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import Type
import Stream
)abbrev package YSTREAM ParadoxicalCombinatorsForStreams
++ Computation of fixed points of mappings on streams
++ Author: Burge, Watt (revised by Williamson)
++ Date Created: 1986
++ Date Last Updated: 21 October 1989
++ Keywords: stream, fixed point
++ Examples:
++ References:
ParadoxicalCombinatorsForStreams(A):Exports == Implementation where
  ++ This package implements fixed-point computations on streams.
  A  :   Type
  ST ==> Stream
  L  ==> List
  I  ==> Integer
 
  Exports ==> with
    Y: (ST A -> ST A) -> ST A
      ++ Y(f) computes a fixed point of the function f.
    Y: (L ST A -> L ST A,I) -> L ST A
      ++ Y(g,n) computes a fixed point of the function g, where g takes
      ++ a list of n streams and returns a list of n streams.
 
  Implementation ==> add
    import %head: ST A -> A    from Foreign Builtin
    import %tail: ST A -> ST A from Foreign Builtin
 
    Y f ==
      y : ST A := %pair(0$I,0$I)$Foreign(Builtin)
      j := f y
      %store(%head y,frst j)$Foreign(Builtin)
      %store(%tail y,rst j)$Foreign(Builtin)
      y
 
    Y(g,n) ==
      x : L ST A := [%pair(0$I,0$I)$Foreign(Builtin) for i in 1..n]
      j := g x
      for xi in x for ji in j repeat
        %store(%head xi,frst ji)$Foreign(Builtin)
        %store(%tail xi,rst ji)$Foreign(Builtin)
      x

