"Every language is a tradition, every word a shared symbol" (Borges).
Definition
Any language expression, without exception, can be shared, that is, it can belong (be common) to several expressions. One mode of sharing is self-sharing: when an expression is shared in its own context.
The sharing specification is realized by generic expressions.
Examples
Sharing by name.
The sequences x and y share the expression v.
(v = 11)
(x = (a ⟨v⟩ b))
(y = (⟨v⟩ c ⟨v⟩))
x // ev. (a 11 b)
y // ev. (11 c 11)
(v = 99) (change v)
x // ev. (a 99 b)
(x changes automatically)
y // ev. (99 c 99)
(y changes automatically)
Sharing of an element of a sequence.
The third element of a sequence y is always defined as the first element of the sequence x:
(x = (a b c d))
(y = (3 7 ⟨x\1⟩ 4 5))
(the third element of y is the first element of x)
y // ev. (3 7 to 4 5)
(x = (u v w)) (change x)
y // ev. (3 7 u 4 5)
(y changes automatically)
Mutual sharing of elements between two sequences.
(x = (a b c ⟨y\1⟩ d))
(the fourth element of x is the first element of y)
(y = (3 7 4 5 ⟨x\(x#)⟩))
(the last element of y is the last element of x)
x // ev. (a b c 3 d)
y // ev. (3 7 4 5 d)
(x/5 = 55)
(we change the last element of x)
(y/1= 11)
(we change the first element of y)
x // ev. (a b c 11 55)
(x changes automatically)
y // ev. (11 7 4 5 55)
(y changes automatically)
Self-sharing. Some elements of a sequence are defined from other elements of the same sequence.
(x = (a b ⟨x\1⟩ ⟨x\2⟩ c))
(the third and fourth elements of x are the first and second, respectively, of the same sequence)
x // ev. (a b a b c)
(x = u)
(we change the first element of x)
(x2 = v)
(we change the second element of x)
x // ev. (u v u v v c)
(x changes automatically)
Auto-sharing of several consecutive elements.
(x = (a b c [⟨x[1...3]⟩])])
(elements 4, 5 and 6 of x are equal to the first three).
x // ev. (a b c a b c)
(x = u)
(we change the first element of x)
(x2 = v)
(we change the second element of x)
x // ev. (u v c u v c)
(x changes automatically)
Sharing the contents of a set.
(x = {a b c d})
(y = {u v ⟨x↓⟩})
(y consists of u, v and the contents of x)
y // ev. {u v a b c d}
(x = {3 4 5 5 6})
(redefine x)
y // ev. {u v 3 4 5 5 6}
(new value of y)
Sharing of a selection.
(x = {1 3 5 7 9})
(y = {u v ⟨x⇓(<6]⟩})
(y consists of u, v and the elements less than 6 of x)
y // ev. {u v 1 3 5}
(x = {2 4 6 8})
(redefines x)
y // ev. {u v 2 4}
(y changes automatically)
Sharing by assigning a name to a shared element.
(x = (a b c d))
(v = ⟨x\3⟩)
(v is always the third element of x)
(y = (3 7 v☆3))
(y consists of 3, 7 and three elements v)
y // ev. (3 7 c c c c)
(x = (e f g g h))
(redefines x)
y // ev. (3 7 g g g g)
(new value of y)
(v = ⟨x\4⟩)
(redefine v)
y // ev. (3 7 d d d d d)
(new value of y)
Circular sequence
It is a sequence that "bites its own tail", i.e., the next element from the last is the first. The general form is:
⟨( xi = xi - i÷(x#)) )⟩
That is, the remainder of the division between i and the length of the sequence is always used. For example,
(x = (a b c d)
x\5 // ev. a
x\10 // ev. b
x\100 // ev. d
x\101 // ev. a
Shared expressions structures
Using the sharing technique, it is possible to define all kinds of structures. For example, if we symbolize a sequence by a line ending in an arrow, and a set by a circle, we can specify structures such as the following:
