Add a README.

README.md

@@ -0,0 +1,74 @@
+# libabacus
+A math-centered programming language library.
+
+## About
+libabacus is effectively a stripped down, embeddable programming language.
+It relies on the program it's embedded into to provide the standard library. In fact,
+it doesn't even provide an underlying implementation for numbers - the client code
+provides a means of convering a string into a number, and a way of freeing that value.
+libabacus takes care of the rest. The features of libabacus are geared towards 
+calculators, so it does not provide higher-level abstractions like OOP.
+
+## Syntax
+libabacus has fairly simple syntax. A simple number expression is
+```
+42
+```
+If an operator `+` is registered with libabacus, then an expression using
+that operator looks like
+```
+21+21
+```
+If two functions, `f` and `g` are registered with libabacus, where `f` takes
+one argument and `g` takes two, then the syntax for calling these functions is
+```
+f(42)
+g(21, 21)
+```
+Blocks are a way to combine a sequence of expressions into one. The value of a block
+is the result of the last expression in that block. Expressions are delimited by the
+`;` character. For example,
+```
+{ 3; 2; 1 }
+```
+evalutes to `1`. Blocks are the first bit of syntax we've seen that can evalute to
+a value that isn't a number. For instance, the empty block, `{}`, does not
+evaluate to a number. Instead, it evalutes to `()`. This is a value of the `unit` type,
+which only has one possible value, `()`.
+
+User-defined functions are supported by libabacus:
+```
+fun square(a: num): num { a*a }
+```
+Let's pick this apart. The first part of a function declaration is the `fun` keyword. The name
+of the function is next, followed by the list of parameters that this function accepts. Parameters
+are listed in the form `[name]:[type]`. The return type of the function must also be specified.
+Lastly, the block used to evaluate the function is needed. 
+
+The block captures the scope in which the function was declared. For instance, in the following piece of code,
+```
+a = 0;
+fun test(): num { 
+    a = a + 1
+}
+```
+`test` actually has access to `a`, and calling `test` many times will yield increasing values of a.
+
+Although all parameters must specify a type, this type can be
+arbitrary to allow for polymorphic functions. For instance, a function to apply another function to an argument
+twice can be written as:
+```
+fun apply_twice(func: ('T)->'T, a: 'T): 'T {
+    func(a);
+    func(a)
+}
+```
+
+## Integration
+Everything in libabacus revolves around the `libab` struct. This struct is used to keep all the state related to the evaluation,
+and also contains the garbage collector. It needs to be instantiated using the `libab_init` function.
+```C
+libab ab;
+libab_init(&ab, parse_function, free_function);
+```
+Please see `interactive.c` for an example of a simple yet complete implementation.