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DeleteMe °è¼Ó Ãß°¡ µË´Ï´Ù. --ÀÛÀº³ª¹«

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1 Logic
1.1 Áø¸®°ª°ú ±× ¿¬»êÀÚµé
1.2 Á¶°Ç¹®
2 ¸®½ºÆ®

Âü°í¹®Çå
  • List in TeX's Mouth, Alan Jeffrey
  • THE COMPUTER SCIENCE OF TeX AND LaTeX, Victor Eijkhout

1 Logic

1.1 Áø¸®°ª°ú ±× ¿¬»êÀÚµé

°£´ÜÇÏÁö¸¸ À¯¿ëÇÑ ¸ÅÅ©·ÎºÎÅÍ Á¤ÀÇÇÑ´Ù.
\def\Ignore#1{}
\def\Identity#1{#1}
\def\First#1#2{#1}
\def\Second#1#2{#2}
»ç¿ë·Ê
Taking first argument:
  input : \First {first}{second}
  output : first
Taking second argument:
  input : \Second {first}{second}
  output : second
Áø¸®°ªÀ» Á¤ÀÇÇÑ´Ù.
\let\True=\First
\let\False=\Second
À§ÀÇ Á¤ÀÇ´ë·Î¶ó¸é, Âü(\True)Àº µÎ°³ÀÇ ÀÎÀÚÁß Ã¹¹ø° ÀÎÀÚÀÇ °ªÀÌ°í, °ÅÁþ(\False)Àº µÎ¹ø° ÀÎÀÚÀÇ °ªÀÌ´Ù. ÀÌ°ÍÀÌ Àǹ̰¡ ÀÖÀ¸·Á¸é, ±× µÎ°³ÀÇ ÀÎÀÚ´Â T¿Í F À̾î¾ß ÇÑ´Ù. Áï \True¿Í \False°¡ ¶æÇÏ´Â Àǹ̴ ´ÙÀ½°ú °°´Ù.
input : \True TF
output: T

input : \False TF
output: F
µû¶ó¼­ ¾ÕÀ¸·Î ³ª¿À´Â ¸ðµç ³í¸®¹® ´ÙÀ½¿¡´Â ¾ðÁ¦³ª µÎ°³ÀÇ ÀÎÀÚ TF°¡ ÀÖ´Â °ÍÀ¸·Î °£ÁÖÇÑ´Ù.

³í¸® ¿¬»êÀÚµéÀ» Á¤ÀÇÇÑ´Ù.
\def\And#1#2{#1{#2}\False}
\def\Or#1#2{#1\True{#2}}
\def\Twiddle#1#2#3{#1{#3}{#2}}
\let\Not=\Twiddle
¼³¸í: \And x y ÀÇ °ªÀº x°¡ ÂüÀ̸é, yÀÇ °ªÀÌ°í, x°¡ °ÅÁþÀ̸é, y °ª¿¡ °ü°è¾øÀÌ °ÅÁþÀÌ´Ù. Áï ÂüÀº ù¹ø° ÀÎÀÚ¸¦ °ÅÁþÀ» µÎ¹ø° ÀÎÀÚ¸¦ ÃëÇÑ´Ù´Â °Í¿¡ Âø¾ÈÇϸé \AndÀÇ Á¤ÀÇ´Â À§¿Í °°Àº °ÍÀÌ°í, \Orµµ ¸¶Âù°¡ÁöÀÌ´Ù.

Áø¸®°ªµé°ú ¿¬»êÀÚµéÀ» Å×½ºÆ® Çغ¸ÀÚ.
True takes first of TF:
  input : \True TF
  output : T
False takes second of TF:
  input : \False TF
  output : F
Not true is false:
  input : \Not \True TF
  output : F
And truth table TrueTrue:
  input : \And \True \True TF
  output : T
And truth table TrueFalse:
  input : \And \True \False TF
  output : F
And truth table FalseTrue:
  input : \And \False \True TF
  output : F
And truth table FalseFalse:
  input : \And \False \False TF
  output : F
Or truth table TrueTrue:
  input : \Or \True \True TF
  output : T
Or truth table TrueFalse:
  input : \Or \True \False TF
  output : T
Or truth table FalseTrue:
  input : \Or \False \True TF
  output : T
Or truth table FalseFalse:
  input : \Or \False \False TF
  output : F
¿¹)
  • \And \True \False TF, \ANDÀÇ Á¤ÀÇ´ë·Î Àü°³Çϸé,
    \And \True \False TF 
    ==> \True{\False}\False TF
    ==> \False TF
    ==> F
    
  • \Not \True TF, \NOTÀÇ Á¤ÀÇ´ë·Î Àü°³Çϸé,
    \Not \True TF
    ==> \True{F}{T}
    ==> F
    


1.2 Á¶°Ç¹®

±âº» ¸ÅÅ©·ÎµéÀ» Á¤ÀÇÇÑ´Ù.
\def\gobblefalse\else\gobbletrue\fi#1#2{\fi#1}
\def\gobbletrue\fi#1#2{\fi#2}
\def\TeXIf#1#2{#1#2 \gobblefalse\else\gobbletrue\fi}
»ç¿ë ¹®¹ý
\TeXIf <test> <arg>
Å×½ºÆ® ÇÑ´Ù:
\def\IfIsPositive{\TeXIf{\ifnum0<}}

Numerical test:
  input : \IfIsPositive {3} TF
  output : T
Numerical test:
  input : \IfIsPositive {-2} TF
  output : F
¼³¸í)
  • \IfIsPositive { 3 } TF¸¦ Á¤ÀÇ´ë·Î Àü°³Çϸé,
    \IfIsPositive {3} TF
    ==> \TeXIf{\ifnum0<}{3}TF
    ==> \ifnum0<3\gobblefalse\else\gobbletrue\fi TF
    ==> \ifnum0<3\fi T
    ==> T
    

2 ¸®½ºÆ®

¸®½ºÆ®´Â ¸Ó¸®(head)¿Í ²¿¸®(tail)·Î Á¤ÀÇ µÇ´Âµ¥, ¸Ó¸®´Â ÇÑ ±¸¼º¿ä¼Ò(element) ÀÌ°í, ²¿¸®´Â ¶Ç´Ù¸¥ ¸®½ºÆ®ÀÌ´Ù. Áï ¸®½ºÆ®´Â ±× Á¤ÀÇ°¡ Àç±ÍÀûÀÌ´Ù. ºó ¸®½ºÆ®(empty list)¸¦ Nil·Î Ç¥±âÇÑ´Ù.
\let\Nil=\False
À§ÀÇ ¸®½ºÆ®ÀÇ Á¤ÀǸ¦ µÎ°³ÀÇ ÀÎÀÚ¸¦ °¡Áø ¿¬»êÀÚ·Î ±¸ÇöÇÑ´Ù:
  • ¸¸¾à ¸®½ºÆ®°¡ ºñ¾îÀÖÁö ¾Ê´Ù¸é, ù¹ø° ÀÎÀÚ´Â ¸Ó¸®¿¡ Àû¿ëµÇ°í, ²¿¸®°¡ ±× ¸®½ºÆ®ÀÇ °ªÀÌ µÈ´Ù.
  • ¸¸¾à ¸®½ºÆ®°¡ ºñ¾îÀÖ´Ù¸é, µÎ¹ø° ÀÎÀÚ°¡ ¸®½ºÆ®ÀÌ °ªÀÌ µÈ´Ù.

    \[ La_1a_2 = \left\{ \begin{array}{ll}
                      a_2     & \mbox{if $L=()$} \\
                      a_1(x)Y & \mbox{if $L=(x,Y)$}
                    \end{array}
             \right. \]


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