to this proposal, together with some examples] context: as has been pointed out in the thread on replacing and improving pattern guards, Haskell's pattern matching support, even before pattern guards, is monolithic (built-in case is the only way to handle multiple alternative matches) rather than compositional (lambdas represent individual alternatives, but cannot be composed on match fall-through). this implies increased complexity of the language definition and limited expressiveness of its features, when compared with alternative models (eg, adapting Wolfram's pattern match calculus for Haskell). see, eg.: http://www.haskell.org/pipermail/haskell-prime/2006-October/001713.html http://www.haskell.org/pipermail/haskell-prime/2006-October/001720.html http://www.haskell.org/pipermail/haskell-prime/2006-October/001723.html http://www.haskell.org/pipermail/haskell-prime/2006-October/001724.html in principle, replacing Haskell's current pattern matching support with a simpler, more compositional model, and defining the current constructs on top of that new core is the way forward, IMHO. in practice, however, I suspect that the committee is less than tempted to introduce such a substantial simplification for Haskell'. the present proposal is an attempt at a compromise, suggesting a minimal language change to introduce compositional pattern-match failure and fall-through. with lambda-match, it implements only a single language extension (as syntactic sugar), delegating the rest of the functionality to a library. without the sugar, the result of the by-hand translation becomes so hard to read as to be near unusable, while the chosen form of sugaring allows to provide most of the language features discussed in the earlier threads to be provided as a library. this does seem to be a useable balance. building constructs of the simpler pattern-match model on top of the more complex one is somewhat irksome from a language design perspective, but does at least gain the expressiveness of the simpler model. if programmers make substantial use of this new functionality in Haskell' (as I strongly suspect they will - I have been doing similar translations by hand for some time now), it will be up to Haskell'' to turn the table, and to define the current complex model on top of a compositional one. as a preview of this anticipated language refactoring;), it is instructive to compare the two alternative translations of lambda-match sketched above: - the first directly builds on the existing, complex case constructs with their built-in (pattern) guards and match fall-through support; this eases adding the new, simpler features to implementations that support the old, complex ones (like GHC), but completely foregoes any attempt to simplify those implementations in the process; [the attached patch for GHC follows this route] - the second translation avoids any direct reference to case, employing do-notation instead; this requires slightly more effort, eg. in translating pattern guards into the match monad, but is eminently suitable for adding the new features to implementations that do not support pattern guards yet, or that simply want to reduce the number of built-in constructs. [patchers for Hugs, etc., might want to follow this route?]