Notes on computational linguistics.pdf - UCLA Department of ...

Stabler - Lx 185/209 2003
?- X is 2+3.
X = 5
Yes
?- X is 2ˆ3.
X = 8
Yes
Using this predicate, length is defined this way:
length([],0).
length([_|L],N) :- length(L,N0), N is N0+1.
The first axiom says that the empty sequence has length 0. The second axiom says that any list has length N if
the result of removing the first element of the list has length N0 and N is N0+1. Since these axioms are already
“built in” we can use them immediately with goals like this:
?- length([a,b,1,2],N).
N = 4
Yes
?- length([a,b,[1,2]],N).
N = 3
Yes
We can do a lot with these basic ingredients, but first we should understand what’s going on.
This standard approach to sequences or lists may seem odd at first. The empty list is a named by [], and
non-empty lists are represented as the denotations of the period (often pronounced “cons” for “constructor”),
which is a binary function symbol. A list with one element is denoted by cons of that element and the empty list.
For example, .(a,[]) denotes the sequence which has just the one element a. And.(b,.(a,[])) denotes the
sequence with first element b and second element a. For convenience, we use [b,a] as an alternative notation
for the clumsier .(b,.(a,[])), and we use [A|B] as an alternative notation for .(A,B).
Examples:
If we apply {X↦frege,Y↦[]} to the list [X|Y], wegetthelist[frege].
If we apply {X↦frege,Y↦[hilbert]} to the list [X|Y], wegetthelist[frege,hilbert].
[X|Y] and [frege,hilbert] match after the substitution
{X↦frege,Y↦[hilbert]}.
Using this notation, we presented an axiomatization of the member relation. Another basic thing we need
to be able to do is to put two sequences together, “concatenating” or “appending” them. We can accordingly
define a 3-place relation we call append with the following two simple axioms: 8
append([],L,L).
append([E|L0],L1,[E|L2]) :- append(L0,L1,L2).
The first axiom says that, for all L, the result of appending the empty list and L is L. The second axiom says
that, for all E, L0, L1, andL2, the result of appending [E|L0] with L1 is [E|L2] if the result of appending
8 These axioms are “built in” to SWI-prolog – they are already there, and the system will not let you redefine this relation. However,
you could define the same relation with a different name like myappend.
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