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name = 'len/2'
slug = 'find the length of a list'
description = '''\
<p><code>len(L, Len)</code>: <code>Len</code> is the length of list <code>L</code>.</p>
<pre>
?- len([1,2,3], Len).
Len = 3.
</pre>'''
plan = ['''\
<p>A list is not very long if it's empty, and if it's not empty it must have a head and a tail.</p>
''', '''\
<p>If the tail (list without a head) is of length <code>LenT</code>, then the whole list
is of length <code>LenT + 1</code>.</p>
''', '''\
<p>If I take away the head, and the recursion solves this smaller problem (tail), and if I add 1 to the
result returned by the recursion, then I get the length of the whole list.</p>
''']
hint = {
'eq_instead_of_equ': '''\
<p>The operator <code>==</code> is "stricter" than operator <code>=</code> in the sense that
for the latter it is enough to be able to make the two operands equal (unification). Perhaps by using <code>=</code>
you can make the predicate <code>len/2</code> more general (e.g. able to work with output arguments becoming inputs).</p>
<p>Of course, you can also solve the exercise without explicit use of either of these two operators, just
remember that unification is implicitly performed with the predicate's arguments (head of clause).</p>
''',
'eq_instead_of_equ_markup': '''\
<p>Perhaps the operator for unification (=) would be better?</p>
''',
'base_case': '''\
<p>Did you think of a base case? Which list is the shortest list in the world?</p>
''',
'recursive_case': '''\
<p>The base case is ok. However, what about the general recursive case?</p>
''',
'predicate_always_false': '''\
<p>It seems your predicate is <emph>always</emph> "false". Did you give it the correct name,
or is it perhaps misspelled?</p>
<p>If the name is correct, check whether something else is misspelled, perhaps there is a full stop instead of
a comma or vice versa, or maybe you typed a variable name in lowercase?</p>
<p>It is, of course, also possible that your conditions are too restrictive, or even impossible to satisfy
(as would be, for example, the condition that <code>N</code> is equal to <code>N + 1</code>,
or something similarly impossible).</p>
''',
'timeout': '''\
<p>Is there an infinite recursion at work here? How will it ever stop?</p>
<p>Or perhaps is there a missing, faulty, or simply incompatible (with the general recursive case) base case?</p>
''',
'arbitrary_base_case': '''\
<p>What's the length of an empty list? Give a number!</p>
''',
'args_not_instantiated': '''\
<p>The error that prolog reported means that when it encountered an arithmetic operation, not all the
values were known. Unfortunately, the ordering of goals is important when dealing with arithmetics.</p>
<p>Perhaps you can try moving the arithmetic operation more towards the end of the predicate?</p>
''',
'=_instead_of_is': '''\
<p>Did you use the operator <code>=</code> instead of <code>is</code>? Operator <code>=</code> is used for
unification and tries to leave both its operands with as little modifications as possible while still making
them equal. Operator <code>is</code>, on the other hand, performs actual arithmetic evaluation of its
second operand and only then attempts the unification of both operands.</p>
''',
'+H_instead_of_+1': '''\
<p>Did you really add the element's value instead of its length (one)? ;)</p>
''',
'forcing_result_onto_recursion': '''
<p>Don't force the result onto recursion, don't tell it what it should return. Just assume it will do its job.
If this assumption is correct, then the rule will work for a larger case.</p>
<p>Is your recursive call of the form <code>len(Tail, LenTail + 1)</code>? This forces the recursive call to
return the length of <em>the whole</em> list, not just the tail! This will not work. It is your job to
increase by one the result returned by the recursion. In short, add one outside the recursive call.</p>
''',
'same_var_on_both_sides_of_is': '''\
<p>Does one of your goals look similar to <code>N is N + 1</code>? Let's assume <code>N</code> is equal to 3.
With this goal you just stated that 3 must be equal to 4 (3+1). Prolog is a logical language and will
gladly say "false" to such a statement! Just use a new variable. The garbage collector will take care of
those not needed anymore automatically.</p>
''',
}
|
