Can anyone well versed in lisp explain this joke to me?
I've done some reading on functional programming languages and know that CAR/CDR mean Contents of Address/Decrement Register but I still don't really understand the humour.
In Lisp, a linked list element is called a CONS. It is a data structure with two elements, called the CAR and the CDR for historical reasons. (Some Common Lisp programmers prefer to refer to them using the FIRST and REST functions, while others like CAR and CDR because they fit well with the precomposed versions such as (CADR x) ≡ (CAR (CDR x)).
The joke is a parody of the bumper stickers you sometimes see on beat-up old cars saying "My other car is a Porsche/BMW/etc."
My response to this joke has always been "My other CAR is a CADR. CDR isn't a CAR at all."
Yes, definitely a geek joke.
The names come from the IBM 704, but that's not the joke.
The joke is (bad) pun on "my other car is a ___." But the in-joke is about recursion.
When you loop/manipulate/select/invoke/more in lisp you use a combination of car (the first element in the list) and cdr (the rest of the list) to juggle functions.
So you've got a car, but your other car is your cdr because you can always get a car from a cdr since the cdr is always (in recursion) more elements. Get it? Laugh yet?
You'll probably have to learn lisp to actually chuckle a bit, or not. Of course, by then, you'll probably find yourself chuckling randomly for no apparent reason because:
Lisp makes you loopy.
//Coming from Scheme
Scheme has very few data structures, one of them is a tuple: '(first . second). In this case, car is the first element, and cdr is the second. This construct can be extended to create lists, trees, and other structures.
The joke isn't very funny.
Related
All Lisp developers seem to know what an S-Expression is. But can anybody explain this for non Lisp developers?
There is already a Wikipedia entry (https://en.wikipedia.org/wiki/S-expression). But that is not really helpful if you don't want to go deeply into detail.
What is an S-Expression? What can I express with an S-Expression? For what purpose uses Lisp normally S-Expressions? Are S-Expressions only relevant for Lisp developers?
The term S-expression refers to the printed form(s) of a Lisp object. For instance, the integer zero object can appear as a written S-expression like 0, 000, or #x0. The text (0 . 1) is the S-expression denoting a cons cell object whose fields are the integers zero and one. In Common Lisp, under the default read table, the tokens Foo, fOO, FOO, |FOO| and foo, are all S-expressions denoting the same symbol. They are different read syntax, equivalent through their semantics of denoting the same object.
Why don't we just call those things expressions? Firstly, there are times when we do, when it is clear from the context that we are speaking about character syntax.
The term expression is ambiguous for that reason: it can sometimes refer to a textual, printed expression that, for instance, someone typed into a text file or interactive listener. Most of the time, expression refers to a Lisp object in memory representing code.
We could say printed expression instead of S-expression, but the term is historically entrenched, dating back to a time when Lisp also had M-expressions. Plus, printed expression would only have the same meaning as S-expression when we know we are already talking about nothing but Lisp. The term S-expression in a context outside of Lisp means something like "one of the printed object notations coming from the Lisp family, with symbols written without quotes, and nested lists with parentheses in which items are separated by only whitespace."
Note that the ANSI Common Lisp standard doesn't use the terms S-expression or symbolic expression. No such terms appear in the Glossary, only expression, which is defined like this:
expression n. 1. an object, often used to emphasize the use of the object to encode or represent information in a specialized format, such as program text. "The second expression in a let form is a list of bindings." 2. the textual notation used to notate an object in a source file. "The expression 'sample is equivalent to (quote sample)."
S-expression is more or less the (2) meaning, with historic ties and a broader interpretation outside of any one Lisp dialect. For instance, Ron Rivest, perhaps best known as one of the authors of the RSA cryptosystem. wrote an Internet Draft describing a form of S-expressions for data exchange.
An S-expression is the fundamental unit of storage in Lisp. By the original definition, an S-expression is one of two things.
An atom, or
a cons cell
An atom is the base case. In classical Lisp (the original language proposed by John McCarthy), an atom is just a distinct unit, that we conventionally designate with a name. Conceptually, you can think of it as a string, even though that's not how any modern Lisp would store it internally. So foobar is an atom, and so is potato. They're just strings that are atomic, in the sense that they don't recursively contain any more S-expressions.
Note that modern Lisp dialects extend the definition of "atom" to include things like numbers, so in Common Lisp, 1.0 would be a valid atom which represents a number.
A cons cell is the fundamental unit of composition in Lisp. A cons cell is a structure that points to two other S-expressions. We call the first of these S-expressions the car and the second the cdr. These names are archaic and were originally references to how cons cells were stored on old computers, but Lisp programmers today still use them. You'll hear some people refer to the car as the "first" or "head", and you'll hear some people refer to the cdr as the "tail" or "rest". (Try not to refer to the cdr as the "second" term, as that's ambiguous and could be interpreted as something else, which we'll talk about in a minute)
Now, we write cons cells in parentheses with a dot between them. So a cons cell where the car and cdr are both atoms would look like
(foo . bar)
This is a cons cell whose car is the atom foo and whose cdr is the atom bar. We can also nest cons cells.
((foo . bar) . (baz . potato))
And then we end up with a sort of binary-tree-like structure, where each branch has a left and a right (a car and a cdr, in our terminology), and each leaf is an atom.
So what can we do with this? Well, for one, we can store linked lists. There are several ways to do this, but the prevailing convention in the Lisp community is to use the car to store the current value and the cdr to store the cons cell pointing to the rest of the list. Then, when we reach the end of the list (where we might store a null pointer if we were doing this in C or Java), we pick out a particular atom, called NIL. There's nothing special about the NIL atom in the definition above; we just picked one out because we needed one to use as a convention.
So to represent the list [a, b, c, d], we would store it as
(a . (b . (c . (d . NIL))))
The car of the outermost cons cell is the first element of the list, or a. The cdr stores the rest of the list. The car of the cdr is the second element, b, and so on. (This is why I said not to call the cdr the "second" element, as "second" is often used to mean "car of cdr")
In fact, we do this so often that there's another notational convention in Lisp. If the cdr is another cons cell, then we simply drop the . and the parentheses and understand what it means. So, in general, we say that the following two are equivalent, for any S-expressions a, b, and c.
(a . (b . c)) === (a b . c)
Again, I haven't changed the definition. There's still only two valid S-expressions: atoms and cons cells. I've just invented a more compact way to write them.
Likewise, since we're going to be using NIL a lot to end lists, we simply drop it. If we have a NIL as the cdr of a cons cell, then by convention we remove the . and the NIL. So the following are equivalent for any S-expression a.
(a . NIL) === (a)
Again, I'm just inventing new, compact ways to write things, not changing the definitions.
Finally, as a notational convenience, we might sometimes write the atom NIL as a pair of empty parentheses, since it's supposed to look like the empty list.
NIL === ()
Now, looking at our list from earlier
(a . (b . (c . (d . NIL))))
we can use these rules to simplify it
(a . (b . (c . (d . NIL))))
(a b . (c . (d . NIL)))
(a b c . (d . NIL))
(a b c d . NIL)
(a b c d)
And now this looks remarkably like Lisp syntax. And that's the beauty of S-expressions. The Lisp code you're writing is just a bunch of S-expressions. For example, consider the following Lisp code
(mapcar (lambda (x) (+ x 1)) my-list)
This is ordinary Lisp code, the kind you would see in any everyday program. In Common Lisp, it adds one to each element of my-list. But the beauty is that it's just a big S-expression. If we remove all of the syntax sugar, we get
(mapcar . ((lambda . ((x . NIL) . ((+ . (x . (1 . NIL))) . NIL))) . (my-list . NIL)))
Not pretty, at least aesthetically, but now it's easier to see how this really is just a bunch of cons cells terminated in atoms. Your entire Lisp syntax tree is just that: a binary tree full of code. And you can manipulate it as such. You can write macros that take this tree, as a data structure, and do whatever on earth they want with it. The abstract syntax tree of your Lisp program isn't some opaque construct internal to the language; it's just a tree: an incredibly simple data structure that you already use in everyday programming anyway. The same lists and other structures that you use to store data in your Lisp program are also used to store code.
Modern Lisp dialects extend this with new conventions and, in some cases, new data types. Common Lisp, for instance, adds an array type, so #(1 2 3 4 5) is an array of five elements. It's not a linked list (since, in practice, linked lists are slow for random access), it's something else entirely. Likewise, Lisp dialects add new conventions on top of the NIL ones we've already discussed. In most Lisp dialects, the apostrophe, or single quote, is used to represent a call to the quote special form. That is,
'x === (quote x) (quote . (x . NIL))
For any S-expression x. Different dialects add different features to the original McCarthy definition, but the core concept is: What is the absolute minimum definition we need to be able to comfortably store the code and data of our Lisp program.
The other answers are very Lisp-specific, but actually S-expressions are useful outside of the Lisp world.
An S-expression is a (convenient) way of representing a tree whose leaf are symbols (names, strings, call them how you like). Each parenthesized part of an S-expression is a node, containing exactly the list of its children.
Example: (this (s expression) (could (be represented)) as (this tree))
[..........]
/| | | |
/ . | as .
/ / \ | / \
/ s | . this |
this | |\ tree
| | \
expression | \
could .
|\
be represented
In Lisp, the tree represented by S-expression corresponds to the Concrete Syntax Tree, which is why Lisp is so easy to parse.
However, since this representation of trees is convenient (it's relatively compact, it's very human-friendly and it's straightforward both to parse and to produce for a machine), it's also used in other contexts. For instance, Ocaml's Core library (which is an alternative standard library for that language) provides serialization and deserialization as S-expressions.
Besides this, Lisp also names some of its data structures S-expressions. This goes well with Lisp's homoiconicity, that is, the fact that the code can be manipulated pretty much like data.
So, to answer your questions:
S-expressions are both a syntactic way to represent trees and a tree data structure in Lisp.
With S-expressions you can express trees; the meaning you attach to the tree (its interpretation, if you will) is not specific to S-expressions. S-expression tell you how to write a tree, not what it means — and, in fact, people use them for different purposes, with different meanings.
Lisp uses S-expressions both to represent its own source code, to print values and as a data structure, recursively built from nil and cons (the exact details of all of this vary a lot between all the Lisp dialects).
S-expressions are not only relevant for Lisp developers, see for example the Ocaml serializing / deserializing library Sexp. In practice, other ways of representing data that have stronger typing are more commonly used where S-expressions could be used, such as JSON.
s-expressions are short for Symbolic Expressions.
Basically they are Symbols and nested lists of Symbols.
A Symbol is made of alphanumeric characters.
Examples for symbols and nested lists of symbols:
foo
berlin
fruit
de32211
(apple peach)
(fruit (seller fruit-co))
((apple one) (peach two))
these lists were made of cons cells written as (one . two) and nil as the empty list.
Examples:
(a . (b . nil)) -> (a b)
((a . nil) (b . nil)) -> ((a) (b))
The programming language Lisp (short for List Processor) was designed to process these lists. Lisp contains all kinds of basic operations dealing with nested lists. There the elements of s-expressions can also be numbers, characters, strings, arrays and other data structures.
Symbolic Expressions have the same purpose as JSON and XML: they encode data.
Symbolic Expressions in Lisp also have the purpose to encode Lisp programs themselves.
Example:
((lambda (a b)
(+ a (* 2 b)))
10
20)
Above is both an s-expression and a valid Common Lisp / Scheme program.
Symbolics Expressions were thought to be an universal notation for humans and machines to read/write/process all kinds of data in some calculus.
For example s-expressions could encode a mathematical formula, a Lisp program, a logic expression or data about the configuration of a planning problem. What was missing at the time was a way to describe declaratively valid data schema. s-expressions were typically processed and validated procedural.
How are s-expressions used in Lisp?
for encoding source code
for all kinds of data
mixed source code and data
Are S-Expressions only relevant for Lisp developers?
Mostly, but sometimes code or data exists in the form of s-expressions and programs written in other languages than Lisp want to process this data. Sometimes even developer not using Lisp are choosing s-expressions as a data representation format.
Generally the usage of s-expresssions outside of Lisp is rare. Still, there are a few examples. XML and JSON got much more popular than s-expressions.
In Lisps that have vectors, why are cons cells still necessary? As I understand it, a cons cell is:
A structure with exactly 2 elements
Ordered
Access is O(1)
All these also apply to a 2-vector, though. So what's the difference? Are cons cells just a vestige from before Lisps had vectors? Or are there other differences I'm unaware of?
Although, physically, conses resemble any other two-element aggregate structure, they are not simply an obsolete form of a 2-vector.
Firstly, all types in Lisp are partitioned into cons and atom. Only conses are of type cons; everything else is an atom. A vector is an atom!
Conses form the representational basis for nested lists, which of course are used to write code. They have a special printed notation, such that the object produced by (cons 1 (cons 2 nil)) conveniently prints as (1 2) and the object produced by (cons 1 (cons 2 3)) prints as (1 2 . 3).
The cons versus atom distinction is important in the syntax, because an expression which satisfies the consp test is treated as a compound form. Whereas atoms that are not keyword symbols, t or nil evaluate to themselves.
To get the list itself instead of the value of the compound form, we use quote, for which we have a nice shorthand.
It's useful to have a vector type which is free from being entangled into the evaluation semantics this way: whose instances are just self-evaluating atoms.
Cons cells are not a vestige from before Lisps had vectors. Firstly, there was almost no such a time. The Lisp 1 manual from 1960 already describes arrays. Secondly, new dialects since then still have conses.
Objects that have a similar representation are not simply redundant for each other. Type distinctions are important. For instance, we would not consider the following two to be redundant for each other just because they both have three slots:
(defstruct name first initial last)
(defstruct bank-transaction account type amount)
In the TXR Lisp dialect, I once had it so that the syntactic sugar a..b denoted (cons a b) for ranges. But this meant that ranges were consp, which was silly due to the ambiguity against lists. I eventually changed it so that a..b denotes (rcons a b): a form which constructs a range object, which prints as #R(x y). (and can be specified that way as a literal). This creates a useful nuance because we can distinguish whether a function argument is a range (rangep) or a list (consp). Just like we care whether some object is a bank-transaction or name. Range objects are represented exactly like conses and allocated from the same heaps; just they have a different type which makes them atoms. If evaluated as forms, they evaluate to themselves.
Basically, we must regard type as if it were an extra slot. A two-element vector really has (at least) three properties, not just two: it has a first element, a second element and a type. The vector #(1 1) differs from the cons cell (1 . 1) in that they both have this third aspect, type, which is not the same.
The immutable properties of an object which it shares with all other objects of its kind can still be regarded as "slots". Effectively, all objects have a "type slot". So conses are actually three-property objects having a car, cdr and type:
(car '(a . b)) -> A
(cdr '(a . b)) -> B
(type-of '(a . b)) -> CONS
Her is a fourth "slot":
(class-of '(a . b)) -> #<BUILT-IN-CLASS CONS>
We can't look at objects in terms of just their per-instance storage vector allocated on the heap.
By the way, the 1960's MacLisp dialect extended the concept of a cons into fixed-size aggregate objects that had more named fields (in addition to car and cdr): the cxr-s. These objects were called "hunks" and are documented in Kent Pitman's MacLisp manual. Hunks do not satisify the predicate consp, but hunkp; i.e. they are considered atoms. However, they extend the cons notation with multiple dots.
In a typical Common Lisp implementation, a cons cell will be represented as "two machine words" (one for the car pointer, one for the cdr pointer; the fact that it's a cons cell is encoded in the pointer constructed to reference it). However, arrays are more complicated object and unless you have a dedicated "two-element-only vector of type T", you'd end up with an array header, containing type information and size, in addition to the storage needed to store elements (probably hard to squeeze to less than "four machine words").
So while it would be eminently possible to use two-element vectors/arrays as cons cells, there's some efficiency to be had by using a dedicated type, based on the fact that cons cells and lists are so frequently used in existing Lisp code.
I think that their are different data structures, for example java has vector and list classes. One is suitable for random access and lists are more suitable for sequential access. So in any language vectors and list can coexists.
For implementing a Lisp using your approach, I believe that it is posible, it depends on your implementations details but for ANSI Common Lisp there is a convention because there is not a list datatype:
CL-USER> (type-of (list 1 2 3))
CONS
This is a CONS and the convention says something similar to this (looking at the common lisp hypersec):
list n.
1. a chain of conses in which the car of each cons is an element of the list, and the cdr of each cons is either the next link in the
chain or a terminating atom. See also proper list, dotted list, or
circular list.
2. the type that is the union of null and cons.
So if you create a Lisp using vectors instead of cons, it will be not the ANSI CL
so you can create lists "consing" things, nil is a list and there are diferrent types of list that you can create with consing:
normally you create a proper list:
(list 1 2 3) = (cons 1 (cons 2 (cons 3 nil)))) = '(1 2 3)
when the list does not end with nil it is a dotted list, and a circular list has a reference to itself
So for example if we create a string common lisp, implements it as a simple-array, which is faster for random acces than a list
CL-USER> (type-of "this is a string")
(SIMPLE-ARRAY CHARACTER (16))
Land of lisp (a great book about common lisp) define cons as the glue for building common lisp, and for processing lists, so of course if you replace cons with other thing similar you will build something similar to common lisp.
Finally a tree of the common lisp sequences types, you can find here the complete
Are cons cells just a vestige from before Lisps had vectors?
Exactly. cons, car, cdr were the constructor and accessors of the only compound data structure in the first lisp. To differentiate it with the only atomic type symbols one had atom that were T for symbols but false for cons. This was extended to other types in Lisp 1.5 including vectors (called arrays, see page 35). Common Lisp were a combination of commercial lisps that all built upon lisp 1.5. Perhaps they would have been different if both types were made from the beginning.
If you were to make a Common Lisp implementation you don't need to have two different ways to make them as long as your implementation works according to the spec. If I remember correctly I think racket actually implements struct with vector and vector? is overloaded to be #f for the vectors that are indeed representing an object. In CL you could implement defstruct the same way and implement cons struct and the functions it needs to be compatible with the hyperspec. You might be using vectors when you create cons in your favorite implementation without even knowing it.
Historically you still have the old functions so that John McCarthy code still works even 58 years after the first lisp. It didn't need to but it doesn't hurt to have a little legacy in a language that had features modern languages are getting today.
If you used two-element vectors you would store their size (and type) in every node of the list.
This is ridiculously wasteful.
You can get around this wastefulness by introducing a special 2-element vector type whose elements can be anything.
Or in other words: by re-introducing the cons cell.
On one hand this is an "implementation detail": given vectors, one can implement cons cells (and thus linked lists) using vectors of length 2.
On the other hand this is a fairly important detail: the ANSI Common Lisp standard specifies that the types vector and cons are disjoint, so, in fact, you cannot use the trick to implement an ANSI CL.
I'm trying to emulate Lisp-like list in JavaScript (just an exercise with no practical reason), but I'm struggling to figure out how to best represent an empty list.
Is an empty list just a nil value or is it under the hood stored in a cons cell?
I can:
(car '())
NIL
(cdr '())
NIL
but an empty list for sure can not be (cons nil nil), because it would be indistinguishable from a list storing a single nil. It would need to store some other special value.
On the other hand, if an empty list is not built from a cons cell, it seems impossible to have a consistent high-level interface for appending a single value to an existing list. A function like:
(defun append-value (list value) ...
Would modify its argument, but only if it is not an empty list, which seems ugly.
Believe it or not, this is actually a religious question.
There are dialects that people dare to refer to as some kind of Lisp in which empty lists are conses or aggregate objects of some kind, rather than just an atom like nil.
For example, in "MatzLisp" (better known as Ruby) lists are actually arrays.
In NewLisp, lists are containers: objects of list type which contain a linked list of the items, so empty lists are empty containers. [Reference].
In Lisp languages that aren't spectacular cluster-fumbles of this sort, empty lists are atoms, and non-empty lists are binary cells with a field which holds the first item, and another field that holds the rest of the list. Lists can share suffixes. Given a list like (1 2 3) we can use cons to create (a 1 2 3) and (b c 1 2 3) both of which share the storage for (1 2 3).
(In ANSI Common Lisp, the empty list atom () is the same object as the symbol nil, which evaluates to itself and also serves as Boolean false. In Scheme, () isn't a symbol, and is distinct from the Boolean false #f object. However Scheme lists are still made up of pairs, and terminated by an atom.)
The ability to evaluate (car nil) does not automatically follow from the cons-and-nil representation of lists, and if we look at ancient Lisp documentation, such as the Lisp 1.5 manual from early 1960-something, we will find that this was absent. Initially, car was strictly a way to access a field of the cons cell, and required strictly a cons cell argument.
Good ideas like allowing (car nil) to Just Work (so that hackers could trim many useless lines of code from their programs) didn't appear overnight. The idea of allowing (car nil) may have appeared from InterLisp. In any case, Evolution Of Lisp paper claims that MacLisp (one of the important predecessors of Common Lisp, unrelated to the Apple Macintosh which came twenty years later), imitated this feature from InterLisp (another one of the significant predecessors).
Little details like this make the difference between pleasant programming and swearing at the monitor: see for instance A Short Ballad Dedicated to the Growth of Programs inspired by one Lisp programmer's struggle with a bletcherous dialect in which empty lists cannot be accessed with car, and do not serve as a boolean false.
An empty list is simply the nil symbol (and symbols, by definition, are not conses). car and cdr are defined to return nil if given nil.
As for list-mutation functions, they return a value that you are supposed to reassign to your variable. For example, look at the specification for the nreverse function: it may modify the given list, or not, and you are supposed to use the return value, and not rely on it to be modified in-place.
Even nconc, the quintessential destructive-append function, works that way: its return value is the appended list that you're supposed to use. It is specified to modify the given lists (except the last one) in-place, but if you give it nil as the first argument, it can't very well modify that, so you still have to use the return value.
NIL is somewhat a strange beast in Common Lisp because
it's a symbol (meaning that symbolp returns T)
is a list
is NOT a cons cell (consp returns NIL)
you can take CAR and CDR of it anyway
Note that the reasons behind this are probably also historical and you shouldn't think that this is the only reasonable solution. Other Lisp dialects made different choices.
Try it with your Lisp interpreter:
(eq nil '())
=> t
Several operations are special-cased to do unorthogonal (or even curious :-) things when operating on nil / an empty list. The behavior of car and cdr you were investigating is one of those things.
The idenity of nil as the empty list is one of the first things you learn about Lisp. I tried to come up with a good Google hit but I'll just pick one because there are so many: http://www.cs.sfu.ca/CourseCentral/310/pwfong/Lisp/1/tutorial1.html
Is it good style to use cons for pairs of things or would it be preferable to stick to lists?
like for instance questions and answers:
(list
(cons
"Favorite color?"
"red")
(cons
"Favorite number?"
"123")
(cons
"Favorite fruit?"
"avocado"))
I mean, some things come naturally in pairs; there is no need for something that can hold more than two, so I feel like cons would be the natural choice. However, I also feel like I should be sticking to one thing (lists).
What would be the better or more accepted style?
What you have there is an association list (alist). Alist entries are, indeed, often simple conses rather than lists (though that is a matter of preference: some people use lists for alist entries too), so what you have is fine. Though, I usually prefer to use literal syntax:
'(("Favorite color?" . "red")
("Favorite number?" . "123")
("Favorite fruit?" . "avocado"))
Alists usually use a symbol as the key, because symbols are interned, and so symbol alists can be looked up using assq instead of assoc. Here's how it might look:
'((color . "red")
(number . "123")
(fruit . "avocado"))
The default data-structure for such case should be a HASH-TABLE.
An association list of cons pairs is also a possible variant and was widely used historically. It is a valid variant, because of tradition and simplicity. But you should not use it, when the number of pairs exceeds several (probably, 10 is a good threshold), because search time is linear, while in hash-table it is constant.
Using a list for this task is also possible, but will be both ugly and inefficient.
You would need to decide for yourself based upon circumstances. There isn't a universal answer. Different tasks work differently with structures. Consider the following:
It is faster to search in a hash-table for keys, then it is in the alist.
It is easier to have an iterator and save its state, when working with alist (hash-table would need to export all of its keys as an array or a list and have a pointer into that list, while it is enough to only remember the pointer into alist to be able to restore the iterator's state and continue the iteration.
Alist vs list: they use the same amount of conses for even number of elements, given all other characters are atoms. When using lists vs alists you would have to thus make sure there isn't an odd number of elements (and you may discover it too late), which is bad.
But there are a lot more functions, including the built-in ones, which work on proper lists, and don't work on alists. For example, nth will error on alist, if it hits the cdr, which is not a list.
Some times certain macros would not function as you'd like them to with alists, for example, this:
(destructuring-bind (a b c d)
'((100 . 200) (300 . 400))
(format t "~&~{~s~^,~}" (list a b c d)))
will not work as you might've expected.
On the other hand, certain procedures may be "tricked" into doing something which they don't do for proper lists. For instance, when copying an alist with copy-list, only the conses, whose cdr is a list will be copied anew (depending upon the circumstances this may be a desired result).
Ok I need some help with thinking through this conceputally.
I need to check if a list and another list is structurally equal.
For example:
(a (bc) de)) is the same as (f (gh) ij)), because they have the same structure.
Now cleary the base case will be if both list are empty they are structurally equal.
The recursive case on the other hand I'm not sure where to start.
Some ideas:
Well we are not going to care if the elements are == to each other because that doesn't matter. We just care in the structure. I do know we will car down the list and recursively call the function with the cdr of the list.
The part that confuses me is how do you determine wheter an atom or sublist has the same structure?
Any help will be appreciated.
You're getting there. In the (free, online, excellent) textbook, this falls into section 17.3, "Processing two lists simultaneously: Case 3". I suggest you take a look.
http://www.htdp.org/2003-09-26/Book/curriculum-Z-H-1.html#node_toc_node_sec_17.3
One caveat: it looks like the data definition you're working with is "s-expression", which you can state like this:
;; an s-expression is either
;; - the empty list, or
;; - (cons symbol s-expression), or
;; - (cons s-expression s-expression)
Since this data definition has three cases, there are nine possibilities when considering two of them.
John Clements
(Yes, you could reduce the number of cases by embedding the data in the more general one that includes improper lists. Doesn't sound like a good idea to me.)