📄 iterate.mldoc

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<!-- iterate.mldoc --><!-- Entities.sgml entry <!ENTITY Iterate SDATA "iterate-sig.sml"> --><!DOCTYPE ML-DOC SYSTEM><COPYRIGHT OWNER="Bell Labs, Lucent Technologies" YEAR=1998><VERSION VERID="1.0" YEAR=1998 MONTH=6 DAY=10><TITLE>The Iterate structure</TITLE><INTERFACE><HEAD>The <CD/Iterate/ structure</HEAD><PP>The <STRREF NOLINK/Iterate/ structure provides wrappers for simpleforms of iteration.<STRUCTURE STRID="Iterate">  <SIGBODY SIGID="ITERATE" FILE=ITERATE>    <SPEC>      <VAL>iterate<TY>('a -> 'a) -> int -> 'a -> 'a      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/        <COMMENT>          <PROTOTY>          iterate <ARG/f/ <ARG/cnt/ <ARG/a/          </PROTOTY>          invokes the function <ARG/f/ <ARG/cnt/ times, starting with          the value <ARG/a/, and using the result of one iteration as          the argument in the next. Recursively, we have          <CODE>          iterate f cnt v = iterate f (cnt-1) (f v)          iterate f 0 v = v          </CODE>          Raises the <EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/ exception if          <ARG/cnt/ is negative.    <SPEC>      <VAL>repeat<TY>((int * 'a) -> 'a) -> int -> 'a -> 'a      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/        <COMMENT>          <PROTOTY>          repeat <ARG/f/ <ARG/cnt/ <ARG/a/          </PROTOTY>          is similar to <CD/iterate/ except that the function <ARG/f/          is also passed the iteration index. In particular, it is          equivalent to:          <CODE>          #2(iterate (fn (i,v) => (i+1,f(i,v))) cnt (0,init))          </CODE>    <SPEC>      <VAL>for<TY>((int * 'a) -> 'a) -> (int * int * int) -> 'a -> 'a      <RAISES><EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/        <COMMENT>          <PROTOTY>          for <ARG/f/ (<ARG/start/, <ARG/stop/, <ARG/inc/) <ARG/a/          </PROTOTY>          provides more control over the range and step-size involved          in the interation. Recursively, we have          <CODE>          for f (start,stop,inc) a = for f (start+inc,stop,inc) (f(start,a))          </CODE>          halting when <MATH/<ARG/start/ &GREATER; <ARG/stop// for          negative <ARG/inc/ and halting when           <MATH/<ARG/stop/ &GREATER; <ARG/start// for positive <ARG/inc/.          If <ARG/inc/ is zero, <ARG/start/ and <ARG/~TOP/ must be equal,          and we have          <CODE>          for f (start,stop,0) a = f(start,a)          </CODE>          Raises <EXNREF STRID="General" DOCUMENT=SML-BASIS-DOC/Fail/ if either <ARG/inc/ is          non-positive and <MATH/<ARG/stop/ &GREATER; <ARG/start//,           or if <ARG/inc/ is non-negative and          <MATH/<ARG/start/ &GREATER; <ARG/stop//.</STRUCTURE></INTERFACE>
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