D:\sbornik\...\stgy.DVI Mathematical Problems of Computer Science 32, 5{13, 2009. T he B asic Semantics of Untyped Functional P r ogr ams and Reduction Str ategies Gu r g e n G. H r a c h ya n Yerevan State University gurgen.hrachyan@gmail.com Abstract The paper is devoted to untyped functional programs, which are de¯ned as equation systems with separating variables in the untyped ¸-calculus. The semantics of such programs is usually de¯ned by means of the ¯x-point combinator Y . Previously, it was proved that the semantics of such programs is invariant with respect to the ¯x-point combinator. However, in this paper, we prove that this invariance is no longer valid when the reduction strategy is ¯xed. Refer ences [1 ] H . P . B a r e n d r e g t , \ Th e L a m b d a Ca lc u lu s , It s S yn t a x a n d S e m a n t ic s " , North-Holland P ub. Comp., 1 9 8 1 . [2 ] S . A . N ig iya n a n d S . A . A ve t is ya n , \ On t h e S e m a n t ic s o f U n t yp e d Fu n c t io n a l P r o g r a m s " , P rogramming and Computer Software, V o l. 2 8 , N 3 , p p . 1 1 9 -1 2 6 , 2 0 0 2 . [3 ] G. G. H r a c h ya n , \ Th e In va r ia n c e o f t h e Ma in S e m a n t ic s o f Typ e -Fr e e Fu n c t io n a l P r o - g r a m s R e la t ive ly t o t h e Fixp o in t Co m b in a t o r " , P roceedings of the Conference CSIT-2007, Y e r e va n , p p . 4 8 -5 0 . [4 ] S . A . A ve t is ya n , \ On t h e S e m a n t ic s o f U n t yp e d Fu n c t io n a l P r o g r a m s " , P HD Thesis, Y e r e va n , 2 0 0 5 . ²é³Ýó ïÇå»ñÇ ýáõÝÏóÇáÝ³É Íñ³·ñ»ñÇ ÑÇÙÝ³Ï³Ý ë»Ù³ÝïÇÏ³Ý ¨ 黹áõÏóÇáÝ ëïñ³ï»¹Ç³Ý»ññ ¶. Ðñ³ãÛ³Ý ²Ù÷á÷áõÙ ²ß˳ï³ÝùÁ ÝíÇñí³Í ¿ ³é³Ýó ïÇå»ñÇ ýáõÝÏÇáÝ³Ï³É Íñ³·ñ»ñÇÝ, áñáÝù Çñ»ÝóÇó Ý»ñϳ۳óÝáõÙ »Ý ѳí³ë³ñáõÙÝ»ñÇ Ñ³Ù³Ï³ñ·»ñ ³é³Ýó ïÇå»ñÇ ¸ - ѳßíáõÙ: ÜÙ³Ý Íñ³·ñ»ñÇ ÑÇÙÝ³Ï³Ý ë»Ù³ÝïÇÏ³Ý ÇÝãå»ë ϳÝáÝ ë³ÑÙ³ÝíáõÙ ¿ Y ³Ýß³ñÅ Ï»ïÇ ÏáÙµÇݳáñÇ ÙÇçáóáí: ܳËÏÇÝáõÙ ³å³óáõóí»É ¿ , áñ ÑÇÙÝ³Ï³Ý ë»Ù³ÝïÇÏ³Ý ÇÝí³ñdzÝï ¿ ³Ýß³ñÅ Ï»ïÇ ÏáÙµÇݳïáñÇ Ýϳïٳٵ: ê³Ï³ÛÝ, ³Ûë ³ß˳ï³ÝùÇó Ñ»ï¨áõÙ ¿ , áñ ïñí³Í 黹áõÏóÇáÝ ëïñ³ï»·Ç³ÛÇ Ñ³Ù³ñ ÝÙ³Ý ÇÝí³ñdzÝïáõÃÛáõÝ ï»ÕÇ ãáõÝÇ: 5