A href="module.php?name=Lexikon&file=search&eid=1&query=program transformation">program transformation where several results are returned from a single traversal of a data structure. E.g. mean l = sum l / length l ==> mean l = s/n where (s,n) = sumLen l sumLen [] = (0,0) sumLen (x:xs) = (s+x, n+1) where (s,n) = sumLen xs In href="module.php?name=Lexikon&file=search&eid=1&query=procedural">procedural languages this technique is known as href="module.php?name=Lexikon&file=search&eid=1&query=horizontal loop combination">horizontal loop combination because it uses one loop to calculate several results. Another form of tupling transformation is used to avoid repeated evaluation where a function generates several identical calls to itself. By analysing the pattern of recursion (see href="module.php?name=Lexikon&file=search&eid=1&query=descent function">descent function) it is possible to arrange for these identical calls to share results. E.g. fib 0 = 1 fib 1 = 1 fib n = fib (n-1) + fib (n-2) ==> fib n = v where (_,v) = fibt n fibt 0 = (1,1) fibt n = (u+v,u) where (u,v) = fibt (n-1) (1995-01-12)

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[ href="module.php?name=Lexikon&op=content&tid=31">2 ] [ href="module.php?name=Lexikon&op=content&tid=134">= ] [ href="module.php?name=Lexikon&op=content&tid=396">ag ] [ href="module.php?name=Lexikon&op=content&tid=433">al ] [ href="module.php?name=Lexikon&op=content&tid=544">am ] [ href="module.php?name=Lexikon&op=content&tid=592">an ] [ href="module.php?name=Lexikon&op=content&tid=740">ar ] [ href="module.php?name=Lexikon&op=content&tid=743">arc ] [ href="module.php?name=Lexikon&op=content&tid=800">as ] [ href="module.php?name=Lexikon&op=content&tid=894">at ] [ href="module.php?name=Lexikon&op=content&tid=935">au ] [ href="module.php?name=Lexikon&op=content&tid=996">av ] [ href="module.php?name=Lexikon&op=content&tid=1025">B ] [ href="module.php?name=Lexikon&op=content&tid=1026">b ] [ href="module.php?name=Lexikon&op=content&tid=1181">be ] [ href="module.php?name=Lexikon&op=content&tid=1269">bi ] [ href="module.php?name=Lexikon&op=content&tid=1624">bt ] [ href="module.php?name=Lexikon&op=content&tid=1724">ca ] [ href="module.php?name=Lexikon&op=content&tid=2001">ch ] [ href="module.php?name=Lexikon&op=content&tid=2247">co ] [ href="module.php?name=Lexikon&op=content&tid=2330">com ] [ href="module.php?name=Lexikon&op=content&tid=2332">combination ] [ href="module.php?name=Lexikon&op=content&tid=2900">cu ] [ href="module.php?name=Lexikon&op=content&tid=3006">data ] [ href="module.php?name=Lexikon&op=content&tid=3084">data structure ] [ href="module.php?name=Lexikon&op=content&tid=3151">de ] [ href="module.php?name=Lexikon&op=content&tid=3300">descent function ] [ href="module.php?name=Lexikon&op=content&tid=3752">du ] [ href="module.php?name=Lexikon&op=content&tid=3834">E ] [ href="module.php?name=Lexikon&op=content&tid=3865">ec ] [ href="module.php?name=Lexikon&op=content&tid=3896">ed ] [ href="module.php?name=Lexikon&op=content&tid=3923">edu ] [ href="module.php?name=Lexikon&op=content&tid=3929">ee ] [ href="module.php?name=Lexikon&op=content&tid=4148">er ] [ href="module.php?name=Lexikon&op=content&tid=4150">era ] [ href="module.php?name=Lexikon&op=content&tid=4171">es ] [ href="module.php?name=Lexikon&op=content&tid=4199">et ] [ href="module.php?name=Lexikon&op=content&tid=4246">evaluation ] [ href="module.php?name=Lexikon&op=content&tid=4497">fi ] [ href="module.php?name=Lexikon&op=content&tid=4520">file ] [ href="module.php?name=Lexikon&op=content&tid=4700">fo ] [ href="module.php?name=Lexikon&op=content&tid=4727">for ] [ href="module.php?name=Lexikon&op=content&tid=4828">fr ] [ href="module.php?name=Lexikon&op=content&tid=4940">function ] [ href="module.php?name=Lexikon&op=content&tid=5057">ge ] [ href="module.php?name=Lexikon&op=content&tid=5070">gen ] [ href="module.php?name=Lexikon&op=content&tid=5089">generate ] [ href="module.php?name=Lexikon&op=content&tid=5171">gl ] [ href="module.php?name=Lexikon&op=content&tid=5291">gr ] [ href="module.php?name=Lexikon&op=content&tid=5398">gt ] [ href="module.php?name=Lexikon&op=content&tid=5403">gu ] [ href="module.php?name=Lexikon&op=content&tid=5434">h ] [ href="module.php?name=Lexikon&op=content&tid=5681">hn ] [ href="module.php?name=Lexikon&op=content&tid=5717">horizontal loop combination ] [ href="module.php?name=Lexikon&op=content&tid=5768">hr ] [ href="module.php?name=Lexikon&op=content&tid=5931">id ] [ href="module.php?name=Lexikon&op=content&tid=6013">il ] [ href="module.php?name=Lexikon&op=content&tid=6064">in ] [ href="module.php?name=Lexikon&op=content&tid=6413">io ] [ href="module.php?name=Lexikon&op=content&tid=6446">iq ] [ href="module.php?name=Lexikon&op=content&tid=6482">is ] [ href="module.php?name=Lexikon&op=content&tid=6558">it ] [ href="module.php?name=Lexikon&op=content&tid=6861">kn ] [ href="module.php?name=Lexikon&op=content&tid=6918">la ] [ href="module.php?name=Lexikon&op=content&tid=6950">language ] [ href="module.php?name=Lexikon&op=content&tid=7014">lc ] [ href="module.php?name=Lexikon&op=content&tid=7091">Lex ] [ href="module.php?name=Lexikon&op=content&tid=7107">li ] [ href="module.php?name=Lexikon&op=content&tid=7338">loop ] [ href="module.php?name=Lexikon&op=content&tid=7339">loop combination ] [ href="module.php?name=Lexikon&op=content&tid=7399">ls ] [ href="module.php?name=Lexikon&op=content&tid=7410">lt ] [ href="module.php?name=Lexikon&op=content&tid=7415">lu ] [ href="module.php?name=Lexikon&op=content&tid=7441">ly ] [ href="module.php?name=Lexikon&op=content&tid=7463">ma ] [ href="module.php?name=Lexikon&op=content&tid=8032">mo ] [ href="module.php?name=Lexikon&op=content&tid=8040">mod ] [ href="module.php?name=Lexikon&op=content&tid=8079">module ] [ href="module.php?name=Lexikon&op=content&tid=8386">na ] [ href="module.php?name=Lexikon&op=content&tid=8460">nc ] [ href="module.php?name=Lexikon&op=content&tid=8472">ne ] [ href="module.php?name=Lexikon&op=content&tid=8627">ng ] [ href="module.php?name=Lexikon&op=content&tid=8630">ni ] [ href="module.php?name=Lexikon&op=content&tid=8675">no ] [ href="module.php?name=Lexikon&op=content&tid=8760">ns ] [ href="module.php?name=Lexikon&op=content&tid=8964">om ] [ href="module.php?name=Lexikon&op=content&tid=9014">op ] [ href="module.php?name=Lexikon&op=content&tid=9204">pa ] [ href="module.php?name=Lexikon&op=content&tid=9457">pe ] [ href="module.php?name=Lexikon&op=content&tid=9550">ph ] [ href="module.php?name=Lexikon&op=content&tid=9651">pl ] [ href="module.php?name=Lexikon&op=content&tid=9707">pling ] [ href="module.php?name=Lexikon&op=content&tid=9908">pr ] [ href="module.php?name=Lexikon&op=content&tid=10023">program ] [ href="module.php?name=Lexikon&op=content&tid=10048">program transformation ] [ href="module.php?name=Lexikon&op=content&tid=10253">query ] [ href="module.php?name=Lexikon&op=content&tid=10319">range ] [ href="module.php?name=Lexikon&op=content&tid=10351">rave ] [ href="module.php?name=Lexikon&op=content&tid=10364">rc ] [ href="module.php?name=Lexikon&op=content&tid=10385">re ] [ href="module.php?name=Lexikon&op=content&tid=10431">recursion ] [ href="module.php?name=Lexikon&op=content&tid=10552">repeat ] [ href="module.php?name=Lexikon&op=content&tid=10767">ro ] [ href="module.php?name=Lexikon&op=content&tid=10887">ru ] [ href="module.php?name=Lexikon&op=content&tid=10922">sa ] [ href="module.php?name=Lexikon&op=content&tid=11010">sc ] [ href="module.php?name=Lexikon&op=content&tid=11150">se ] [ href="module.php?name=Lexikon&op=content&tid=11314">sh ] [ href="module.php?name=Lexikon&op=content&tid=11324">shar ] [ href="module.php?name=Lexikon&op=content&tid=11376">si ] [ href="module.php?name=Lexikon&op=content&tid=11934">st ] [ href="module.php?name=Lexikon&op=content&tid=12109">struct ] [ href="module.php?name=Lexikon&op=content&tid=12133">su ] [ href="module.php?name=Lexikon&op=content&tid=12165">sum ] [ href="module.php?name=Lexikon&op=content&tid=12588">th ] [ href="module.php?name=Lexikon&op=content&tid=12721">to ] [ href="module.php?name=Lexikon&op=content&tid=12787">tr ] [ href="module.php?name=Lexikon&op=content&tid=12812">transformation ] [ href="module.php?name=Lexikon&op=content&tid=12841">traversal ] [ href="module.php?name=Lexikon&op=content&tid=12896">tt ] [ href="module.php?name=Lexikon&op=content&tid=12986">ua ] [ href="module.php?name=Lexikon&op=content&tid=13030">um ] [ href="module.php?name=Lexikon&op=content&tid=13146">up ] [ href="module.php?name=Lexikon&op=content&tid=13175">us ] [ href="module.php?name=Lexikon&op=content&tid=13252">va ] [ href="module.php?name=Lexikon&op=content&tid=13310">ve ]