* [[!wikipedia Moses SchÃ¶nfinkel]] * [[!wikipedia Haskell Curry]] * [[!wikipedia Alonzo Church]]

* [[!wikipedia Combinatory logic]] * [Combinatory logic](http://plato.stanford.edu/entries/logic-combinatory/) at the Stanford Encyclopedia of Philosophy * [[!wikipedia SKI combinatory calculus]] * [[!wikipedia B,C,K,W system]] * [Chris Barker's Iota and Jot]() (broken link)

* [[!wikipedia Church-Rosser theorem]] * [[!wikipedia Normalization property]] * [[!wikipedia Turing completeness]]

* [Scooping the Loop Snooper](http://www.cl.cam.ac.uk/teaching/0910/CompTheory/scooping.pdf), a proof of the undecidability of the halting problem in the style of Dr Seuss by Geoffrey K. Pullum * [[!wikipedia Church encoding]] ## Learning Scheme ## * [[!wikipedia Scheme (programming language) desc="Wikipedia overview of Scheme"]] * If you are new to programming or if you have the patience to work through a textbook, you should work through a textbook. Some good choices are The Little Schemer book(s) we recommended for the seminar; and also: + [How to Design Programs](http://www.htdp.org/2003-09-26/), by Matthias Felleisen, et al., which the Racket groups recommends. Whenever the book says "Scheme," you can read it as "Racket." Another warmly-recommended introduction available online is [Teach Yourself Scheme in Fixnum Days](http://www.ccs.neu.edu/home/dorai/t-y-scheme/t-y-scheme.html) This is a short introductory text that introduces common Scheme techniques. * If you're already a programmer and you're in more of a hurry, you could instead look at the [Quick Introduction to Racket](http://docs.racket-lang.org/quick/index.html). This tutorial provides a brief introduction to the Racket programming language by using DrRacket and one of Racket's picture-drawing libraries. * [An Introduction to Lambda Calculus and Scheme](http://www.jetcafe.org/~jim/lambda.html) is also aimed at programmers. * After any of the preceding, you could move on to [Racket Guide](http://docs.racket-lang.org/guide/index.html). This starts with a tutorial on Racket basics; then it describes the rest of the Racket language. This guide is intended for programmers who are new to Racket or new to some part of Racket. It assumes programming experience, so if you are new to programming, you should instead start with one of the textbooks listed above. This Guide describes parts of the Racket language which go beyond the learning-oriented fragments of How to Design Programs. * The [Complete Racket Reference Manual](http://docs.racket-lang.org/reference/index.html) defines the core Racket language and describes its most prominent libraries. The Racket Guide is friendlier; though less precise and less complete. * The Scheme language is standardized; the various implementations of the language usually adhere to what's published in the current standard and add on different handy extensions. The first standard was published in 1975. A revision was published in 1978 called "The revised report on Scheme, a dialect of Lisp." Thereafter, revisions of the standard were titled "The Revised Revised Report..." and so on, or "The Revised^n Report..." for short. One widely implemented standard is [The Revised^5 Report on Scheme](http://www.schemers.org/Documents/Standards/R5RS/HTML/), or R5RS, published in 1998. A new standard [R6RS](http://www.r6rs.org/final/html/r6rs/r6rs.html) ([Libraries for R6RS](http://www.r6rs.org/final/html/r6rs-lib/r6rs-lib.html)) was ratified in 2007, and this is implemented in Racket; but it also has many detractors and has not been fully accepted in the community. As a result, the Scheme language [may in the future split](http://scheme-reports.org/2009/position-statement.html) into a lean, minimal base, closer to R5RS Scheme, and a richer language like R6RS Scheme that standardizes many of the add-ons that programmers tend to build on top of the base. * [Scheme FAQ](http://community.schemewiki.org/?scheme-faq) * [Scheme Requests for Implementation](http://srfi.schemers.org/) (SRFI) * The [Schematics Scheme Cookbook](http://schemecookbook.org/) is a collaborative effort to produce documentation and recipes for using Scheme for common tasks. ## Recursion and the Y Combinator ## * [[!wikipedia Recursion (computer science) desc="Recursion"]] * [[!wikipedia Y combinator]] * [Chapter 9 from The Little Schemer](http://www.ccs.neu.edu/home/matthias/BTLS/sample.ps) on the Y Combinator "...and Again, and Again, and Again..." * [The Y combinator](http://mvanier.livejournal.com/2700.html) * [The Why of Y](http://www.dreamsongs.com/NewFiles/WhyOfY.pdf) * [The Y Combinator (Slight Return), or: How to Succeed at Recursion Without Really Recursing](http://mvanier.livejournal.com/2897.html) * [Y Combinator for Dysfunctional Non-Schemers](http://rayfd.wordpress.com/2007/05/06/y-combinator-for-dysfunctional-non-schemers/) * [The Y Combinator](http://www.ece.uc.edu/~franco/C511/html/Scheme/ycomb.html) * [The Y Combinator](http://dangermouse.brynmawr.edu/cs245/ycomb_jim.html) derives the applicative-order Y-combinator from scratch, in Scheme. This derivation is similar in flavor to the derivation found in The Little Schemer, but uses a slightly different starting approach... ## Evaluation Order ## * [[!wikipedia Evaluation strategy]] * [[!wikipedia Eager evaluation]] * [[!wikipedia Lazy evaluation]] * [[!wikipedia Strict programming language]] ## Types ## * [[!wikipedia Tagged union]] * [[!wikipedia Algebraic data type]] * [[!wikipedia Recursive data type]] * [[!wikipedia Pattern matching]] * [[!wikipedia Unit type]] * [[!wikipedia Bottom type]] * [[!wikipedia Typed lambda calculus]] * [[!wikipedia Simply typed lambda calculus]] * [Type Theory](http://plato.stanford.edu/entries/type-theory/) at the Stanford Encyclopedia of Philosophy * [Church's Type Theory](http://plato.stanford.edu/entries/type-theory-church/) at the Stanford Encyclopedia of Philosophy * The [[!wikipedia Curry-Howard isomorphism]] * [The Curry-Howard correspondence in Haskell](http://www.thenewsh.com/~newsham/formal/curryhoward/) * [The Curry-Howard Isomorphism](http://en.wikibooks.org/wiki/Haskell/The_Curry-Howard_isomorphism) at Haskell wiki

* [[!wikipedia Type polymorphism]] * [[!wikipedia System F]] ## Learning OCaml ## * [[!wikipedia Objective Caml desc="Wikipedia overview of OCaml"]] * [A Concise Introduction to Objective Caml](http://www.csc.villanova.edu/~dmatusze/resources/ocaml/ocaml.html) * Here are [two](http://www.cs.jhu.edu/~scott/pl/lectures/caml-intro.html) [other](http://pauillac.inria.fr/caml/FAQ/stephan.html) brief overviews of OCaml, aimed at readers who already have some programming experience. Here are [two](http://pauillac.inria.fr/caml/FAQ/exemples-eng.html) [more](http://pauillac.inria.fr/caml/FAQ/qrg-eng.html), even briefer. * Here's a [more detailed tutorial](http://www.ocaml-tutorial.org/) for OCaml. * The start of the [OCaml Reference Manual](http://caml.inria.fr/pub/docs/manual-ocaml/manual003.html) has another tutorial. * Jason Hickey has posted a [draft of a nice book introducing OCaml](http://www.cs.caltech.edu/courses/cs134/cs134b/book.pdf). * FAQs for [OCaml Beginners](http://pauillac.inria.fr/caml/FAQ/FAQ_DEBUTANT-eng.html), and [a few more](http://caml.inria.fr/resources/doc/faq/). Also FAQs for [OCaml Experts](http://pauillac.inria.fr/caml/FAQ/FAQ_EXPERT-eng.html). ## Side-effects / mutation ## * [[!wikipedia Side effect (computer science) desc="Side effects"]] * [[!wikipedia Reference (computer science) desc="References"]] * [[!wikipedia Pointer (computing) desc="Pointers"]] * [Pointers in OCaml](http://caml.inria.fr/resources/doc/guides/pointers.html) ## Monads ## * [[!wikipedia Monad (functional programming) desc="Monads in Functional Programming"]] * [A Gentle Intro to Haskell: About Monads](http://www.haskell.org/tutorial/monads.html) * [Understanding Haskell Monads](http://ertes.de/articles/monads.html) * [The State Monad: a tutorial for the confused?](http://coder.bsimmons.name/blog/2009/10/the-state-monad-a-tutorial-for-the-confused/) * [Beyond Monads](http://blog.sigfpe.com/2009/02/beyond-monads.html) * [Simple Explanation of a Monad](http://math.stackexchange.com/questions/405/simple-explanation-of-a-monad) * [What is a Monad?](http://stackoverflow.com/questions/44965/what-is-a-monad) * [Can Anyone Explain Monads?](http://stackoverflow.com/questions/2366/can-anyone-explain-monads) * [Monad in Plain English...](http://stackoverflow.com/questions/2704652/monad-in-plain-english-for-the-oop-programmer-with-no-fp-background) * [Monad in non-programming terms](http://stackoverflow.com/questions/3261729/monad-in-non-programming-terms) * [Real World Haskell: chapter on Monads](http://book.realworldhaskell.org/read/monads.html) * [Learn You a Haskell for Great Good: chapter on Functors, Applicative Functors and Monoids](http://www.learnyouahaskell.com/functors-applicative-functors-and-monoids) * Monads are Elephants: [Part 1](http://james-iry.blogspot.com/2007/09/monads-are-elephants-part-1.html) [Part 2](http://james-iry.blogspot.com/2007/10/monads-are-elephants-part-2.html) [Part 3](http://james-iry.blogspot.com/2007/10/monads-are-elephants-part-3.html) [Part 4](http://james-iry.blogspot.com/2007/11/monads-are-elephants-part-4.html) * [Brian Beckman: Don't fear the Monad (67 minute video)](http://channel9.msdn.com/shows/Going+Deep/Brian-Beckman-Dont-fear-the-Monads/) * [A monad non-tutorial...or why you shouldn't ask what a monad is](http://strongtyped.blogspot.com/2010/01/monad-non-tutorial.html) * [The Mother of all Monads](http://blog.sigfpe.com/2008/12/mother-of-all-monads.html) * [You Could Have Invented Monads! (And Maybe You Already Have.)](http://blog.sigfpe.com/2006/08/you-could-have-invented-monads-and.html) * [Monads! (and Why Monad Tutorials Are All Awful)](http://ahamsandwich.wordpress.com/2007/07/26/monads-and-why-monad-tutorials-are-all-awful/) * [Of monads and spacesuits (archived)](http://www.iterasi.net/openviewer.aspx?sqrlitid=ixx7fcluvek_9lfolsxr_g) * [Haskell wikibook: Understanding monads](http://en.wikibooks.org/wiki/Haskell/Understanding_monads) * Haskell state monads: [part 1](http://mvanier.livejournal.com/1765.html) [part 2](http://mvanier.livejournal.com/1901.html) * [How not to explain Haskell monads](http://mvanier.livejournal.com/1205.html) * Yet Another Monad Tutorial: [part 1](http://mvanier.livejournal.com/3917.html) [part 2](http://mvanier.livejournal.com/4305.html) [part 3](http://mvanier.livejournal.com/4586.html) [part 4](http://mvanier.livejournal.com/4647.html) * [Research Papers/Monads and Arrows](http://www.haskell.org/haskellwiki/Research_papers/Monads_and_arrows) * [Philip Wadler. Monads for Functional Programming](http://homepages.inf.ed.ac.uk/wadler/papers/marktoberdorf/baastad.pdf): in M. Broy, editor, *Marktoberdorf Summer School on Program Design Calculi*, Springer Verlag, NATO ASI Series F: Computer and systems sciences, Volume 118, August 1992. Also in J. Jeuring and E. Meijer, editors, *Advanced Functional Programming*, Springer Verlag, LNCS 925, 1995. Some errata fixed August 2001. The use of monads to structure functional programs is described. Monads provide a convenient framework for simulating effects found in other languages, such as global state, exception handling, output, or non-determinism. Three case studies are looked at in detail: how monads ease the modification of a simple evaluator; how monads act as the basis of a datatype of arrays subject to in-place update; and how monads can be used to build parsers. * [Philip Wadler. The essence of functional programming](http://homepages.inf.ed.ac.uk/wadler/papers/essence/essence.ps): invited talk, *19'th Symposium on Principles of Programming Languages*, ACM Press, Albuquerque, January 1992. This paper explores the use monads to structure functional programs. No prior knowledge of monads or category theory is required. Monads increase the ease with which programs may be modified. They can mimic the effect of impure features such as exceptions, state, and continuations; and also provide effects not easily achieved with such features. The types of a program reflect which effects occur. The first section is an extended example of the use of monads. A simple interpreter is modified to support various extra features: error messages, state, output, and non-deterministic choice. The second section describes the relation between monads and continuation-passing style. The third section sketches how monads are used in a compiler for Haskell that is written in Haskell. ## Monads in Category Theory ## * [Category Theory at SEP](http://plato.stanford.edu/entries/category-theory/) * [[!wikipedia Category theory]] * [[!wikipedia Category (mathematics) desc="Category"]] * [[!wikipedia Morphism]] * [[!wikipedia Functor]] * [[!wikipedia Natural transformation]] * [[!wikipedia Monad (category theory) desc="Monads in category theory"]] * [Haskell/Category Theory](http://en.wikibooks.org/wiki/Haskell/Category_theory) * [Category Theory & Functional Programming](http://blog.mestan.fr/2009/01/09/category-theory-functional-programming/) * [Learning Haskell through Category Theory, and Adventuring in Category Land](http://dekudekuplex.wordpress.com/2009/01/16/learning-haskell-through-category-theory-and-adventuring-in-category-land-like-flatterland-only-about-categories/) * [Resources for learning practical category theory](http://mathoverflow.net/questions/903/resources-for-learning-practical-category-theory) * [A Partial Ordering of some Category Theory applied to Haskell](http://blog.sigfpe.com/2010/03/partial-ordering-of-some-category.html) ## Continuations ## * [[!wikipedia Continuation]] * [[!wikipedia Continuation-passing style]] * [[!wikipedia Call-with-current-continuation]] * [Intro to call/cc](http://community.schemewiki.org/?call-with-current-continuation) at SchemeWiki * [Call With Current Continuation](http://www.c2.com/cgi/wiki?CallWithCurrentContinuation) * [Continuations Made Simple and Illustrated](http://www.ps.uni-saarland.de/~duchier/python/continuations.html) * [Continuation kata](http://programming-musings.org/2006/02/12/continuation-kata/) * [Understanding continuations](http://keithdevens.com/weblog/archive/2004/Jul/11/continuations) [Commentary](http://lambda-the-ultimate.org/node/86) * [Continuations In Scheme](http://tech.phillipwright.com/2010/05/23/continuations-in-scheme/) * [Understanding Scheme Continuations](http://sanjaypande.blogspot.com/2004/06/understanding-scheme-continuations.html). This is tagged "Part I" but I think there's no further parts. * [Continuations for Curmudgeons](http://www.intertwingly.net/blog/2005/04/13/Continuations-for-Curmudgeons) [Commentary](http://lambda-the-ultimate.org/node/643) * [Haskell wiki on Continuations](http://www.haskell.org/haskellwiki/Continuation)

* [[!wikipedia Delimited continuation]] * [Composable Continuations Tutorial](http://community.schemewiki.org/?composable-continuations-tutorial) at SchemeWiki * [Post by Ken](http://lambda-the-ultimate.org/node/1197#comment-12927) on Lambda the Ultimate explaining difference between undelimited and delimited continuations * [shift, reset and streams](http://chneukirchen.org/blog/archive/2005/04/shift-reset-and-streams.html) * [guile and delimited continuations](http://www.wingolog.org/archives/2010/02/26/guile-and-delimited-continuations) * [Delimited continuations in Scala](http://blog.richdougherty.com/2009/02/delimited-continuations-in-scala_24.html) * [Delimited Continuations Explained (in Scala)](http://dcsobral.blogspot.com/2009/07/delimited-continuations-explained-in.html) * [Partial Continuations](http://www.bluishcoder.co.nz/articles/scheme/partial-continuations.html) * Delimited Continuations in MzScheme: [Part 1](http://schemekeys.blogspot.com/2006/11/prompts-their-interaction-with-dynamic.html) [Part 2](http://schemekeys.blogspot.com/2006/12/delimited-continuations-in-mzscheme.html) [Part 3](http://schemekeys.blogspot.com/2007/01/going-further-with-primitives.html) [Part 4](http://schemekeys.blogspot.com/2007/01/odd-and-ends.html)

* [Online Bibliography of Scheme Research: Continuations and Continuation Passing Style](http://library.readscheme.org/page6.html) * [Delimited continuations in natural language semantics](http://okmij.org/ftp/gengo/) ## Linear Logic ## * [[!wikipedia Linear logic]]