The Derivative of a Fixed Point computes what has changed between iterations . So The Derivative is the Irreducible Residue that is left from the previous iteration. And the last and final iteration results in an Irreducible Residue that is itself irreducible . These in essence remind me of Euclidean primes, which satisfy the same characteristics.
So... the first 15 minutes reinvents C# 3.0 (2007) using list comprehensions in place of LINQ. In the second 15 minutes, I don't know what "!y" is supposed to mean, but it looks like something that could be implemented as a macro in a language with LISP-style macros. For example, in Enhanced C# one could write a macro that recognizes "fix" such that the ancestor set is generated by something like fix Set ancestor = parent | from (x, y) in parent from (y, z) in ancestor select (x, z); Set parent = .... // Set type from Loyc.Collections Since macros run arbitrary code at compile-time, the macro could optimize the query at compile-time. Or using ordinary C#, one could write a `fix(ancestor => ...)` function whose argument is an expression tree, which optimizes the query at run-time. In either case, `fix` could be implemented based on the discussion in the last part of this video. So we don't actually need to invent a new programming language in order to obtain a programming language that supports new functionality. And even if you decide you need a new programming language, you don't necessarily need to invent a syntax for it ( see loyc.net/les )
The Derivative of a Fixed Point computes what has changed between iterations . So The Derivative is the Irreducible Residue that is left from the previous iteration. And the last and final iteration results in an Irreducible Residue that is itself irreducible . These in essence remind me of Euclidean primes, which satisfy the same characteristics.
So... the first 15 minutes reinvents C# 3.0 (2007) using list comprehensions in place of LINQ.
In the second 15 minutes, I don't know what "!y" is supposed to mean, but it looks like something that could be implemented as a macro in a language with LISP-style macros. For example, in Enhanced C# one could write a macro that recognizes "fix" such that the ancestor set is generated by something like
fix Set ancestor = parent |
from (x, y) in parent
from (y, z) in ancestor
select (x, z);
Set parent = .... // Set type from Loyc.Collections
Since macros run arbitrary code at compile-time, the macro could optimize the query at compile-time. Or using ordinary C#, one could write a `fix(ancestor => ...)` function whose argument is an expression tree, which optimizes the query at run-time. In either case, `fix` could be implemented based on the discussion in the last part of this video.
So we don't actually need to invent a new programming language in order to obtain a programming language that supports new functionality. And even if you decide you need a new programming language, you don't necessarily need to invent a syntax for it ( see loyc.net/les )
He's giving the background, explaining the history of the stuff that lead to LINQ/list comprehensions/etc in the first section.
Where is the “general purpose programming is functional programming” coming from?
For me, functional programming is imperative programming.