Unification
The concept of unification is one of the main ideas behind Prolog. It represents the mechanism of binding the contents of variables and can be viewed as a kind of one-time assignment. In Prolog, this operation is denoted by symbol "=".
- An uninstantiated variable X (i.e. no previous unification were performed on it) can be unified with an uninstantiated variable (and effectively becomes its alias), an atom or a term.
- An atom can be unified only with the same atom.
- A term is unified with another term, if the heads and arities of the terms are identic and the parameters are unified (note that this is a recursive behaviour).
Due to its declarative nature, the order in a sequence of unifications doesn't play (usually) any role.
Examples of unification
- A=A
- Succeeds (tautology)
- A=B, B=abc
- Both A and B are unified with the atom abc
- xyz=C, C=D
- Unification is symmetric
- abc=abc
- Unification succeeds
- abc=xyz
- Fails to unify, atoms are different
- f(A)=f(B)
- A is unified with B
- f(A)=g(B)
- Fails, the heads of terms are different
- f(A)=f(B,C)
- Fails to unify, because terms have different arity
- f(g(A))=f(B)
- Unifies B with the term g(A)
- f(g(A), A)=f(B, xyz)
- Unifies A with the atom xyz and B with the term g(xyz)
- A=f(A)
- Infinite unification, A is unified with f(f(f(f(...)))).
- A=abc, xyz=X, A=X
- Fails to unify; effectively abc=xyz
die of it, the price shall be demanded of thee, and that will be
two hands, for thou.html">thou.html">thou.html">thou.html">thou.html">thou hast taken from me the thing that in this world.html">world.html">world
captive that I did bring from a strange country. Yea, I bought her
her, and made her my daughter in go/go.html">go/go.html">go/go.html">go/god.html">God. And I have cherished her, and
bread honourably. With this hast thou naught to make, but do thou
deem thee to have gained, hadst thou made her thy leman, and taken
for in Hell would thy soul have lain while the world endures, and
only to have Nicolete, my sweet lady that I love.html">love so well.html">well. For into
these same old priests, and halt old men and maimed, who all day and
such folk as wear old amices and old clouted frocks, and naked folk
thirst, and of cold, and of little ease. These be they that go into
fain go; for into Hell fare the goodly clerks, and goodly knights
men noble. With these would I liefly go. And thither pass the
lords also thereto. Thither goes the gold, and the silver, and
prince of this world. With these I would gladly go, let me but have
never shalt thou see her; and if thou hadst word with her, and thy
thyself might well be sore adread."
"That is even what irketh me," quoth Aucassin. So he went from the
Here singeth one:
Much in dole and heavy at heart
None might bring him any cheer,
To the palace doth he fare
Passeth to a chamber there,
For his lady and love so fair.
"Nicolete how fair art thou,
Sweet the mirth of thy replies,
Sweet thy lips and sweet thy brow,
All for thee I sorrow now,
Whence I ne'er may go my ways
So say they, speak they, tell they the Tale:
.
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