Lambda the Ultimate

Say we have a declarative language, where a = b is an assertion that governs the rest of the code, not an assignment operation. To this language we add the notion of explicit scopes -- assignments only apply within a scope, it's okay to have multiple contradictory assignments in different scopes. On top of this, we add one more idea -- scopes can inherit from one another, which is to say that children can overwrite assignments of their parents but otherwise maintain the same environment. For example:

foo(a, b, c)
  gamma = a * b
  rho = b * c
  gamma * rho

bar(a, b, c) extends foo
  gamma = a * a

is a piece of code in which bar assigns a different value to gamma but otherwise runs exactly as foo does, computing gamma * rho and returning the result. What I am talking about is function inheritance. In the above example, foo and bar must have the same signature for it to work -- but there are ideas from object oriented programming that can be leveraged to get around that.

Of course, the above example is little bit simplistic. Far more interesting is the use of the implies operator (->) for matching:

foo(a, b, c)
  'a' -> a
  'b' -> b
  'c' -> c
  'foo' -> 'foo'

bar(a, b, c) extends foo
  'foo' -> 'bar extending foo'

Here we use the implies operator to mean "when x is injected into my symbol space there is y" or in other words "a message x gets a response of y". Now, this example also offers up some real problems -- how do we specify tail recursion or termination in this language? -- but I'm willing to bet that a little study would reveal straightforward syntactic forms for this kind of thing.

Now that I have thought this language up, I have to work on it. I swore there would never be a day when I would stray from the well settled lands of software development to wander in the wilds of language design! Alas, I am doomed. All I ask from ltu is some thoughtful criticism of my idea, some pointers to earlier work in this domain and some suggestions about the syntax. What I want in the end is a language that is process/message oriented like Erlang but also has straightforward syntax for the notion of 'inheritance'.

See Felix's explanations.