Prolog中指数为负时计算幂的规则？

我有幂函数pow试图计算的值B的力量E。到目前为止我处理的案件-
1.指数为0
2. 指数非零

pow(B,0,1).
pow(B,E,Result):-   E2 is E - 1,
                    pow(B,E2,Result2),
                    Result is B*Result2.

如何添加幂函数可以处理负指数的另一种情况？

First, one should consider how to define 0⁰. Formally speaking it is indeterminate. It could be zero or it could be 1. As Wolfram's Mathworld says in its article on powers and in its article on zero:

0⁰ (zero to the zeroth power) itself is undefined. The lack of a well-defined meaning for this quantity follows from the mutually contradictory facts that a⁰ is always 1, so 0⁰ should equal 1, but 0^a is always 0 (for a > 0), so 0^a should equal 0. The choice of definition for 0⁰ is usually defined to be indeterminate, although defining 0⁰ = 1 allows some formulas to be expressed simply (Knuth 1992; Knuth 1997, p. 57).

So you should first choose how to define the special case of 0⁰: Is it 0? Is it 1? Is it undefined?

我选择将其视为未定义。

That being said, you can look at a positive exponent as indicated repeated multiplication (e.g. 10³ is 10*10*10, or 1,000), and you can look at a negative exponent as indicating repeated division (e.g, 10^-3 is (((1/10)/10)/10), or 0.001). My inclination, partly because I like the symmetry of this approach and partly to avoid the cuts (since a cut is often a signal that you've not defined the solution properly), would be something like this:

% -----------------------------
% The external/public predicate
% -----------------------------
pow( 0 , 0 , _ ) :- ! , fail .
pow( X , N , R ) :-
  pow( X , N , 1 , R )
  .

% -----------------------------------
% the tail-recursive worker predicate
% -----------------------------------
pow( _ , 0 , R , R  ).
pow( X , N , T , R  ) :-
  N > 0 ,
  T1 is T * X ,
  N1 is N-1   ,
  pow( X , N1 , T1 , R )
  .
pow( _ , 0 , R , R  ) :-
  N < 0 ,
  T1 is T / X ,
  N1 is N+1   ,
  pow( X , N1 , T1 , R )
  .

The other approach, as others have noted, is to define a positive exponent as indicating repeated multiplication, and a negative exponent as indicating the reciprocal of the positive exponent, so 10³ is 10*10*10 or 1,000, and 10^-3 is 1/(10³), or 1/1,000 or 0.001. To use this definition, I'd again avoid the cuts and do something like this:

% -----------------------------
% the external/public predicate
% -----------------------------
pow( 0 , 0 , _ ) :-  % 0^0 is indeterminate. Is it 1? Is it 0? Could be either.
  ! ,
  fail
  .
pow( X , N , R ) :-
  N > 0 ,
  pow( X , N , 1 , R )
  .
pow( X , N , R ) :-
  N < 0 ,
  N1 = - N ,
  pow( X , N1 , 1 , R1 ) ,
  R is 1 / R1
  .

% -----------------------------------
% The tail-recursive worker predicate
% -----------------------------------
pow( _ , 0 , R , R  ).
pow( X , N , T , R  ) :-
  N > 0 ,
  T1 is T * X ,
  N1 is N-1   ,
  pow( X , N1 , T1 , R )
  .