Church numerals: Difference between revisions
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GordonBGood (talk | contribs) (→{{header|Julia}}: add Extended Church functions...) |
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<pre>[7, 12, 81, 64, 1, 0, 3, 8, 3, 4]</pre> |
<pre>[7, 12, 81, 64, 1, 0, 3, 8, 3, 4]</pre> |
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Note that Haskell has directly recursive functions so the y-Combinator is not used to implement recursion in the Church division function. |
Note that Haskell has directly recursive functions so the y-Combinator is not used to implement recursion in the Church division function. |
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=={{header|J}}== |
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Implementation: |
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<lang J>chget=: {{(0;1;1;1) {:: y}} |
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chset=: {{ |
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'A B'=.;y |
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'C D'=.B |
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'E F'=.D |
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<A;<C;<E;<<.x |
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}} |
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ch0=: {{ |
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if.0=#y do.y=.;:'>:' end. NB. replace empty gerund with increment |
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0 chset y`:6^:2`'' |
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}} |
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apply=: `:6 |
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chNext=: {{(1+chget y) chset y}} |
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chAdd=: {{(x +&chget y) chset y}} |
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chSub=: {{(x -&chget y) chset y}} |
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chMul=: {{(x *&chget y) chset y}} |
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chExp=: {{(x ^&chget y) chset y}} |
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int2ch=: {{y chset ch0 ''}} |
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ch2int=: chget</lang> |
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Task example: |
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<lang J>three=: chNext^:3 ch0'' |
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four=: chNext^:4 ch0'' |
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sixtyfour=: four chExp three |
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eightyone=: three chExp four |
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four apply 1 |
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16 |
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chget three |
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3 |
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chget four |
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4 |
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chget sixtyfour |
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64 |
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chget eightyone |
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81 |
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</lang> |
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Illustration of the difference between a church numeral and the represented functions: |
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<lang J> |
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three apply 0 |
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3 |
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three apply 10 |
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13 |
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four=: 4 chset ch0 {{2*y}}`'' |
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chget four |
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4 |
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four apply 0 |
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0 |
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four apply 10 |
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160</lang> |
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=={{header|Java}}== |
=={{header|Java}}== |
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