* [[!wikipedia Haskell Curry]] * [[!wikipedia Moses SchÃ¶nfinkel]] * [[!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]] * [[!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) was ratified in 2007, but this has many detractors and has not been fully accepted in the community. ([Libraries for R6RS](http://www.r6rs.org/final/html/r6rs-lib/r6rs-lib.html)) * [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 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/)