The benefits of programming in a functional style are well known. In particular, algorithms that are expressed as compositions of functions operating on series/vectors/streams of data elements are much easier to understand and modify than equivalent algorithms expressed as loops. Unfortunately, many programmers hesitate to use series expressions. In part, this is due to the fact that series expressions are typically implemented very inefficiently.A Common Lisp macro package (called Series) has been implemented that can evaluate a wide class of series expressions very efficiently by transforming them into iterative loops. When using this class of series expressions, programmers can obtain the advantages of expressing computations as series expressions without incurring any run-time overhead.http://series.sourceforge.net/My translation into TclReading the documentation on SERIES, I started off with what they call scanners. The script below presents Tcl procedures that create a "series". For the sake of this page: a series is a procedure that returns the next value in an (in principle) endless series of values.Currently they have two subcommands:- next: return the next value
- restart: start from the beginning
- simple arithmetic progressions, like 1, 3, 5, 7, 9, 11, ... or 1, 3, 5, 1, 3, 5, ...
- function-based series, like the Fibonaci series
# rangefunc.tcl --
# Provide procedures that can return sequences of numbers (ranges,
# Fibonaci numbers ...) in a lazy way
#
namespace eval ::Series {
variable privcnt 0
}
# make-range --
# Make a range procedure
# Arguments:
# start Starting value
# end End value (if empty: infinite; defaults to {})
# step Step to take (defaults to 1)
# Returns:
# Name of the new procedure
#
proc ::Series::make-range {start {end {}} {step 1}} {
variable privcnt
interp alias {} ::Series::RANGE$privcnt {} ::Series::RANGE ::Series::RANGE$privcnt $start $end $step $start
set prev $privcnt
incr privcnt
return ::Series::RANGE$prev
}
# RANGE --
# Private procedure implementing a range
# Arguments:
# alias Alias for this range command
# start Starting value
# end End value (if empty: infinite; defaults to {})
# step Step to take (defaults to 1)
# current Current value
# cmd Command (subrange, next, restart)
# Returns:
# Value or a list of values
#
proc ::Series::RANGE {alias start end step current cmd} {
switch -- $cmd {
"next" {
set next [expr {$current+$step}]
if { $end != {} } {
if { $step > 0 && $next > $end } {
set next $start
}
if { $step < 0 && $next < $end } {
set next $start
}
}
interp alias {} $alias {} ::Series::RANGE $alias $start $end $step $next
return $current
}
"restart" {
interp alias {} $alias {} ::Series::RANGE $alias $start $end $step $step
}
default {
return -code error "Unknown subcommand: $cmd"
}
}
}
# make-fct-series --
# Make a procedure that generates a series via a function
# Arguments:
# fct Function to be invoked
# first First number
# values List of values with which to generate the second number
# Returns:
# Name of the new procedure
# Note:
# fct is the name of a function that behaves thus:
# - It accepts a list of values with which it can determine the _next_ value
# - It returns a list of two elements, the first is the new value
# and the second is the list of values for the next entry in the
# series
# See fibonaci for a simple example
#
proc ::Series::make-fct-series {fct first values} {
variable privcnt
interp alias {} ::Series::FCT$privcnt {} ::Series::FCT ::Series::FCT$privcnt $fct $first $values $values $first
set prev $privcnt
incr privcnt
return ::Series::FCT$prev
}
# FCT --
# Private procedure implementing a series determined by a function
# Arguments:
# alias Alias for this range command
# fct Name of the function to invoke
# firstvalue First value in the series
# initvalues Initial arguments to the function for determining the first value
# values Arguments to the function for determining the next value
# current Current value
# cmd Command (subrange, next, restart)
# Returns:
# Value or a list of values
#
proc ::Series::FCT {alias fct firstvalue initvalues values current cmd} {
switch -- $cmd {
"next" {
foreach {next newvalues} [$fct $values] break
interp alias {} $alias {} ::Series::FCT $alias $fct $firstvalue $initvalues $newvalues $next
return $current
}
"restart" {
interp alias {} $alias {} ::Series::FCT $alias $fct $firstvalue $initvalues $initvalues $firstvalue
}
default {
return -code error "Unknown subcommand: $cmd"
}
}
}
# fibonaci --
# Sample procedure to generate a series of numbers
# Arguments:
# values Arguments to the function for determining the next value
# Returns:
# List of two elements, the next value and the list of arguments for
# determining the value after that
#
proc fibonaci {values} {
foreach {first second} $values break
set next [expr {$first+$second}]
return [list $next [list $second $next]]
}
# main --
# Testing what we have sofar
#
set r [::Series::make-range 0 {} 1]
set x [$r next]
while { $x < 10 } {
puts $x
set x [$r next]
}
puts "Restarting ..."
$r restart
puts [$r next]
puts "New range"
set r [::Series::make-range 0 10 2]
set x [$r next]
set c 0
while { $c < 10 } {
puts $x
set x [$r next]
incr c
}
puts "Now somewhat adacious: Fibonaci series"
#
# Note: the start is somewhat different than usual - we want to capture
# the first value too
#
set f [::Series::make-fct-series fibonaci 1 {0 1}]
set c 0
while { $c < 30 } {
puts -nonewline "[$f next] "
incr c
if { $c == 10 } {
puts "\nRestart ..."
$f restart
}
}See also iterators, generators.iu2 - You might find interesting Python's addictive syntax for generators [1] and the itertools library [2]
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