LISP vs WolframLang

By Xah Lee. Date: . Last updated: .

The major influence of WolframLang is LISP and APL. [see LISP/APL Root in Mathematica / Wolfram Language]

WolframLang has all the characteristics of LISP:

Here's a table of comparison of LISP and WolframLang, for easy learning WolframLang.

lispWolfram Lang
(f a b c) f[a, b, c]
; comment (* comment *)
lispWolfram Lang
print Print
lispWolfram Lang
+ Plus
- Minus
* Times
/ Divide
% Mod
expt Power
floor Floor
ceiling Ceiling
round Round
lispWolfram Lang
t True
nil False Null
and And
or Or
not Not
> Greater
>= GreaterEqual
< Less
<= LessEqual
=, eq, equal, string-equal Equal, SameQ WolframLang: Equality Test
lispWolfram Lang
set, setq Set WolframLang: Set and SetDelayed
lispWolfram Lang
let, let* Module, Block, With. WolframLang: Local Variable
Flow Control
lispWolfram Lang
if If WolframLang: If Then Else (Conditionals, Branching)
cond Which, Switch. WolframLang: Which, Switch
throw catch Throw Catch
error Abort
Loop, Iteration
lispWolfram Lang
while While WolframLang: Loop
mapcar Map WolframLang: Map Function to List
mapc Scan
dotimes Do
Data Structure
lispWolfram Lang
cons there's no cons in WolframLang. use List[a,b] if you want. WolframLang List is LISP's vector.
list, vector List WolframLang: List
association list, hash table WolframLang: Association (Key Value Pairs)
lispWolfram Lang
defun, lambda Function WolframLang: Define Function
defmacro SetDelayed WolframLang: Set and SetDelayed
funcall, apply Apply
lispWolfram Lang
lispWolfram language
progn CompoundExpression WolframLang: CompoundExpression and Semicolon
Reader Macro / evaluation control
lispWolfram language
quote or ' ` Hold HoldComplete
“unquote” ,

Reader Macro, vs WolframLang Short Syntax

now, all those LISP quote, backtick, dot, comma, comma at, are implemented by what's called “reader macros”.

a “Reader”, exists in all LISPs, in emacs lisp, common lisp, scheme lisp, clojure lisp. (also in WolframLang, called Read).

Reader is part of lisp compiler that is called as the first thing, to transform what user typed into a lisp list syntax (aka “real lisp syntax”).

Now in every language, what you typed, a valid source code, is called the lang's syntax. In lisp, the lisp fanatics, call lisp source code as “surface syntax”. After the lisp reader did the syntactical transformation, the lisp fanatics call that the real lisp syntax. This lisp idiocy generates lots of confusion.

you have hard to understand problem like this

(setq xxa (list 'a 'b))
(setq xxb (list 'a . ('b)))
(equal xxa xxb)
;; t
(equal (cons 'a 'b)
       '(a . b))
;; t

(equal (cons 'a 'b)
       (quote (a . b)))
;; t

 '(("a" . aa)
   ("b" . bb))
  (cons "a" 'aa)
  (cons "b" 'bb)))
;; t

(equal (cons 'a 'b)
        '('a . 'b))
;; nil

so but why is lisp no have some functional form for some of the “syntactic shortcuts” such as backtick or # or comma or comma at? well, simply put, bad design. Again, the lisp reader transform them, and if the end result has the form (f x y z etc) , then it's fine, lisp fanatics see no need to have a (f x y z etc) to stand for the short syntaxes.

this problem, gets deep. it is very hard to understand the effect of quote, etc or see exactly which are syntactical equivalences. The whole thing, is part of the complexity of evaluation.

by the way, the complexity of evaluation of WolframLang is not better. You have Hold, HoldForm, ReleaseHold, HoldAll, HoldAllComplete, Evaluate, Unevaluated, Activate, Inactivate, etc.

Lisp Macro

so far, we have not mentioned lisp macros. lisp macro is a lang feature that allow user to control evaluation, and effectively, create syntactical transformation ( but this syntactical transformation, is not powerful enough to get out of the nested parenthesis syntax).

builtin macros (such as if, while ), are called special forms in lisp.

[see also Fundamental Problems of Lisp]

Lisp Macros is Beginning of Term Rewriting System

in WolframLang, the whole language, entire evaluation strategy, can be considered as lisp macros. More properly called, term rewriting system.

In essence, how WolframLang works, is that source code is just a sequence of Symbols and operators. Evaluation is done by just continuously doing syntactical transformation, to end up with a different sequence of symbols, which we take as the result.

The syntactical transformation, follow by “transformation rules”, either builtin, or user defined. (this part is analogous to lisp macros). this syntactical transformation continues until no more rule applies. (that is, no pattern matches)

Function Memoization (Function that Cache Values)

by the way, the way this works is that assignment returns a value. a = b returs b. and, = has higher stickiness than := , so

f[x_] := f[x] = expensive[x] is f[x_] := (f[x] = expensive[x])

then, more specific pattern matching transformation is done before more general one. so, if WolframLang sees f[3], and if there's already a rule for f[3] , it becomes value of expensive[x] right away. But if there is no rule for f[3] , the delayed transformation rule f[x_] kicks in, so it get replaced by f[x] = expensive[x]

it's important to note, a = b FullForm is Set[a,b]. Which means, create a rule, so whever a occure, replace it by b.

and a := b FullForm is SetDelayed[a,b]. Which means, create a rule, so whever a occur, replace it by b, but eval b only at the time of replacement.

WolframLang History and Lisp