* [[!wikipedia Church encoding]]
* [[!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]]
* Jeroen Fokker, "The Systematic Construction of a One-combinator Basis for Lambda-Terms" Formal Aspects of Computing 4 (1992), pp. 776-780.

* [To Dissect a Mockingbird](http://dkeenan.com/Lambda/index.htm) * [Combinator Birds](http://www.angelfire.com/tx4/cus/combinator/birds.html) * [Les deux combinateurs et la totalite](http://www.paulbraffort.net/j_et_i/j_et_i.html) by Paul Braffort. ## Evaluation Order ## * [[!wikipedia Evaluation strategy]] * [[!wikipedia Eager evaluation]] * [[!wikipedia Lazy evaluation]] * [[!wikipedia Strict programming language]] ## Confluence, Normalization, Undecidability ## * [[!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 ## 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... * [The church of the least fixed point, by Sans Pareil](http://www.springerlink.com/content/n4t2v573m58g2755/) ## 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 * [[!wikipedia Type polymorphism]] * [[!wikipedia System F]] ##[[Learning OCaml]]## ## 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) ## The Curry-Howard Correspondence ## * 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

## 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]]