+* Our [[Lambda evaluator]] +* [Chris Barker's Lambda Tutorial](http://homepages.nyu.edu/~cb125/Lambda) +* [Lambda Animator](http://thyer.name/lambda-animator/) +* [Penn lambda calculator](http://www.ling.upenn.edu/lambda/) Pedagogical software developed by Lucas Champollion, Josh Tauberer and Maribel Romero.

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

+* [[!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 SKI combinatory calculus]] * [[!wikipedia B,C,K,W system]] -* [[!wikipedia Church-Rosser theorem]] -* [[!wikipedia Normalization property]] -* [[!wikipedia Turing completeness]]

-* [[!wikipedia Church encoding]] -* [[!wikipedia Y combinator]]

-* [[!wikipedia Curry-Howard isomorphism]]

+* Jeroen Fokker, "The Systematic Construction of a One-combinator Basis for Lambda-Terms" Formal Aspects of Computing 4 (1992), pp. 776-780. + +* [Chris Barker's Iota and Jot](http://semarch.linguistics.fas.nyu.edu/barker/Iota/)

+ +* [To Dissect a Mockingbird](http://dkeenan.com/Lambda/index.htm) + +## 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]] @@ -81,14 +109,77 @@ get more out of out. (Rinse and repeat.) * [[!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