1.4.11 Trees

(alphorder x y) → t

x : (atom x)

y : (atom y)

Determines if x is lexicographically less than y. Works on any atomic input.

Examples:

> (alphorder 6 4)

()

> (alphorder 4 6)

t

> (alphorder 4 4)

t

> (alphorder "abc" "bcd")

t

> (alphorder "bcd" "abc")

()

> (alphorder #\a "a")

t

> (alphorder "a" #\a)

()

(atom x) → t

x : t

Returns true if x is not a cons pair.

Examples:

> (atom 4)

t

> (atom 'hello)

t

> (atom (cons 4 nil))

()

(eq x y) → t

x : t

y : (or (symbolp x) (symbolp y))

Tests two symbols for equality.

Examples:

> (eq 'yes 'yes)

t

> (eq 'yes 'no)

()

(eql x y) → t

x : t

y : (or (eqlablep x) (eqlablep y))

Tests equality of two numbers, symbols, or characters.

Examples:

> (eql 'yes 'yes)

t

> (eql 'yes 'no)

()

> (eql 5 5)

t

> (eql #\a #\b)

()

> (eql #\5 5)

()

(eqlablep x) → t

x : t

Returns t if and only if x is either a number, a symbol, or a character.

Examples:

> (eqlablep nil)

t

> (eqlablep 4)

t

> (eqlablep #\a)

t

> (eqlablep 'symbol)

t

> (eqlablep "string")

()

(equal x y)

Tests x and y for equality. Returns t if and only if they are the same value.

Examples:

> (equal "yes" "yes")

t

> (equal 'yes "no")

()

> (equal 'yes "yes")

()

(identity x) → t

x : t

The identity function. Returns its argument unchanged.

Examples:

> (identity 'x)

x

(lexorder a b) → t

a : t

b : t

Determines if the two given items are in lexicographic order.

Examples:

> (lexorder 6 4)

()

> (lexorder 4 6)

t

> (lexorder #\a #\b)

t

> (lexorder #\b #\a)

()

> (lexorder 'a 'b)

t

> (lexorder 'b 'a)

()

> (lexorder "abc" "bcd")

t

> (lexorder "bcd" "abc")

()

> (lexorder (list 1 2) (list 3 4))

t

> (lexorder (list 3 4) (list 1 2))

()

(caar x)

(cdar x)

(cadr x)

(cddr x)

(caaar x)

(cdaar x)

(cadar x)

(cddar x)

(caadr x)

(cdadr x)

(caddr x)

(cdddr x)

(caaaar x)

(cdaaar x)

(cadaar x)

(cddaar x)

(caadar x)

(cdadar x)

(caddar x)

(cdddar x)

(caaadr x)

(cdaadr x)

(cadadr x)

(cddadr x)

(caaddr x)

(cdaddr x)

(cadddr x)

(cddddr x)

Shorthand macros for compositions of car and cdr. For instance, (caddr x) is equivalent to (car (cdr (cdr x))).

Examples:
> (defconst *tree*       (cons (cons (cons (cons 0 1) (cons 2 3))                   (cons (cons 4 5) (cons 6 7)))             (cons (cons (cons 8 9) (cons 10 11))                   (cons (cons 12 13) (cons 14 15)))))
> (caar *tree*)
((0 . 1) 2 . 3)
> (cdar *tree*)
((4 . 5) 6 . 7)
> (cadr *tree*)
((8 . 9) 10 . 11)
> (cddr *tree*)
((12 . 13) 14 . 15)
> (caaar *tree*)
(0 . 1)
> (cdaar *tree*)
(2 . 3)
> (cadar *tree*)
(4 . 5)
> (cddar *tree*)
(6 . 7)
> (caadr *tree*)
(8 . 9)
> (cdadr *tree*)
(10 . 11)
> (caddr *tree*)
(12 . 13)
> (cdddr *tree*)
(14 . 15)
> (caaaar *tree*)
0
> (cdaaar *tree*)
1
> (cadaar *tree*)
2
> (cddaar *tree*)
3
> (caadar *tree*)
4
> (cdadar *tree*)
5
> (caddar *tree*)
6
> (cdddar *tree*)
7
> (caaadr *tree*)
8
> (cdaadr *tree*)
9
> (cadadr *tree*)
10
> (cddadr *tree*)
11
> (caaddr *tree*)
12
> (cdaddr *tree*)
13
> (cadddr *tree*)
14
> (cddddr *tree*)
15

(quote ...)

Examples:

> 'a

a

> '(1 2 3 4)

(1 2 3 4)

(quasiquote ...)

Examples:

> `a

a

> `(1 2 3 4)

(1 2 3 4)

(unquote ...)

Examples:

> '(list ,a  b c d)

(list ,a b c d)

(subst new old tree) → t

new : t

old : (eqlablep old)

tree : t

Substitutes every occurrence of old with new in the given tree. Uses eql as the test.

Examples:

> (subst 2 1 (list 1 1 1 3 1 1 1))

(2 2 2 3 2 2 2)

> (subst 'z 'a (list 'a 'b (list 'd 'a (list 'a 'e)) 'a))

(z b (d z (z e)) z)

(acl2-count v) → natp

v : t

Calculates the size of a value. This is the default recursion metric used for ACL2 termination proofs.

The size of a cons-pair is one more than the sum of the sizes of its car and cdr. The size of an integer is its absolute value, the size of a rational number is the sum of the sizes of its numerator and denominator, and the size of a complex number is one more than the sum of the sizes of its real and imaginary parts. The size of a string is its length. The size of all other values (characters and symbols) is 0.

Examples:
> (acl2-count 3/4)
7
> (acl2-count (complex 3 4))
8
> (acl2-count "ABCD")
4
> (acl2-count 'ABCD)
0
> (acl2-count '(a b c d))
4