sandbox/lpn/ch05/notes.md

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2018-01-19 00:30:58 +00:00
## Chapter 5: Arithmetic in Prolog
Prolog provides basic arithmetic operators.
Ex.
```
?- 8 is 6+2.
yes
?- 12 is 6*2.
yes
?- -2 is 6-8.
yes
?- 3 is 6/2.
yes
?- 1 is mod(7,2).
yes
?- X is 12/4.
X = 3.
```
The operators don't actually do arithmetic:
```
?- X = 2 + 3.
X = 2+3.
```
The default is just to do unification; `is` must be used. The arithmetic
expression must be on the RHS. This part of Prolog is a black box that
handles this, and isn't part of the normal KB and unification parts.
### Arithmetic and lists
A recursive list length calculator:
```
len([], 0).
len([_|T], N) :-
len(T, X),
N is X+1.
```
A tail-recursive length calculator:
```
alen_([], A, A).
alen_([_|H], A, L) :-
A2 is A+1,
alen_(H, A2, L).
alen(X, L) :- alen_(X, 0, L).
```
Standard notes about tail recursion efficiency apply here.
### Comparing integers
* *x < y* &rarr; `X < Y.`
* *x ≤ y* &rarr; `X =< Y.`
* *x = y* &rarr; `X =:= Y.`
* *x ≠ y* &rarr; `X =\= Y.`
* *x ≥ y* &rarr; `X >= Y`
* *x > y* &rarr; `X > Y`
Note the difference between `=` and `=:=`.
Let's write a `max` function:
```