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mm0821 committed Dec 1, 2023
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des <span class="RktSym">make-person</span> Konstruktors ein:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym">promote</span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="hspace">&nbsp;</span><span class="RktSym">t</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._cond%29%29" class="RktStxLink" data-pltdoc="x">cond</a></span><span class="hspace">&nbsp;</span><span class="RktPn">[</span><span class="RktPn">(</span><span class="RktSym">person?</span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym">make-person</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28def._htdp-beginner._%28%28lib._lang%2Fhtdp-beginner..rkt%29._string-append%29%29" class="RktValLink" data-pltdoc="x">string-append</a></span><span class="hspace">&nbsp;</span><span class="RktSym">t</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym">person-name</span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym">promote</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym">person-father</span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="RktPn">)</span><span class="hspace">&nbsp;</span><span class="RktSym">t</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym">promote</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym">person-mother</span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="RktPn">)</span><span class="hspace">&nbsp;</span><span class="RktSym">t</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">]</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">[</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._else%29%29" class="RktStxLink" data-pltdoc="x">else</a></span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="RktPn">]</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><h4>9.3<tt>&nbsp;</tt><a name="(part._.Formale_.Signaturen_f_r_rekursive_.Datentypen)"></a>Formale Signaturen f&#252;r rekursive Datentypen</h4><p>Wir k&#246;nnen formale Signaturen auch f&#252;r rekursive Datentypen verwenden.
Den &#228;u&#223;eren Summentyp k&#246;nnen wir &#252;ber den Signaturkonstruktur <span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._mixed%29%29" class="RktStxLink" data-pltdoc="x">mixed</a></span>
abbilden. Wichtig an der formalen Signatur <span class="RktSym">FamilyTree</span> ist, dass die
Definition selber rekursiv ist.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._define-struct%29%29" class="RktStxLink" data-pltdoc="x">define-struct</a></span><span class="hspace">&nbsp;</span><span class="RktSym">person</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/teachpack/2htdpuniverse.html#%28form._world._%28%28lib._2htdp%2Funiverse..rkt%29._name%29%29" class="RktStxLink" data-pltdoc="x">name</a></span><span class="hspace">&nbsp;</span><span class="RktSym">father</span><span class="hspace">&nbsp;</span><span class="RktSym">mother</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._signature%29%29" class="RktStxLink" data-pltdoc="x">signature</a></span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._mixed%29%29" class="RktStxLink" data-pltdoc="x">mixed</a></span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._enum%29%29" class="RktStxLink" data-pltdoc="x">enum</a></span><span class="hspace">&nbsp;</span><span class="RktVal">#false</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym">PersonOf</span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28def._htdp-beginner._%28%28lib._lang%2Fhtdp-beginner..rkt%29._.String%29%29" class="RktValLink" data-pltdoc="x">String</a></span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>Diese Datentyp kann nun wie gewohnt in Signaturen verwendet werden,
Definition selber rekursiv ist.</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._define-struct%29%29" class="RktStxLink" data-pltdoc="x">define-struct</a></span><span class="hspace">&nbsp;</span><span class="RktSym">person</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/teachpack/2htdpuniverse.html#%28form._world._%28%28lib._2htdp%2Funiverse..rkt%29._name%29%29" class="RktStxLink" data-pltdoc="x">name</a></span><span class="hspace">&nbsp;</span><span class="RktSym">father</span><span class="hspace">&nbsp;</span><span class="RktSym">mother</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._signature%29%29" class="RktStxLink" data-pltdoc="x">signature</a></span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._mixed%29%29" class="RktStxLink" data-pltdoc="x">mixed</a></span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28def._htdp-beginner._%28%28lib._lang%2Fhtdp-beginner..rkt%29._.False%29%29" class="RktValLink" data-pltdoc="x">False</a></span></td></tr><tr><td><span class="hspace">&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;</span><span class="RktPn">(</span><span class="RktSym">PersonOf</span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28def._htdp-beginner._%28%28lib._lang%2Fhtdp-beginner..rkt%29._.String%29%29" class="RktValLink" data-pltdoc="x">String</a></span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr></table></blockquote><p>Dieser Datentyp kann nun wie gewohnt in Signaturen verwendet werden,
beispielsweise:</p><blockquote class="SCodeFlow"><table cellspacing="0" cellpadding="0" class="RktBlk"><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._~3a%29%29" class="RktStxLink" data-pltdoc="x">:</a></span><span class="hspace">&nbsp;</span><span class="RktSym">Bob</span><span class="hspace">&nbsp;</span><span class="RktSym">FamilyTree</span><span class="RktPn">)</span></td></tr><tr><td><span class="hspace">&nbsp;</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._~3a%29%29" class="RktStxLink" data-pltdoc="x">:</a></span><span class="hspace">&nbsp;</span><span class="RktSym">person-has-ancestor</span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym">FamilyTree</span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28def._htdp-beginner._%28%28lib._lang%2Fhtdp-beginner..rkt%29._.String%29%29" class="RktValLink" data-pltdoc="x">String</a></span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._-~3e%29%29" class="RktStxLink" data-pltdoc="x"><span class="nobreak">-&gt;</span></a></span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28def._htdp-beginner._%28%28lib._lang%2Fhtdp-beginner..rkt%29._.Boolean%29%29" class="RktValLink" data-pltdoc="x">Boolean</a></span><span class="RktPn">)</span><span class="RktPn">)</span></td></tr><tr><td><span class="RktPn">(</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._define%29%29" class="RktStxLink" data-pltdoc="x">define</a></span><span class="hspace">&nbsp;</span><span class="RktPn">(</span><span class="RktSym">person-has-ancestor</span><span class="hspace">&nbsp;</span><span class="RktSym">p</span><span class="hspace">&nbsp;</span><span class="RktSym">a</span><span class="RktPn">)</span><span class="hspace">&nbsp;</span><span class="RktSym"><a href="http://docs.racket-lang.org/htdp-langs/beginner.html#%28form._%28%28lib._lang%2Fhtdp-beginner..rkt%29._......%29%29" class="RktStxLink" data-pltdoc="x">...</a></span><span class="RktPn">)</span></td></tr></table></blockquote><h4>9.4<tt>&nbsp;</tt><a name="(part._.Listen)"></a>Listen</h4><p>Die <span class="RktSym">FamilyTree</span> Datendefinition von oben steht f&#252;r eine Menge von B&#228;umen, in denen
jeder Knoten genau zwei ausgehende Kanten hat. Selbstverst&#228;ndlich k&#246;nnen wir auch auf die
gleiche Weise B&#228;ume repr&#228;sentieren, die drei oder f&#252;nf ausgehende Kanten haben &#8212;<wbr></wbr> indem wir
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