Fused multiply-add in Racket - racket

Is is it possible to use fused multiply-add in Racket?
I'm attempting to port some numerical code that relies on the single rounding of the fused operation, but after several searches haven't found any way to use fma or similar in Racket.
Thanks!!

You can get it from the C library using the FFI:
(require ffi/unsafe ffi/unsafe/define)
(define-ffi-definer define-libc #f)
(define-libc fma (_fun _double _double _double -> _double))
(fma 3.0 2.0 1.0)
;; => 7.0
That works for me on Linux. On Windows you may need to give a different library to define-ffi-definer.
You can also use _double* instead of _double for the arguments to automatically convert Racket's other numeric types to doubles.
If the performance is critical, you may need compiler and/or runtime support to avoid the overhead the FFI imposes. In that case, you might want to ask on the Racket Users mailing list.

Related

Implementing language translators in racket

I am implementing an interpreter that codegen to another language using Racket. As a novice I'm trying to avoid macros to the extent that I can ;) Hence I came up with the following "interpreter":
(define op (open-output-bytes))
(define (interpret arg)
(define r
(syntax-case arg (if)
[(if a b) #'(fprintf op "if (~a) {~a}" a b)]))
; other cases here
(eval r))
This looks a bit clumsy to me. Is there a "best practice" for doing this? Am I doing a totally crazy thing here?
Short answer: yes, this is a reasonable thing to do. The way in which you do it is going to depend a lot on the specifics of your situation, though.
You're absolutely right to observe that generating programs as strings is an error-prone and fragile way to do it. Avoiding this, though, requires being able to express the target language at a higher level, in order to circumvent that language's parser.
Again, it really has a lot to do with the language that you're targeting, and how good a job you want to do. I've hacked together things like this for generating Python myself, in a situation where I knew I didn't have time to do things right.
EDIT: oh, you're doing Python too? Bleah! :)
You have a number of different choices. Your cleanest choice is to generate a representation of Python AST nodes, so you can either inject them directly or use existing serialization. You're going to ask me whether there are libraries for this, and ... I fergits. I do believe that the current Python architecture includes ... okay, yes, I went and looked, and you're in good shape. Python's "Parser" module generates ASTs, and it looks like the AST module can be constructed directly.
https://docs.python.org/3/library/ast.html#module-ast
I'm guessing your cleanest path would be to generate JSON that represents these AST modules, then write a Python stub that translates these to Python ASTs.
All of this assumes that you want to take the high road; there's a broad spectrum of in-between approaches involving simple generalizations of python syntax (e.g.: oh, it looks like this kind of statement has a colon followed by an indented block of code, etc.).
If your source language shares syntax with Racket, then use read-syntax to produce a syntax-object representing the input program. Then use recursive descent using syntax-case or syntax-parse to discern between the various constructs.
Instead of printing directly to an output port, I recommend building a tree of elements (strings, numbers, symbols etc). The last step is then to print all the elements of the tree. Representing the output using a tree is very flexible and allows you to handle sub expressions out of order. It also allows you to efficiently concatenate output from different sources.
Macros are not needed.

require vs load vs include vs import in Racket

The Racket docs indicate that Racket has separate forms for: require, load, include, and import. Many other languages only contain one of these and are generally used synonymously (although obviously with language specific differences such as #include in C, and import in Java).
Since Racket has all four of these, what is the difference between each one and which should I be using in general? Also if each has a specific use, when should I use an alternative type? Also, this question seems to indicate that require (paired with provide) is preferred, why?
1. Require
You are correct, the default one you want is almost always require (paired with a provide). These two forms go hand in hand with Racket's modules and allows you to more easily determine what variables should be scoped in which files. For example, the following file defines three variables, but only exports 2.
#lang racket ; a.rkt
(provide b c)
(define a 1)
(define b 2)
(define c 3)
As per the Racket style guide, the provide should ideally be the first form in your file after the #lang so that you can easily tell what a module provides. There are a few cases where this isn't possible, but you probably won't encounter those until you start making your own Racket libraries you intend for public distribution. Personally, I still put a file's require before its provide, but I do sometimes get flack for it.
In a repl, or another module, you can now require this file and see the variables it provides.
Welcome to Racket v6.12.
> (require "a.rkt")
> c
3
> b
2
> a
; a: undefined;
; cannot reference undefined identifier
; [,bt for context]
There are ways to get around this, but this serves as a way for a module to communicate what its explicit exports are.
2. Load
This is a more dynamic variant of require. In general you should not use it, and instead use dynamic-require when you need to load a module dynamically. In this case, load is effectively a primitive that require uses behind the scenes. If you are explicitly looking to emulate the top level however (which, to be clear, you almost never do), then load is a fine option. Although in those rare cases, I would still direct you to the racket/load language. Which interacts exactly as if each form was entered into the repl directly.
#lang racket/load
(define x 5)
(displayln x) ; => prints 5
(define x 6)
(displayln x) ; => prints 6
3. Include
Include is similar to #include in C. There are even fewer cases where you should use it. The include form grabs the s-expression syntax of the given path, and puts it directly in the file where the include form was. At first, this can appear as a nice solution to allow you to split up a single module into multiple files, or to have a module 'piece' you want to put in multiple files. There are however better ways to do both of those things without using include, that also don't come with the confusing side effects you get with include.1 One thing to remember if you still insist on using import, is that the file you are importing probably shouldn't have a #lang line unless you are explicitly wanting to embed a submodule. (In which case you will also need to have a require form in addition to the include).
4. Import
Finally, import is not actually a core part of Racket, but is part of its unit system. Units are similar in some ways to modules, but allow for circular dependencies (unit A can depend on Unit B while Unit B depends on Unit A). They have fallen out of favor in recent years due to the syntactic overhead they have.
Also unlike the other forms import (and additionally export), take signatures, and relies on an external linker to decide which actual units should get linked together. Units are themselves a complex topic and deserve their own question on how to create and link them.
Conclusion (tldr)
TLDR; Use require and provide. They are the best supported and easiest to understand. The other forms do have their uses, but should be thought of 'advanced uses' only.
1These side effects are the same as you would expect for #include in C. Such as order being important, and also with expressions getting intermixed in very unpredictable ways.

Any Lisp extensions for CUDA?

I just noted that one of the first languages for the Connection-Machine of W.D. Hillis was *Lisp, an extension of Common Lisp with parallel constructs. The Connection-Machine was a massively parallel computer with SIMD architecture, much the same as modern GPU cards.
So, I would expect that an adaptation of *Lisp to GPGPU - maybe to nVidia CUDA, as it is the most advanced de facto standard - would be quite natural.
So far, besides the nVidia SDK for C/C++, I only found PyCUDA, a Python environment. Has anybody heard anything about Lisp?
Penumbra is an idiomatic wrapper for OpenGL in Clojure. Calx is an idiomatic wrapper for OpenCL to target CPUs, GPUs, and more exotic hardware. See also calling CUDA from Clojure.
CL-OPENGL is a set of Common Lisp bindings to the OpenGL, GLU and GLUT APIs. CL-GPU is a translator from a subset of Common Lisp to CUDA for writing GPU kernels. ECL-COMPUTE is a DSL for SSE/CUDA computation in Embeddable Common Lisp.
I recently start developing cl-cuda which is a library to use NVIDIA CUDA in Common Lisp programs. Although it has just been started and in the very early stage of development, you can try some simple sample codes like large vector addition.
Please see,
https://github.com/takagi/cl-cuda
If you are interested in this project, any feedbacks are welcome.
A while ago I made a library to call CUDA-functions/libraries from common lisp. Its purpose was to do things like
(let ((myarray (make-array ...))
(another-array (make-array ...)))
;fill myarray
(cublas-saxpy n -1.0 another-array 1 myarray 1)
(cufft-nocopy myarray n :forward t :normalize nil)
;use results
)
Check it out at https://github.com/knutgj/cl-cudalib
The specific functions are currently limited to what I have had use for, but it is trivial to extend to complete cuBLAS and cuFFT as well as roll your own CUDA libraries. Currently only SBCL is supported, but this should also be easy to extend.
I am considering to make a similar package for openCL and the AMD APPML.
For Clojure, fast matrix calculations using gpu, neanderthal and clojureCUDA by Dragan Djuric will bring it.
From the same author, clojurecl is for OpenGL.
For Tensors and Neural Networks deep-diamond.

Really minimum lisp

What is the minimum set of primitives required such that a language is Turing complete and a lisp variant?
Seems like car, cdr and some flow control and something for REPL is enough. It be nice if there is such list.
Assume there are only 3 types of data, integers, symbols and lists.(like in picolisp)
The lambda calculus is turing complete. It has one primitive - the lambda. Translating that to a lisp syntax is pretty trivial.
There's a good discussion of this in the Lisp FAQ. It depends on your choice of primitives. McCarthy's original "LISP 1.5 Programmer's Manual" did it with five functions: CAR, CDR, CONS, EQ, and ATOM.
I believe the minimum set is what John McCarthy published in the original paper.
The Roots of Lisp.
The code.
The best way to actually know this for sure is if you implement it. I used 3 summers to create Zozotez which is a McCarty-ish LISP running on Brainfuck.
I tried to find out what I needed and on a forum you'll find a thread that says You only need lambda. Thus, you can make a whole LISP in lambda calculus if you'd like. I found it interesting, but it's hardly the way to go if you want something that eventually has side effects and works in the real world.
For a Turing complete LISP I used Paul Grahams explanation of McCarthy's paper and all you really need is:
symbol-evaluation
special form quote
special form if (or cond)
special form lambda (similar to quote)
function eq
function atom
function cons
function car
function cdr
function-dispatch (basically apply but not actually exposed to the system so it handles a list where first element is a function)
Thats 10. In addition to this, to have a implementation that you can test and not just on a drawing board:
function read
function write
Thats 12. In my Zozotez I implemeted set and flambda (anonymous macroes, like lambda) as well. I could feed it a library implementing any dynamic bound lisp (Elisp, picoLisp) with the exception of file I/O (because the underlying BF does not support it other than stdin/stdout).
I recommend anyone to implement a LISP1-interpreter, in both LISP and (not LISP), to fully understand how a language is implemented. LISP has a very simple syntax so it's a good starting point. For all other programming languages how you implement an interpreter is very similar. Eg. in the SICP videos the wizards make an interpreter for a logical language, but the structure and how to implement it is very similar to a lisp interpreter even though this language is completely different than Lisp.

What makes Lisp macros so special?

Reading Paul Graham's essays on programming languages one would think that Lisp macros are the only way to go. As a busy developer, working on other platforms, I have not had the privilege of using Lisp macros. As someone who wants to understand the buzz, please explain what makes this feature so powerful.
Please also relate this to something I would understand from the worlds of Python, Java, C# or C development.
To give the short answer, macros are used for defining language syntax extensions to Common Lisp or Domain Specific Languages (DSLs). These languages are embedded right into the existing Lisp code. Now, the DSLs can have syntax similar to Lisp (like Peter Norvig's Prolog Interpreter for Common Lisp) or completely different (e.g. Infix Notation Math for Clojure).
Here is a more concrete example:Python has list comprehensions built into the language. This gives a simple syntax for a common case. The line
divisibleByTwo = [x for x in range(10) if x % 2 == 0]
yields a list containing all even numbers between 0 and 9. Back in the Python 1.5 days there was no such syntax; you'd use something more like this:
divisibleByTwo = []
for x in range( 10 ):
if x % 2 == 0:
divisibleByTwo.append( x )
These are both functionally equivalent. Let's invoke our suspension of disbelief and pretend Lisp has a very limited loop macro that just does iteration and no easy way to do the equivalent of list comprehensions.
In Lisp you could write the following. I should note this contrived example is picked to be identical to the Python code not a good example of Lisp code.
;; the following two functions just make equivalent of Python's range function
;; you can safely ignore them unless you are running this code
(defun range-helper (x)
(if (= x 0)
(list x)
(cons x (range-helper (- x 1)))))
(defun range (x)
(reverse (range-helper (- x 1))))
;; equivalent to the python example:
;; define a variable
(defvar divisibleByTwo nil)
;; loop from 0 upto and including 9
(loop for x in (range 10)
;; test for divisibility by two
if (= (mod x 2) 0)
;; append to the list
do (setq divisibleByTwo (append divisibleByTwo (list x))))
Before I go further, I should better explain what a macro is. It is a transformation performed on code by code. That is, a piece of code, read by the interpreter (or compiler), which takes in code as an argument, manipulates and the returns the result, which is then run in-place.
Of course that's a lot of typing and programmers are lazy. So we could define DSL for doing list comprehensions. In fact, we're using one macro already (the loop macro).
Lisp defines a couple of special syntax forms. The quote (') indicates the next token is a literal. The quasiquote or backtick (`) indicates the next token is a literal with escapes. Escapes are indicated by the comma operator. The literal '(1 2 3) is the equivalent of Python's [1, 2, 3]. You can assign it to another variable or use it in place. You can think of `(1 2 ,x) as the equivalent of Python's [1, 2, x] where x is a variable previously defined. This list notation is part of the magic that goes into macros. The second part is the Lisp reader which intelligently substitutes macros for code but that is best illustrated below:
So we can define a macro called lcomp (short for list comprehension). Its syntax will be exactly like the python that we used in the example [x for x in range(10) if x % 2 == 0] - (lcomp x for x in (range 10) if (= (% x 2) 0))
(defmacro lcomp (expression for var in list conditional conditional-test)
;; create a unique variable name for the result
(let ((result (gensym)))
;; the arguments are really code so we can substitute them
;; store nil in the unique variable name generated above
`(let ((,result nil))
;; var is a variable name
;; list is the list literal we are suppose to iterate over
(loop for ,var in ,list
;; conditional is if or unless
;; conditional-test is (= (mod x 2) 0) in our examples
,conditional ,conditional-test
;; and this is the action from the earlier lisp example
;; result = result + [x] in python
do (setq ,result (append ,result (list ,expression))))
;; return the result
,result)))
Now we can execute at the command line:
CL-USER> (lcomp x for x in (range 10) if (= (mod x 2) 0))
(0 2 4 6 8)
Pretty neat, huh? Now it doesn't stop there. You have a mechanism, or a paintbrush, if you like. You can have any syntax you could possibly want. Like Python or C#'s with syntax. Or .NET's LINQ syntax. In end, this is what attracts people to Lisp - ultimate flexibility.
You will find a comprehensive debate around lisp macro here.
An interesting subset of that article:
In most programming languages, syntax is complex. Macros have to take apart program syntax, analyze it, and reassemble it. They do not have access to the program's parser, so they have to depend on heuristics and best-guesses. Sometimes their cut-rate analysis is wrong, and then they break.
But Lisp is different. Lisp macros do have access to the parser, and it is a really simple parser. A Lisp macro is not handed a string, but a preparsed piece of source code in the form of a list, because the source of a Lisp program is not a string; it is a list. And Lisp programs are really good at taking apart lists and putting them back together. They do this reliably, every day.
Here is an extended example. Lisp has a macro, called "setf", that performs assignment. The simplest form of setf is
(setf x whatever)
which sets the value of the symbol "x" to the value of the expression "whatever".
Lisp also has lists; you can use the "car" and "cdr" functions to get the first element of a list or the rest of the list, respectively.
Now what if you want to replace the first element of a list with a new value? There is a standard function for doing that, and incredibly, its name is even worse than "car". It is "rplaca". But you do not have to remember "rplaca", because you can write
(setf (car somelist) whatever)
to set the car of somelist.
What is really happening here is that "setf" is a macro. At compile time, it examines its arguments, and it sees that the first one has the form (car SOMETHING). It says to itself "Oh, the programmer is trying to set the car of somthing. The function to use for that is 'rplaca'." And it quietly rewrites the code in place to:
(rplaca somelist whatever)
Common Lisp macros essentially extend the "syntactic primitives" of your code.
For example, in C, the switch/case construct only works with integral types and if you want to use it for floats or strings, you are left with nested if statements and explicit comparisons. There's also no way you can write a C macro to do the job for you.
But, since a lisp macro is (essentially) a lisp program that takes snippets of code as input and returns code to replace the "invocation" of the macro, you can extend your "primitives" repertoire as far as you want, usually ending up with a more readable program.
To do the same in C, you would have to write a custom pre-processor that eats your initial (not-quite-C) source and spits out something that a C compiler can understand. It's not a wrong way to go about it, but it's not necessarily the easiest.
Lisp macros allow you to decide when (if at all) any part or expression will be evaluated. To put a simple example, think of C's:
expr1 && expr2 && expr3 ...
What this says is: Evaluate expr1, and, should it be true, evaluate expr2, etc.
Now try to make this && into a function... thats right, you can't. Calling something like:
and(expr1, expr2, expr3)
Will evaluate all three exprs before yielding an answer regardless of whether expr1 was false!
With lisp macros you can code something like:
(defmacro && (expr1 &rest exprs)
`(if ,expr1 ;` Warning: I have not tested
(&& ,#exprs) ; this and might be wrong!
nil))
now you have an &&, which you can call just like a function and it won't evaluate any forms you pass to it unless they are all true.
To see how this is useful, contrast:
(&& (very-cheap-operation)
(very-expensive-operation)
(operation-with-serious-side-effects))
and:
and(very_cheap_operation(),
very_expensive_operation(),
operation_with_serious_side_effects());
Other things you can do with macros are creating new keywords and/or mini-languages (check out the (loop ...) macro for an example), integrating other languages into lisp, for example, you could write a macro that lets you say something like:
(setvar *rows* (sql select count(*)
from some-table
where column1 = "Yes"
and column2 like "some%string%")
And thats not even getting into Reader macros.
Hope this helps.
I don't think I've ever seen Lisp macros explained better than by this fellow: http://www.defmacro.org/ramblings/lisp.html
A lisp macro takes a program fragment as input. This program fragment is represented a data structure which can be manipulated and transformed any way you like. In the end the macro outputs another program fragment, and this fragment is what is executed at runtime.
C# does not have a macro facility, however an equivalent would be if the compiler parsed the code into a CodeDOM-tree, and passed that to a method, which transformed this into another CodeDOM, which is then compiled into IL.
This could be used to implement "sugar" syntax like the for each-statement using-clause, linq select-expressions and so on, as macros that transforms into the underlying code.
If Java had macros, you could implement Linq syntax in Java, without needing Sun to change the base language.
Here is pseudo-code for how a lisp-style macro in C# for implementing using could look:
define macro "using":
using ($type $varname = $expression) $block
into:
$type $varname;
try {
$varname = $expression;
$block;
} finally {
$varname.Dispose();
}
Since the existing answers give good concrete examples explaining what macros achieve and how, perhaps it'd help to collect together some of the thoughts on why the macro facility is a significant gain in relation to other languages; first from these answers, then a great one from elsewhere:
... in C, you would have to write a custom pre-processor [which would probably qualify as a sufficiently complicated C program] ...
—Vatine
Talk to anyone that's mastered C++ and ask them how long they spent learning all the template fudgery they need to do template metaprogramming [which is still not as powerful].
—Matt Curtis
... in Java you have to hack your way with bytecode weaving, although some frameworks like AspectJ allows you to do this using a different approach, it's fundamentally a hack.
—Miguel Ping
DOLIST is similar to Perl's foreach or Python's for. Java added a similar kind of loop construct with the "enhanced" for loop in Java 1.5, as part of JSR-201. Notice what a difference macros make. A Lisp programmer who notices a common pattern in their code can write a macro to give themselves a source-level abstraction of that pattern. A Java programmer who notices the same pattern has to convince Sun that this particular abstraction is worth adding to the language. Then Sun has to publish a JSR and convene an industry-wide "expert group" to hash everything out. That process--according to Sun--takes an average of 18 months. After that, the compiler writers all have to go upgrade their compilers to support the new feature. And even once the Java programmer's favorite compiler supports the new version of Java, they probably ''still'' can't use the new feature until they're allowed to break source compatibility with older versions of Java. So an annoyance that Common Lisp programmers can resolve for themselves within five minutes plagues Java programmers for years.
—Peter Seibel, in "Practical Common Lisp"
Think of what you can do in C or C++ with macros and templates. They're very useful tools for managing repetitive code, but they're limited in quite severe ways.
Limited macro/template syntax restricts their use. For example, you can't write a template which expands to something other than a class or a function. Macros and templates can't easily maintain internal data.
The complex, very irregular syntax of C and C++ makes it difficult to write very general macros.
Lisp and Lisp macros solve these problems.
Lisp macros are written in Lisp. You have the full power of Lisp to write the macro.
Lisp has a very regular syntax.
Talk to anyone that's mastered C++ and ask them how long they spent learning all the template fudgery they need to do template metaprogramming. Or all the crazy tricks in (excellent) books like Modern C++ Design, which are still tough to debug and (in practice) non-portable between real-world compilers even though the language has been standardised for a decade. All of that melts away if the langauge you use for metaprogramming is the same language you use for programming!
I'm not sure I can add some insight to everyone's (excellent) posts, but...
Lisp macros work great because of the Lisp syntax nature.
Lisp is an extremely regular language (think of everything is a list); macros enables you to treat data and code as the same (no string parsing or other hacks are needed to modify lisp expressions). You combine these two features and you have a very clean way to modify code.
Edit: What I was trying to say is that Lisp is homoiconic, which means that the data structure for a lisp program is written in lisp itself.
So, you end up with a way of creating your own code generator on top of the language using the language itself with all its power (eg. in Java you have to hack your way with bytecode weaving, although some frameworks like AspectJ allows you to do this using a different approach, it's fundamentally a hack).
In practice, with macros you end up building your own mini-language on top of lisp, without the need to learn additional languages or tooling, and with using the full power of the language itself.
Lisp macros represents a pattern that occurs in almost any sizeable programming project. Eventually in a large program you have a certain section of code where you realize it would be simpler and less error prone for you to write a program that outputs source code as text which you can then just paste in.
In Python objects have two methods __repr__ and __str__. __str__ is simply the human readable representation. __repr__ returns a representation that is valid Python code, which is to say, something that can be entered into the interpreter as valid Python. This way you can create little snippets of Python that generate valid code that can be pasted into your actually source.
In Lisp this whole process has been formalized by the macro system. Sure it enables you to create extensions to the syntax and do all sorts of fancy things, but it's actual usefulness is summed up by the above. Of course it helps that the Lisp macro system allows you to manipulate these "snippets" with the full power of the entire language.
In short, macros are transformations of code. They allow to introduce many new syntax constructs. E.g., consider LINQ in C#. In lisp, there are similar language extensions that are implemented by macros (e.g., built-in loop construct, iterate). Macros significantly decrease code duplication. Macros allow embedding «little languages» (e.g., where in c#/java one would use xml to configure, in lisp the same thing can be achieved with macros). Macros may hide difficulties of using libraries usage.
E.g., in lisp you can write
(iter (for (id name) in-clsql-query "select id, name from users" on-database *users-database*)
(format t "User with ID of ~A has name ~A.~%" id name))
and this hides all the database stuff (transactions, proper connection closing, fetching data, etc.) whereas in C# this requires creating SqlConnections, SqlCommands, adding SqlParameters to SqlCommands, looping on SqlDataReaders, properly closing them.
While the above all explains what macros are and even have cool examples, I think the key difference between a macro and a normal function is that LISP evaluates all the parameters first before calling the function. With a macro it's the reverse, LISP passes the parameters unevaluated to the macro. For example, if you pass (+ 1 2) to a function, the function will receive the value 3. If you pass this to a macro, it will receive a List( + 1 2). This can be used to do all kinds of incredibly useful stuff.
Adding a new control structure, e.g. loop or the deconstruction of a list
Measure the time it takes to execute a function passed in. With a function the parameter would be evaluated before control is passed to the function. With the macro, you can splice your code between the start and stop of your stopwatch. The below has the exact same code in a macro and a function and the output is very different. Note: This is a contrived example and the implementation was chosen so that it is identical to better highlight the difference.
(defmacro working-timer (b)
(let (
(start (get-universal-time))
(result (eval b))) ;; not splicing here to keep stuff simple
((- (get-universal-time) start))))
(defun my-broken-timer (b)
(let (
(start (get-universal-time))
(result (eval b))) ;; doesn't even need eval
((- (get-universal-time) start))))
(working-timer (sleep 10)) => 10
(broken-timer (sleep 10)) => 0
One-liner answer:
Minimal syntax => Macros over Expressions => Conciseness => Abstraction => Power
Lisp macros do nothing more than writing codes programmatically. That is, after expanding the macros, you got nothing more than Lisp code without macros. So, in principle, they achieve nothing new.
However, they differ from macros in other programming languages in that they write codes on the level of expressions, whereas others' macros write codes on the level of strings. This is unique to lisp thanks to their parenthesis; or put more precisely, their minimal syntax which is possible thanks to their parentheses.
As shown in many examples in this thread, and also Paul Graham's On Lisp, lisp macros can then be a tool to make your code much more concise. When conciseness reaches a point, it offers new levels of abstractions for codes to be much cleaner. Going back to the first point again, in principle they do not offer anything new, but that's like saying since paper and pencils (almost) form a Turing machine, we do not need an actual computer.
If one knows some math, think about why functors and natural transformations are useful ideas. In principle, they do not offer anything new. However by expanding what they are into lower-level math you'll see that a combination of a few simple ideas (in terms of category theory) could take 10 pages to be written down. Which one do you prefer?
I got this from the common lisp cookbook and I think it explained why lisp macros are useful.
"A macro is an ordinary piece of Lisp code that operates on another piece of putative Lisp code, translating it into (a version closer to) executable Lisp. That may sound a bit complicated, so let's give a simple example. Suppose you want a version of setq that sets two variables to the same value. So if you write
(setq2 x y (+ z 3))
when z=8 both x and y are set to 11. (I can't think of any use for this, but it's just an example.)
It should be obvious that we can't define setq2 as a function. If x=50 and y=-5, this function would receive the values 50, -5, and 11; it would have no knowledge of what variables were supposed to be set. What we really want to say is, When you (the Lisp system) see (setq2 v1 v2 e), treat it as equivalent to (progn (setq v1 e) (setq v2 e)). Actually, this isn't quite right, but it will do for now. A macro allows us to do precisely this, by specifying a program for transforming the input pattern (setq2 v1 v2 e)" into the output pattern (progn ...)."
If you thought this was nice you can keep on reading here:
http://cl-cookbook.sourceforge.net/macros.html
In python you have decorators, you basically have a function that takes another function as input. You can do what ever you want: call the function, do something else, wrap the function call in a resource acquire release, etc. but you don't get to peek inside that function. Say we wanted to make it more powerful, say your decorator received the code of the function as a list then you could not only execute the function as is but you can now execute parts of it, reorder lines of the function etc.