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Author: igorw

README.md

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+# lambda-php
+
+Lambda calculus interpreter in PHP.
+
+## What?
+
+Lambda calculus is a very minimal programming language that was invented in
+1936 by Alonzo Church. It is the functional equivalent of the Turing Machine.
+
+Lambda calculus has only three concepts: Function definitions, lexically
+scoped variables, function application.
+
+An example term would be the identity function:
+
+    λx.x
+
+The first part `λx` defines a function that takes an `x`, the `.` signifies
+that the part that follows is the function body. The body just returns `x`.
+
+In PHP, you would write the same thing as follows:
+
+    function ($x) {
+        return $x;
+    }
+
+You can nest function definitions. Here is a function returning a function:
+
+    λx.λy.x
+
+And you can also *apply* a function to an argument, which just means calling
+the function.
+
+    λf.λg.f g
+
+Which is the short hand (left-associative) form of writing
+
+    λf.λg.(f g)
+
+Nested calls like:
+
+    λf.λg.λh.f g h
+
+Are interpreted as:
+
+    λf.λg.λh.((f g) h)
+
+If you want to change the grouping to be right-associative, you need to
+explicitly group them in parentheses:
+
+    λf.λg.λh.(f (g h))
+
+Interestingly, lambda calculus is turing complete. Using just these three
+concepts you can represent *any* computation.
+
+## REPL
+
+This project ships with a read-eval-print-loop that you can use to evaluate
+lambda calculus expressions:
+
+    $ php repl.php
+
+By default, it is in *int-mode*, expecting the result of the expression to be
+a church-encoded number. Example:
+
+    $ php repl.php
+    i> λf.λx.f (f (f x))
+    3
+
+You can switch to *bool-mode* by sending the `b` command:
+
+    $ php repl.php
+    i> b
+    b> λx.λy.x
+    true
+
+## Further reading
+
+* [Lambda Calculus - Wikipedia](http://en.wikipedia.org/wiki/Lambda_calculus)
+* [Matt Might: 7 lines of code, 3 minutes](http://matt.might.net/articles/implementing-a-programming-language/)
+* [Tom Stuart: Programming with Nothing](http://codon.com/programming-with-nothing)
+* [Erkki Lindpere: Parsing Lambda Calculus in Scala](http://zeroturnaround.com/rebellabs/parsing-lambda-calculus-in-scala/)