Editing Module:Params

	---                                        ---
	---     LOCAL ENVIRONMENT                  ---
	---    ________________________________    ---
	---                                        ---



	--[[ Abstract utilities ]]--
	----------------------------


-- Helper function for `string.gsub()` (for managing zero-padded numbers)
local function zero_padded (str)
	return ('%03d%s'):format(#str, str)
end


-- Helper function for `table.sort()` (for natural sorting)
local function natural_sort (var1, var2)
	return tostring(var1):gsub('%d+', zero_padded) <
		tostring(var2):gsub('%d+', zero_padded)
end


-- Return a copy or a reference to a table
local function copy_or_ref_table (src, refonly)
	if refonly then return src end
	newtab = {}
	for key, val in pairs(src) do newtab[key] = val end
	return newtab
end


-- Remove some numeric elements from a table, shifting everything to the left
local function remove_numeric_keys (tbl, idx, len)
	local cache = {}
	local tmp = idx + len - 1
	for key, val in pairs(tbl) do
		if type(key) == 'number' and key >= idx then
			if key > tmp then cache[key - len] = val end
			tbl[key] = nil
		end
	end
	for key, val in pairs(cache) do tbl[key] = val end
end


-- Make a reduced copy of a table (shifting in both directions if necessary)
local function copy_table_reduced (tbl, idx, len)
	local ret = {}
	local tmp = idx + len - 1
	if idx > 0 then
		for key, val in pairs(tbl) do
			if type(key) ~= 'number' or key < idx then
				ret[key] = val
			elseif key > tmp then ret[key - len] = val end
		end
	elseif tmp > 0 then
		local nshift = 1 - idx
		for key, val in pairs(tbl) do
			if type(key) ~= 'number' then ret[key] = val
			elseif key > tmp then ret[key - tmp] = val
			elseif key < idx then ret[key + nshift] = val end
		end
	else
		for key, val in pairs(tbl) do
			if type(key) ~= 'number' or key > tmp then
				ret[key] = val
			elseif key < idx then ret[key + len] = val end
		end
	end
	return ret
end


-- Make an expanded copy of a table (shifting in both directions if necessary)
--[[
local function copy_table_expanded (tbl, idx, len)
	local ret = {}
	local tmp = idx + len - 1
	if idx > 0 then
		for key, val in pairs(tbl) do
			if type(key) ~= 'number' or key < idx then
				ret[key] = val
			else ret[key + len] = val end
		end
	elseif tmp > 0 then
		local nshift = idx - 1
		for key, val in pairs(tbl) do
			if type(key) ~= 'number' then ret[key] = val
			elseif key > 0 then ret[key + tmp] = val
			elseif key < 1 then ret[key + nshift] = val end
		end
	else
		for key, val in pairs(tbl) do
			if type(key) ~= 'number' or key > tmp then
				ret[key] = val
			else ret[key - len] = val end
		end
	end
	return ret
end
]]--


-- Move a key from a table to another, but only if under a different name and
-- always parsing numeric strings as numbers
local function steal_if_renamed (val, src, skey, dest, dkey)
	local realkey = tonumber(dkey) or dkey:match'^%s*(.-)%s*$'
	if skey ~= realkey then
		dest[realkey] = val
		src[skey] = nil
	end
end



	--[[ Public strings ]]--
	------------------------


-- Special match keywords (functions and modifiers MUST avoid these names)
local mkeywords = {
	['or'] = 0,
	pattern = 1,
	plain = 2,
	strict = 3
}


-- Sort functions (functions and modifiers MUST avoid these names)
local sortfunctions = {
	--alphabetically = false, -- Simply uncommenting enables the option
	naturally = natural_sort
}


-- Callback styles for the `mapping_*` and `renaming_*` class of modifiers
-- (functions and modifiers MUST avoid these names)
--[[

Meanings of the columns:

  col[1] = Loop type (0-3)
  col[2] = Number of module arguments that the style requires (1-3)
  col[3] = Minimum number of sequential parameters passed to the callback
  col[4] = Name of the callback parameter where to place each parameter name
  col[5] = Name of the callback parameter where to place each parameter value
  col[6] = Argument in the modifier's invocation that will override `col[4]`
  col[7] = Argument in the modifier's invocation that will override `col[5]`

A value of `-1` indicates that no meaningful value is stored (i.e. `nil`)

]]--
local mapping_styles = {
	names_and_values = { 3, 2, 2, 1, 2, -1, -1 },
	values_and_names = { 3, 2, 2, 2, 1, -1, -1 },
	values_only = { 1, 2, 1, -1, 1, -1, -1 },
	names_only = { 2, 2, 1, 1, -1, -1, -1 },
	names_and_values_as = { 3, 4, 0, -1, -1, 2, 3 },
	names_only_as = { 2, 3, 0, -1, -1, 2, -1 },
	values_only_as = { 1, 3, 0, -1, -1, -1, 2 },
	blindly = { 0, 2, 0, -1, -1, -1, -1 }
}


-- Memory slots (functions and modifiers MUST avoid these names)
local memoryslots = {
	i = 'itersep',
	l = 'lastsep',
	p = 'pairsep',
	h = 'header',
	f = 'footer',
	n = 'ifngiven'
}


-- Possible trimming modes for the `parsing` modifier
local trim_parse_opts = {
	trim_none = { false, false },
	trim_positional = { false, true },
	trim_named = { true, false },
	trim_all = { true, true }
}


-- Possible string modes for the iteration separator in the `parsing` and
-- `reinterpreting` modifiers
local isep_parse_opts = {
	with_pattern_isep = false,
	with_plain_isep = true
}


-- Possible string modes for the key-value separator in the `parsing` and
-- `reinterpreting` modifiers
local psep_parse_opts = {
	with_pattern_psep = false,
	with_plain_psep = true
}


-- Functions and modifiers MUST avoid these names too: `let`



	--[[ Module's private environment ]]--
	--------------------------------------


-- Hard-coded name of the module (to avoid going through `frame:getTitle()`)
local modulename = 'Module:Params'


-- The functions listed here declare that they don't need the `frame.args`
-- metatable to be copied into a regular table; if they are modifiers they also
-- guarantee that they will make their own (modified) copy available
local refpipe = {
	count = true,
	value_of = true,
	list = true,
	list_values = true,
	coins = true,
	for_each = true,
	call_for_each_group = true
}


-- The functions listed here declare that they don't need the
-- `frame:getParent().args` metatable to be copied into a regular table; if 
-- they are modifiers they also guarantee that they will make their own
-- (modified) copy available
local refparams = {
	--inserting = true,
	with_name_matching = true,
	grouping_by_calling = true,
	combining_by_calling = true,
	count = true,
	concat_and_call = true,
	concat_and_invoke = true,
	concat_and_magic = true,
	value_of = true,
	call_for_each_group = true
}


-- Maximum number of numeric parameters that can be filled, if missing (we
-- chose an arbitrary number for this constant; you can discuss about its
-- optimal value at Module talk:Params)
local maxfill = 1024


-- The private table of functions
local library = {}


-- Functions and modifiers that can only be invoked in first position
local static_iface = {}


-- Create a new context
local function context_new (frame)
	local ctx = {}
	ctx.frame = frame
	ctx.oparams = frame.args
	ctx.firstposonly = static_iface
	ctx.iterfunc = pairs
	ctx.sorttype = 0
	ctx.n_parents = 0
	ctx.n_children = 0
	ctx.n_available = maxfill
	return ctx
end


-- Move to the next action within the user-given list
local function context_iterate (ctx, n_forward)
	local nextfn
	if ctx.pipe[n_forward] ~= nil then
		nextfn = ctx.pipe[n_forward]:match'^%s*(.*%S)'
	end
	if nextfn == nil then error(modulename ..
		': You must specify a function to call', 0) end
	if library[nextfn] == nil then
		if ctx.firstposonly[nextfn] == nil then error(modulename ..
			': The function ‘' .. nextfn .. '’ does not exist', 0)
		else error(modulename .. ': The ‘' .. nextfn ..
			'’ directive can only appear in first position', 0)
		end
	end
	remove_numeric_keys(ctx.pipe, 1, n_forward)
	return library[nextfn]
end


-- Main loop
local function main_loop (ctx, start_with)
	local fn = start_with
	repeat fn = fn(ctx) until not fn
	if ctx.n_parents > 0 then error(modulename ..
		': One or more ‘merging_substack’ directives are missing', 0) end
	if ctx.n_children > 0 then error(modulename ..
		', For some of the snapshots either the ‘flushing’ directive is missing or a group has not been properly closed with ‘merging_substack’', 0) end
end


-- Add a new stack of parameters to `ctx.children`
local function push_cloned_stack (ctx, tbl)
	local newparams = {}
	local currsnap = ctx.n_children + 1
	if ctx.children == nil then ctx.children = { newparams }
	else ctx.children[currsnap] = newparams end
	for key, val in pairs(tbl) do newparams[key] = val end
	ctx.n_children = currsnap
end


-- Parse optional user arguments of type `...|[let]|[...][number of additional
-- parameters]|[parameter 1]|[parameter 2]|[...]`
local function load_child_opts (src, start_from, append_after)
	local names
	local tmp
	local tbl = {}
	local pin = start_from
	if src[pin] ~= nil and src[pin]:match'^%s*let%s*$' then
		names = {}
		repeat
			tmp = src[pin + 1] or ''
			names[tonumber(tmp) or tmp:match'^%s*(.-)%s*$' or ''] =
				src[pin + 2]
			pin = pin + 3
		until src[pin] == nil or not src[pin]:match'^%s*let%s*$'
	end
	tmp = tonumber(src[pin])
	if tmp ~= nil then
		if tmp < 0 then tmp = -1 end
		local shf = append_after - pin
		for idx = pin + 1, pin + tmp do tbl[idx + shf] = src[idx] end
		pin = pin + tmp + 1
	end
	if names ~= nil then
		for key, val in pairs(names) do tbl[key] = val end
	end
	return tbl, pin
end


-- Load the optional arguments of some of the `mapping_*` and `renaming_*`
-- class of modifiers
local function load_callback_opts (src, n_skip, default_style)
	local style
	local shf
	local tmp = src[n_skip + 1]
	if tmp ~= nil then style = mapping_styles[tmp:match'^%s*(.-)%s*$'] end
	if style == nil then
		style = default_style
		shf = n_skip - 1
	else shf = n_skip end
	local n_exist = style[3]
	local karg = style[4]
	local varg = style[5]
	tmp = style[6]
	if tmp > -1 then
		tmp = src[tmp + shf]
		karg = tonumber(tmp)
		if karg == nil then karg = tmp:match'^%s*(.-)%s*$'
		else n_exist = math.max(n_exist, karg) end
	end
	tmp = style[7]
	if tmp > -1 then
		tmp = src[tmp + shf]
		varg = tonumber(tmp)
		if varg == nil then varg = tmp:match'^%s*(.-)%s*$'
		else n_exist = math.max(n_exist, varg) end
	end
	local dest, nargs = load_child_opts(src, style[2] + shf, n_exist)
	tmp = style[1]
	if (tmp == 3 or tmp == 2) and dest[karg] ~= nil then
		tmp = tmp - 2 end
	if (tmp == 3 or tmp == 1) and dest[varg] ~= nil then
		tmp = tmp - 1 end
	return dest, nargs, tmp, karg, varg
end


-- Parse the arguments of some of the `mapping_*` and `renaming_*` class of
-- modifiers
local function load_replace_args (opts, fname)
	if opts[1] == nil then error(modulename ..
		', ‘' .. fname .. '’: No pattern string was given', 0) end
	if opts[2] == nil then error(modulename ..
		', ‘' .. fname .. '’: No replacement string was given', 0) end
	local ptn = opts[1]
	local repl = opts[2]
	local argc = 3
	local nmax = tonumber(opts[3])
	if nmax ~= nil or (opts[3] or ''):match'^%s*$' ~= nil then argc = 4 end
	local flg = opts[argc]
	if flg ~= nil then flg = mkeywords[flg:match'^%s*(.-)%s*$'] end
	if flg == 0 then flg = nil elseif flg ~= nil then argc = argc + 1 end
	return ptn, repl, nmax, flg == 3, argc, (nmax ~= nil and nmax < 1) or
		(flg == 3 and ptn == repl)
end


-- Parse the arguments of the `with_*_matching` class of modifiers
local function load_pattern_args (opts, fname)
	local state = 0
	local cnt = 1
	local keyw
	local nptns = 0
	local ptns = {}
	for _, val in ipairs(opts) do
		if state == 0 then
			nptns = nptns + 1
			ptns[nptns] = { val, false, false }
			state = -1
		else
			keyw = val:match'^%s*(.*%S)'
			if keyw == nil or mkeywords[keyw] == nil or (
				state > 0 and mkeywords[keyw] > 0
			) then break
			else
				state = mkeywords[keyw]
				if state > 1 then ptns[nptns][2] = true end
				if state == 3 then ptns[nptns][3] = true end
			end
		end
		cnt = cnt + 1
	end
	if state == 0 then error(modulename .. ', ‘' .. fname ..
		'’: No pattern was given', 0) end
	return ptns, nptns, cnt
end


-- Load the optional arguments of the `parsing` and `reinterpreting` modifiers
local function load_parse_opts (opts, start_from)
	local argc = start_from
	local tmp
	local optslots = { true, true, true }
	local noptslots = 3
	local trimn = true
	local trimu = false
	local iplain = true
	local pplain = true
	local isp = '|'
	local psp = '='
	repeat
		noptslots = noptslots - 1
		tmp = opts[argc]
		if tmp == nil then break end
		tmp = tmp:match'^%s*(.-)%s*$'
		if optslots[1] ~= nil and trim_parse_opts[tmp] ~= nil then
			tmp = trim_parse_opts[tmp]
			trimn = tmp[1]
			trimu = tmp[2]
			optslots[1] = nil
		elseif optslots[2] ~= nil and isep_parse_opts[tmp] ~= nil then
			argc = argc + 1
			iplain = isep_parse_opts[tmp]
			isp = opts[argc]
			optslots[2] = nil
		elseif optslots[3] ~= nil and psep_parse_opts[tmp] ~= nil then
			argc = argc + 1
			pplain = psep_parse_opts[tmp]
			psp = opts[argc]
			optslots[3] = nil
		else break end
		argc = argc + 1
	until noptslots < 1
	return isp, iplain, psp, pplain, trimn, trimu, argc
end


-- Map parameters' values using a custom callback and a referenced table
local value_maps = {
	[0] = function (tbl, margs, karg, varg, fn)
		for key in pairs(tbl) do tbl[key] = fn() end
	end,
	[1] = function (tbl, margs, karg, varg, fn)
		for key, val in pairs(tbl) do
			margs[varg] = val
			tbl[key] = fn()
		end
	end,
	[2] = function (tbl, margs, karg, varg, fn)
		for key in pairs(tbl) do
			margs[karg] = key
			tbl[key] = fn()
		end
	end,
	[3] = function (tbl, margs, karg, varg, fn)
		for key, val in pairs(tbl) do
			margs[karg] = key
			margs[varg] = val
			tbl[key] = fn()
		end
	end
}


-- Private table for `map_names()`
local name_thieves_maps = {
	[0] = function (cache, tbl, rargs, karg, varg, fn)
		for key, val in pairs(tbl) do
			steal_if_renamed(val, tbl, key, cache, fn())
		end
	end,
	[1] = function (cache, tbl, rargs, karg, varg, fn)
		for key, val in pairs(tbl) do
			rargs[varg] = val
			steal_if_renamed(val, tbl, key, cache, fn())
		end
	end,
	[2] = function (cache, tbl, rargs, karg, varg, fn)
		for key, val in pairs(tbl) do
			rargs[karg] = key
			steal_if_renamed(val, tbl, key, cache, fn())
		end
	end,
	[3] = function (cache, tbl, rargs, karg, varg, fn)
		for key, val in pairs(tbl) do
			rargs[karg] = key
			rargs[varg] = val
			steal_if_renamed(val, tbl, key, cache, fn())
		end
	end
}


-- Map parameters' names using a custom callback and a referenced table
local function map_names (tbl, rargs, karg, varg, looptype, fn)
	local cache = {}
	name_thieves_maps[looptype](cache, tbl, rargs, karg, varg, fn)
	for key, val in pairs(cache) do tbl[key] = val end
end


-- Return a new table that contains `src` regrouped according to the numeric
-- suffixes in its keys
local function make_groups (src)
	-- NOTE: `src` might be the original metatable!
	local tmp
	local prefix
	local gid
	local groups = {}
	for key, val in pairs(src) do
		-- `key` must only be a string or a number...
		gid = tonumber(key)
		if gid == nil then
			prefix, gid = key:match'^%s*(.-)%s*(%-?%d*)%s*$'
			gid = tonumber(gid) or ''
		else prefix = '' end
		if groups[gid] == nil then groups[gid] = {} end
		tmp = tonumber(prefix)
		if tmp ~= nil then
			if tmp < 1 then prefix = tmp - 1 else prefix = tmp end
		end
		groups[gid][prefix] = val
	end
	return groups
end


-- Populate a table by parsing a parameter string
local function parse_parameter_string (tbl, str, isp, ipl, psp, ppl, trn, tru)
	local key
	local val
	local spos1
	local spos2
	local pos1
	local pos2
	local pos3 = 0
	local idx = 1
	local lenplone = #str + 1
	if isp == nil or isp == '' then
		if psp == nil or psp == '' then
			if tru then tbl[idx] = str:match'^%s*(.-)%s*$'
			else tbl[idx] = str end
			return tbl
		end
		spos1, spos2 = str:find(psp, 1, ppl)
		if spos1 == nil then
			key = idx
			if tru then val = str:match'^%s*(.-)%s*$'
			else val = str end
			idx = idx + 1
		else
			key = str:sub(1, spos1 - 1)
			key = tonumber(key) or key:match'^%s*(.-)%s*$'
			val = str:sub(spos2 + 1)
			if trn then val = val:match'^%s*(.-)%s*$' end
		end
		tbl[key] = val
		return tbl
	end
	if psp == nil or psp == '' then
		repeat
			pos1 = pos3 + 1
			pos2, pos3 = str:find(isp, pos1, ipl)
			val = str:sub(pos1, (pos2 or lenplone) - 1)
			if tru then val = val:match'^%s*(.-)%s*$' end
			tbl[idx] = val
			idx = idx + 1
		until pos2 == nil
		return tbl
	end
	repeat
		pos1 = pos3 + 1
		pos2, pos3 = str:find(isp, pos1, ipl)
		val = str:sub(pos1, (pos2 or lenplone) - 1)
		spos1, spos2 = val:find(psp, 1, ppl)
		if spos1 == nil then
			key = idx
			if tru then val = val:match'^%s*(.-)%s*$' end
			idx = idx + 1
		else
			key = val:sub(1, spos1 - 1)
			key = tonumber(key) or key:match'^%s*(.-)%s*$'
			val = val:sub(spos2 + 1)
			if trn then val = val:match'^%s*(.-)%s*$' end
		end
		tbl[key] = val
	until pos2 == nil
	return tbl
end


-- Concatenate the numeric keys from the table of parameters to the numeric
-- keys from the table of options; non-numeric keys from the table of options
-- will prevail over colliding non-numeric keys from the table of parameters
local function concat_params (ctx)
	local tbl = ctx.params
	local nmax = table.maxn(ctx.pipe)
	local retval = {}
	if ctx.subset == 1 then
		-- We need only the sequence
		for key, val in ipairs(tbl) do retval[key + nmax] = val end
	else
		if ctx.subset == -1 then
			for key in ipairs(tbl) do tbl[key] = nil end
		end
		for key, val in pairs(tbl) do
			if type(key) == 'number' and key > 0 then
				retval[key + nmax] = val
			else retval[key] = val end
		end
	end
	for key, val in pairs(ctx.pipe) do retval[key] = val end
	return retval
end


-- Flush the parameters by calling a custom function for each value (after this
-- function has been invoked `ctx.params` will be no longer usable)
local function flush_params (ctx, fn)
	local tbl = ctx.params
	if ctx.subset == 1 then
		for key, val in ipairs(tbl) do fn(key, val) end
		return
	end
	if ctx.subset == -1 then
		for key, val in ipairs(tbl) do tbl[key] = nil end
	end
	if ctx.sorttype > 0 then
		local nums = {}
		local words = {}
		local nn = 0
		local nw = 0
		for key, val in pairs(tbl) do
			if type(key) == 'number' then
				nn = nn + 1
				nums[nn] = key
			else
				nw = nw + 1
				words[nw] = key
			end
		end
		table.sort(nums)
		table.sort(words, natural_sort)
		if ctx.sorttype == 2 then
			for idx = 1, nw do fn(words[idx], tbl[words[idx]]) end
			for idx = 1, nn do fn(nums[idx], tbl[nums[idx]]) end
			return
		end
		for idx = 1, nn do fn(nums[idx], tbl[nums[idx]]) end
		for idx = 1, nw do fn(words[idx], tbl[words[idx]]) end
		return
	end
	if ctx.subset ~= -1 then
		for key, val in ipairs(tbl) do
			fn(key, val)
			tbl[key] = nil
		end
	end
	for key, val in pairs(tbl) do fn(key, val) end
end



	--[[ Modifiers ]]--
	-----------------------------


-- Syntax:  #invoke:params|sequential|pipe to
library.sequential = function (ctx)
	if ctx.subset == -1 then error(modulename ..
		': The two directives ‘non-sequential’ and ‘sequential’ are in contradiction with each other', 0) end
	if ctx.sorttype > 0 then error(modulename ..
		': The ‘all_sorted’ and ‘reassorted’ directives are redundant when followed by ‘sequential’', 0) end
	ctx.iterfunc = ipairs
	ctx.subset = 1
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|non-sequential|pipe to
library['non-sequential'] = function (ctx)
	if ctx.subset == 1 then error(modulename ..
		': The two directives ‘sequential’ and ‘non-sequential’ are in contradiction with each other', 0) end
	ctx.iterfunc = pairs
	ctx.subset = -1
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|all_sorted|pipe to
library.all_sorted = function (ctx)
	if ctx.subset == 1 then error(modulename ..
		': The ‘all_sorted’ directive is redundant after ‘sequential’', 0) end
	if ctx.sorttype == 2 then error(modulename ..
		': The two directives ‘reassorted’ and ‘sequential’ are in contradiction with each other', 0) end
	ctx.sorttype = 1
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|reassorted|pipe to
library.reassorted = function (ctx)
	if ctx.subset == 1 then error(modulename ..
		': The ‘reassorted’ directive is redundant after ‘sequential’', 0) end
	if ctx.sorttype == 1 then error(modulename ..
		': The two directives ‘sequential’ and ‘reassorted’ are in contradiction with each other', 0) end
	ctx.sorttype = 2
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|setting|directives|...|pipe to
library.setting = function (ctx)
	local opts = ctx.pipe
	local cmd = opts[1]
	if cmd ~= nil then
		cmd = cmd:gsub('%s+', ''):gsub('/+', '/'):match'^/*(.*[^/])'
	end
	if cmd == nil then error(modulename ..
		', ‘setting’: No directive was given', 0) end
	local sep = string.byte('/')
	local argc = 2
	local dest = {}
	local vname
	local chr
	for idx = 1, #cmd do
		chr = cmd:byte(idx)
		if chr == sep then
			for key, val in ipairs(dest) do
				ctx[val] = opts[argc]
				dest[key] = nil
			end
			argc = argc + 1
		else
			vname = memoryslots[string.char(chr)]
			if vname == nil then error(modulename ..
				', ‘setting’: Unknown slot ‘' ..
				string.char(chr) .. '’', 0) end
			table.insert(dest, vname)
		end
	end
	for key, val in ipairs(dest) do ctx[val] = opts[argc] end
	return context_iterate(ctx, argc + 1)
end


-- Syntax:  #invoke:params|squeezing|pipe to
library.squeezing = function (ctx)
	local tbl = ctx.params
	local store = {}
	local indices = {}
	local newlen = 0
	for key, val in pairs(tbl) do
		if type(key) == 'number' then
			newlen = newlen + 1
			indices[newlen] = key
			store[key] = val
			tbl[key] = nil
		end
	end
	table.sort(indices)
	for idx = 1, newlen do tbl[idx] = store[indices[idx]] end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|filling_the_gaps|pipe to
library.filling_the_gaps = function (ctx)
	local tbl = ctx.params
	local nmin = 1
	local nmax = nil
	local nnums = -1
	local tmp = {}
	for key, val in pairs(tbl) do
		if type(key) == 'number' then
			if nmax == nil then
				if key < nmin then nmin = key end
				nmax = key
			elseif key > nmax then nmax = key
			elseif key < nmin then nmin = key end
			nnums = nnums + 1
			tmp[key] = val
		end
	end
	if nmax ~= nil and nmax - nmin > nnums then
		ctx.n_available = ctx.n_available + nmin + nnums - nmax
		if ctx.n_available < 0 then error(modulename ..
			', ‘filling_the_gaps’: It is possible to fill at most ' ..
			tostring(maxfill) .. ' parameters', 0) end
		for idx = nmin, nmax, 1 do tbl[idx] = '' end
		for key, val in pairs(tmp) do tbl[key] = val end
	end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|clearing|pipe to
library.clearing = function (ctx)
	local tbl = ctx.params
	local numerics = {}
	for key, val in pairs(tbl) do
		if type(key) == 'number' then
			numerics[key] = val
			tbl[key] = nil
		end
	end
	for key, val in ipairs(numerics) do tbl[key] = val end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|cutting|left cut|right cut|pipe to
library.cutting = function (ctx)
	local lcut = tonumber(ctx.pipe[1])
	if lcut == nil then error(modulename ..
		', ‘cutting’: Left cut must be a number', 0) end
	local rcut = tonumber(ctx.pipe[2])
	if rcut == nil then error(modulename ..
		', ‘cutting’: Right cut must be a number', 0) end
	local tbl = ctx.params
	local len = #tbl
	if lcut < 0 then lcut = len + lcut end
	if rcut < 0 then rcut = len + rcut end
	local tot = lcut + rcut
	if tot > 0 then
		local cache = {}
		if tot >= len then
			for key in ipairs(tbl) do tbl[key] = nil end
			tot = len
		else
			for idx = len - rcut + 1, len, 1 do tbl[idx] = nil end
			for idx = 1, lcut, 1 do tbl[idx] = nil end
		end
		for key, val in pairs(tbl) do
			if type(key) == 'number' and key > 0 then
				if key > len then cache[key - tot] = val
				else cache[key - lcut] = val end
				tbl[key] = nil
			end
		end
		for key, val in pairs(cache) do tbl[key] = val end
	end
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|cropping|left crop|right crop|pipe to
library.cropping = function (ctx)
	local lcut = tonumber(ctx.pipe[1])
	if lcut == nil then error(modulename ..
		', ‘cropping’: Left crop must be a number', 0) end
	local rcut = tonumber(ctx.pipe[2])
	if rcut == nil then error(modulename ..
		', ‘cropping’: Right crop must be a number', 0) end
	local tbl = ctx.params
	local nmin
	local nmax
	for key in pairs(tbl) do
		if type(key) == 'number' then
			if nmin == nil then
				nmin = key
				nmax = key
			elseif key > nmax then nmax = key
			elseif key < nmin then nmin = key end
		end
	end
	if nmin ~= nil then
		local len = nmax - nmin + 1
		if lcut < 0 then lcut = len + lcut end
		if rcut < 0 then rcut = len + rcut end
		if lcut + rcut - len > -1 then
			for key in pairs(tbl) do
				if type(key) == 'number' then tbl[key] = nil end
			end
		elseif lcut + rcut > 0 then
			for idx = nmax - rcut + 1, nmax do tbl[idx] = nil end
			for idx = nmin, nmin + lcut - 1 do tbl[idx] = nil end
			local lshift = nmin + lcut - 1
			if lshift > 0 then
				for idx = lshift + 1, nmax, 1 do
					tbl[idx - lshift] = tbl[idx]
					tbl[idx] = nil
				end
			end
		end
	end
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|purging|start offset|length|pipe to
library.purging = function (ctx)
	local idx = tonumber(ctx.pipe[1])
	if idx == nil then error(modulename ..
		', ‘purging’: Start offset must be a number', 0) end
	local len = tonumber(ctx.pipe[2])
	if len == nil then error(modulename ..
		', ‘purging’: Length must be a number', 0) end
	local tbl = ctx.params
	if len < 1 then
		len = len + table.maxn(tbl)
		if idx > len then return context_iterate(ctx, 3) end
		len = len - idx + 1
	end
	ctx.params = copy_table_reduced(tbl, idx, len)
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|backpurging|start offset|length|pipe to
library.backpurging = function (ctx)
	local last = tonumber(ctx.pipe[1])
	if last == nil then error(modulename ..
		', ‘backpurging’: Start offset must be a number', 0) end
	local len = tonumber(ctx.pipe[2])
	if len == nil then error(modulename ..
		', ‘backpurging’: Length must be a number', 0) end
	local idx
	local tbl = ctx.params
	if len > 0 then
		idx = last - len + 1
	else
		for key in pairs(tbl) do
			if type(key) == 'number' and (idx == nil or
				key < idx) then idx = key end
		end
		if idx == nil then return context_iterate(ctx, 3) end
		idx = idx - len
		if last < idx then return context_iterate(ctx, 3) end
		len = last - idx + 1
	end
	ctx.params = copy_table_reduced(ctx.params, idx, len)
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|rotating|pipe to
library.rotating = function (ctx)
	local tbl = ctx.params
	local numerics = {}
	local nmax = 0
	for key, val in pairs(tbl) do
		if type(key) == 'number' then
			numerics[key] = val
			tbl[key] = nil
			if key > nmax then nmax = key end
		end
	end
	for key, val in pairs(numerics) do tbl[nmax - key + 1] = val end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|pivoting|pipe to
--[[
library.pivoting = function (ctx)
	local tbl = ctx.params
	local shift = #tbl + 1
	if shift < 2 then return library.rotating(ctx) end
	local numerics = {}
	for key, val in pairs(tbl) do
		if type(key) == 'number' then
			numerics[key] = val
			tbl[key] = nil
		end
	end
	for key, val in pairs(numerics) do tbl[shift - key] = val end
	return context_iterate(ctx, 1)
end
]]--


-- Syntax:  #invoke:params|mirroring|pipe to
--[[
library.mirroring = function (ctx)
	local tbl = ctx.params
	local numerics = {}
	local nmax
	local nmin
	for key, val in pairs(tbl) do
		if type(key) == 'number' then
			numerics[key] = val
			tbl[key] = nil
			if nmax == nil then
				nmax = key
				nmin = key
			elseif key > nmax then nmax = key
			elseif key < nmin then nmin = key end
		end
	end
	for key, val in pairs(numerics) do tbl[nmax + nmin - key] = val end
	return context_iterate(ctx, 1)
end
]]--


-- Syntax:  #invoke:params|swapping|pipe to
--[[
library.swapping = function (ctx)
	local tbl = ctx.params
	local cache = {}
	local nsize = 0
	local tmp
	for key in pairs(tbl) do
		if type(key) == 'number' then
			nsize = nsize + 1
			cache[nsize] = key
		end
	end
	table.sort(cache)
	for idx = math.floor(nsize / 2), 1, -1 do
		tmp = tbl[cache[idx] ]
		tbl[cache[idx] ] = tbl[cache[nsize - idx + 1] ]
		tbl[cache[nsize - idx + 1] ] = tmp
	end
	return context_iterate(ctx, 1)
end
]]--


-- Syntax:  #invoke:params|sorting_sequential_values|[criterion]|pipe to
library.sorting_sequential_values = function (ctx)
	local sortfn
	if ctx.pipe[1] ~= nil then sortfn = sortfunctions[ctx.pipe[1]] end
	if sortfn then table.sort(ctx.params, sortfn)
	else table.sort(ctx.params) end -- i.e. either `false` or `nil`
	if sortfn == nil then return context_iterate(ctx, 1) end
	return context_iterate(ctx, 2)
end


-- Syntax:  #invoke:params|inserting|position|how many|...|pipe to
--[[
library.inserting = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable! As a modifier,
	-- this function MUST create a copy of it before returning
	local idx = tonumber(ctx.pipe[1])
	if idx == nil then error(modulename ..
		', ‘inserting’: Position must be a number', 0) end
	local len = tonumber(ctx.pipe[2])
	if len == nil or len < 1 then error(modulename ..
		', ‘inserting’: The amount must be a number greater than zero', 0) end
	local opts = ctx.pipe
	local tbl = copy_table_expanded(ctx.params, idx, len)
	for key = idx, idx + len - 1 do tbl[key] = opts[key - idx + 3] end
	ctx.params = tbl
	return context_iterate(ctx, len + 3)
end
]]--


-- Syntax:  #invoke:params|imposing|name|value|pipe to
library.imposing = function (ctx)
	if ctx.pipe[1] == nil then error(modulename ..
		', ‘imposing’: Missing parameter name to impose', 0) end
	local key = ctx.pipe[1]:match'^%s*(.-)%s*$'
	ctx.params[tonumber(key) or key] = ctx.pipe[2]
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|providing|name|value|pipe to
library.providing = function (ctx)
	if ctx.pipe[1] == nil then error(modulename ..
		', ‘providing’: Missing parameter name to provide', 0) end
	local key = ctx.pipe[1]:match'^%s*(.-)%s*$'
	key = tonumber(key) or key
	if ctx.params[key] == nil then ctx.params[key] = ctx.pipe[2] end
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|discarding|name|[how many]|pipe to
library.discarding = function (ctx)
	if ctx.pipe[1] == nil then error(modulename ..
		', ‘discarding’: Missing parameter name to discard', 0) end
	local key = ctx.pipe[1]
	local len = tonumber(ctx.pipe[2])
	if len == nil then
		ctx.params[tonumber(key) or key:match'^%s*(.-)%s*$'] = nil
		return context_iterate(ctx, 2)
	end
	key = tonumber(key)
	if key == nil then error(modulename ..
		', ‘discarding’: A range was provided, but the initial parameter name is not numeric', 0) end
	if len < 1 then error(modulename ..
		', ‘discarding’: A range can only be a number greater than zero', 0) end
	for idx = key, key + len - 1 do ctx.params[idx] = nil end
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|excluding_non-numeric_names|pipe to
library['excluding_non-numeric_names'] = function (ctx)
	local tmp = ctx.params
	for key, val in pairs(tmp) do
		if type(key) ~= 'number' then tmp[key] = nil end
	end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|excluding_numeric_names|pipe to
library.excluding_numeric_names = function (ctx)
	local tmp = ctx.params
	for key, val in pairs(tmp) do
		if type(key) == 'number' then tmp[key] = nil end
	end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|with_name_matching|target 1|[plain flag 1]|[or]
--            |[target 2]|[plain flag 2]|[or]|[...]|[target N]|[plain flag
--            N]|pipe to
library.with_name_matching = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable! As a modifier,
	-- this function MUST create a copy of it before returning
	local targets, nptns, argc = load_pattern_args(ctx.pipe, targets,
		'with_name_matching')
	local tmp
	local ptn
	local tbl = ctx.params
	local newparams = {}
	for idx = 1, nptns do
		ptn = targets[idx]
		if ptn[3] then
			tmp = tonumber(ptn[1]) or ptn[1]
			newparams[tmp] = tbl[tmp]
		else
			for key, val in pairs(tbl) do
				if tostring(key):find(ptn[1], 1, ptn[2]) then
					newparams[key] = val
				end
			end
		end
	end
	ctx.params = newparams
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|with_name_not_matching|target 1|[plain flag 1]
--            |[and]|[target 2]|[plain flag 2]|[and]|[...]|[target N]|[plain
--            flag N]|pipe to
library.with_name_not_matching = function (ctx)
	local targets, nptns, argc = load_pattern_args(ctx.pipe, targets,
		'with_name_not_matching')
	local tbl = ctx.params
	if nptns == 1 and targets[1][3] then
		local tmp = targets[1][1]
		tbl[tonumber(tmp) or tmp] = nil
		return context_iterate(ctx, argc)
	end
	local yesmatch
	local ptn
	for key in pairs(tbl) do
		yesmatch = true
		for idx = 1, nptns do
			ptn = targets[idx]
			if ptn[3] then
				if tostring(key) ~= ptn[1] then
					yesmatch = false
					break
				end
			elseif not tostring(key):find(ptn[1], 1, ptn[2]) then
				yesmatch = false
				break
			end
		end
		if yesmatch then tbl[key] = nil end
	end
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|with_value_matching|target 1|[plain flag 1]|[or]
--            |[target 2]|[plain flag 2]|[or]|[...]|[target N]|[plain flag
--            N]|pipe to
library.with_value_matching = function (ctx)
	local tbl = ctx.params
	local targets, nptns, argc = load_pattern_args(ctx.pipe, targets,
		'with_value_matching')
	local nomatch
	local ptn
	for key, val in pairs(tbl) do
		nomatch = true
		for idx = 1, nptns do
			ptn = targets[idx]
			if ptn[3] then
				if val == ptn[1] then
					nomatch = false
					break
				end
			elseif val:find(ptn[1], 1, ptn[2]) then
				nomatch = false
				break
			end
		end
		if nomatch then tbl[key] = nil end
	end
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|with_value_not_matching|target 1|[plain flag 1]
--            |[and]|[target 2]|[plain flag 2]|[and]|[...]|[target N]|[plain
--            flag N]|pipe to
library.with_value_not_matching = function (ctx)
	local tbl = ctx.params
	local targets, nptns, argc = load_pattern_args(ctx.pipe, targets,
		'with_value_not_matching')
	local yesmatch
	local ptn
	for key, val in pairs(tbl) do
		yesmatch = true
		for idx = 1, nptns do
			ptn = targets[idx]
			if ptn[3] then
				if val ~= ptn[1] then
					yesmatch = false
					break
				end
			elseif not val:find(ptn[1], 1, ptn[2]) then
				yesmatch = false
				break
			end
		end
		if yesmatch then tbl[key] = nil end
	end
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|trimming_values|pipe to
library.trimming_values = function (ctx)
	local tbl = ctx.params
	for key, val in pairs(tbl) do tbl[key] = val:match'^%s*(.-)%s*$' end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|mapping_by_calling|template name|[call
--            style]|[let]|[...][number of additional parameters]|[parameter
--            1]|[parameter 2]|[...]|[parameter N]|pipe to
library.mapping_by_calling = function (ctx)
	local opts = ctx.pipe
	local tname
	if opts[1] ~= nil then tname = opts[1]:match'^%s*(.*%S)' end
	if tname == nil then error(modulename ..
		', ‘mapping_by_calling’: No template name was provided', 0) end
	local margs, argc, looptype, karg, varg = load_callback_opts(opts, 1,
		mapping_styles.values_only)
	local model = { title = tname, args = margs }
	value_maps[looptype](ctx.params, margs, karg, varg, function ()
		return ctx.frame:expandTemplate(model)
	end)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|mapping_by_invoking|module name|function
--            name|[call style]|[let]|[...]|[number of additional
--            arguments]|[argument 1]|[argument 2]|[...]|[argument N]|pipe to
library.mapping_by_invoking = function (ctx)
	local opts = ctx.pipe
	local mname
	local fname
	if opts[1] ~= nil then mname = opts[1]:match'^%s*(.*%S)' end
	if mname == nil then error(modulename ..
		', ‘mapping_by_invoking’: No module name was provided', 0) end
	if opts[2] ~= nil then fname = opts[2]:match'^%s*(.*%S)' end
	if fname == nil then error(modulename ..
		', ‘mapping_by_invoking’: No function name was provided', 0) end
	local margs, argc, looptype, karg, varg = load_callback_opts(opts, 2,
		mapping_styles.values_only)
	local model = { title = 'Module:' .. mname, args = margs }
	local mfunc = require(model.title)[fname]
	if mfunc == nil then error(modulename ..
		', ‘mapping_by_invoking’: The function ‘' .. fname ..
		'’ does not exist', 0) end
	value_maps[looptype](ctx.params, margs, karg, varg, function ()
		return tostring(mfunc(ctx.frame:newChild(model)))
	end)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|mapping_by_magic|parser function|[call
--            style]|[let]|[...][number of additional arguments]|[argument
--            1]|[argument 2]|[...]|[argument N]|pipe to
library.mapping_by_magic = function (ctx)
	local opts = ctx.pipe
	local magic
	if opts[1] ~= nil then magic = opts[1]:match'^%s*(.*%S)' end
	if magic == nil then error(modulename ..
		', ‘mapping_by_magic’: No parser function was provided', 0) end
	local margs, argc, looptype, karg, varg = load_callback_opts(opts, 1,
		mapping_styles.values_only)
	value_maps[looptype](ctx.params, margs, karg, varg, function ()
		return ctx.frame:callParserFunction(magic, margs)
	end)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|mapping_by_replacing|target|replace|[count]|[plain
--            flag]|pipe to
library.mapping_by_replacing = function (ctx)
	local ptn, repl, nmax, is_strict, argc, die =
		load_replace_args(ctx.pipe, 'mapping_by_replacing')
	if die then return context_iterate(ctx, argc) end
	local tbl = ctx.params
	if is_strict then
		for key, val in pairs(tbl) do
			if val == ptn then tbl[key] = repl end
		end
	else
		if flg == 2 then
			-- Copied from Module:String's `str._escapePattern()`
			ptn = ptn:gsub('[%(%)%.%%%+%-%*%?%[%^%$%]]', '%%%0')
		end
		for key, val in pairs(tbl) do
			tbl[key] = val:gsub(ptn, repl, nmax)
		end
	end
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|renaming_by_calling|template name|[call
--            style]|[let]|[...][number of additional parameters]|[parameter
--            1]|[parameter 2]|[...]|[parameter N]|pipe to
library.renaming_by_calling = function (ctx)
	local opts = ctx.pipe
	local tname
	if opts[1] ~= nil then tname = opts[1]:match'^%s*(.*%S)' end
	if tname == nil then error(modulename ..
		', ‘renaming_by_calling’: No template name was provided', 0) end
	local rargs, argc, looptype, karg, varg = load_callback_opts(opts, 1,
		mapping_styles.names_only)
	local model = { title = tname, args = rargs }
	map_names(ctx.params, rargs, karg, varg, looptype, function ()
		return ctx.frame:expandTemplate(model)
	end)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|renaming_by_invoking|module name|function
--            name|[call style]|[let]|[...]|[number of additional
--            arguments]|[argument 1]|[argument 2]|[...]|[argument N]|pipe to
library.renaming_by_invoking = function (ctx)
	local opts = ctx.pipe
	local mname
	local fname
	if opts[1] ~= nil then mname = opts[1]:match'^%s*(.*%S)' end
	if mname == nil then error(modulename ..
		', ‘renaming_by_invoking’: No module name was provided', 0) end
	if opts[2] ~= nil then fname = opts[2]:match'^%s*(.*%S)' end
	if fname == nil then error(modulename ..
		', ‘renaming_by_invoking’: No function name was provided', 0) end
	local rargs, argc, looptype, karg, varg = load_callback_opts(opts, 2,
		mapping_styles.names_only)
	local model = { title = 'Module:' .. mname, args = rargs }
	local mfunc = require(model.title)[fname]
	if mfunc == nil then error(modulename ..
		', ‘renaming_by_invoking’: The function ‘' .. fname ..
		'’ does not exist', 0) end
	map_names(ctx.params, rargs, karg, varg, looptype, function ()
		local tmp = mfunc(ctx.frame:newChild(model))
		return tonumber(tmp) or tostring(tmp)
	end)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|renaming_by_magic|parser function|[call
--            style]|[let]|[...][number of additional arguments]|[argument
--            1]|[argument 2]|[...]|[argument N]|pipe to
library.renaming_by_magic = function (ctx)
	local opts = ctx.pipe
	local magic
	if opts[1] ~= nil then magic = opts[1]:match'^%s*(.*%S)' end
	if magic == nil then error(modulename ..
		', ‘renaming_by_magic’: No parser function was provided', 0) end
	local rargs, argc, looptype, karg, varg = load_callback_opts(opts, 1,
		mapping_styles.names_only)
	map_names(ctx.params, rargs, karg, varg, looptype, function ()
		return ctx.frame:callParserFunction(magic, rargs)
	end)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|renaming_by_replacing|target|replace|[count]|[plain
--            flag]|pipe to
library.renaming_by_replacing = function (ctx)
	local ptn, repl, nmax, is_strict, argc, die =
		load_replace_args(ctx.pipe, 'renaming_by_replacing')
	if die then return context_iterate(ctx, argc) end
	local tbl = ctx.params
	if is_strict then
		local key = tonumber(ptn) or ptn:match'^%s*(.-)%s*$'
		local val = tbl[key]
		tbl[key] = nil
		tbl[tonumber(repl) or repl:match'^%s*(.-)%s*$'] = val
	else
		if flg == 2 then
			-- Copied from Module:String's `str._escapePattern()`
			ptn = ptn:gsub('[%(%)%.%%%+%-%*%?%[%^%$%]]', '%%%0')
		end
		local cache = {}
		for key, val in pairs(tbl) do
			steal_if_renamed(val, tbl, key, cache,
				tostring(key):gsub(ptn, repl, nmax))
		end
		for key, val in pairs(cache) do tbl[key] = val end
	end
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|grouping_by_calling|template
--            name|[let]|[...]|[number of additional arguments]|[argument
--            1]|[argument 2]|[...]|[argument N]|pipe to
library.grouping_by_calling = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable! As a modifier,
	-- this function MUST create a copy of it before returning
	local opts = ctx.pipe
	local tmp
	if opts[1] ~= nil then tmp = opts[1]:match'^%s*(.*%S)' end
	if tmp == nil then error(modulename ..
		', ‘grouping_by_calling’: No template name was provided', 0) end
	local model = { title = tmp }
	local tmp, argc = load_child_opts(opts, 2, 0)
	local gargs = {}
	for key, val in pairs(tmp) do
		if type(key) == 'number' and key < 1 then gargs[key - 1] = val
		else gargs[key] = val end
	end
	local groups = make_groups(ctx.params)
	for gid, group in pairs(groups) do
		for key, val in pairs(gargs) do group[key] = val end
		group[0] = gid
		model.args = group
		groups[gid] = ctx.frame:expandTemplate(model)
	end
	ctx.params = groups
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|parsing|string to parse|[trim flag]|[iteration
--            delimiter setter]|[...]|[key-value delimiter setter]|[...]|pipe to
library.parsing = function (ctx)
	local opts = ctx.pipe
	if opts[1] == nil then error(modulename ..
		', ‘parsing’: No string to parse was provided', 0) end
	local isep, iplain, psep, pplain, trimnamed, trimunnamed, argc =
		load_parse_opts(opts, 2)
	parse_parameter_string(ctx.params, opts[1], isep, iplain, psep, pplain,
		trimnamed, trimunnamed)
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|reinterpreting|parameter to reinterpret|[trim
--            flag]|[iteration delimiter setter]|[...]|[key-value delimiter
--            setter]|[...]|pipe to
library.reinterpreting = function (ctx)
	local opts = ctx.pipe
	if opts[1] == nil then error(modulename ..
		', ‘reinterpreting’: No parameter to reinterpret was provided', 0) end
	local isep, iplain, psep, pplain, trimnamed, trimunnamed, argc =
		load_parse_opts(opts, 2)
	local tbl = ctx.params
	local tmp = tonumber(opts[1]) or opts[1]:match'^%s*(.-)%s*$'
	local str = tbl[tmp]
	if str ~= nil then
		tbl[tmp] = nil
		parse_parameter_string(tbl, str, isep, iplain, psep, pplain,
			trimnamed, trimunnamed)
	end
	return context_iterate(ctx, argc)
end


-- Syntax:  #invoke:params|combining_by_calling|template name|new parameter
--            name|pipe to
library.combining_by_calling = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable! As a modifier,
	-- this function MUST create a copy of it before returning
	local tname = ctx.pipe[1]
	if tname ~= nil then tname = tname:match'^%s*(.*%S)'
	else error(modulename ..
		', ‘combining_by_calling’: No template name was provided', 0) end
	local merge_into = ctx.pipe[2]
	if merge_into == nil then error(modulename ..
		', ‘combining_by_calling’: No parameter name was provided', 0) end
	merge_into = tonumber(merge_into) or merge_into:match'^%s*(.-)%s*$'
	ctx.params = {
		[merge_into] = ctx.frame:expandTemplate{
			title = tname,
			args = ctx.params
		}
	}
	return context_iterate(ctx, 3)
end


-- Syntax:  #invoke:params|snapshotting|pipe to
library.snapshotting = function (ctx)
	push_cloned_stack(ctx, ctx.params)
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|remembering|pipe to
library.remembering = function (ctx)
	push_cloned_stack(ctx, ctx.oparams)
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|entering_substack|[new]|pipe to
library.entering_substack = function (ctx)
	local tbl = ctx.params
	local ncurrparent = ctx.n_parents + 1
	if ctx.parents == nil then ctx.parents = { tbl }
	else ctx.parents[ncurrparent] = tbl end
	ctx.n_parents = ncurrparent
	if ctx.pipe[1] ~= nil and ctx.pipe[1]:match'^%s*new%s*$' then
		ctx.params = {}
		return context_iterate(ctx, 2)
	end
	local currsnap = ctx.n_children
	if currsnap > 0 then
		ctx.params = ctx.children[currsnap]
		ctx.children[currsnap] = nil
		ctx.n_children = currsnap - 1
	else
		local newparams = {}
		for key, val in pairs(tbl) do newparams[key] = val end
		ctx.params = newparams
	end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|pulling|parameter name|pipe to
library.pulling = function (ctx)
	local opts = ctx.pipe
	if opts[1] == nil then error(modulename ..
		', ‘pulling’: No parameter to pull was provided', 0) end
	local parent
	local tmp = ctx.n_parents
	if tmp < 1 then parent = ctx.oparams else parent = ctx.parents[tmp] end
	tmp = tonumber(opts[1]) or opts[1]:match'^%s*(.-)%s*$'
	if parent[tmp] ~= nil then ctx.params[tmp] = parent[tmp] end
	return context_iterate(ctx, 2)
end


-- Syntax:  #invoke:params|detaching_substack|pipe to
library.detaching_substack = function (ctx)
	local ncurrparent = ctx.n_parents
	if ncurrparent < 1 then error(modulename ..
		', ‘detaching_substack’: No substack has been created', 0) end
	local parent = ctx.parents[ncurrparent]
	for key in pairs(ctx.params) do parent[key] = nil end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|leaving_substack|pipe to
library.leaving_substack = function (ctx)
	local ncurrparent = ctx.n_parents
	if ncurrparent < 1 then error(modulename ..
		', ‘leaving_substack’: No substack has been created', 0) end
	local currsnap = ctx.n_children + 1
	if ctx.children == nil then ctx.children = { ctx.params }
	else ctx.children[currsnap] = ctx.params end
	ctx.params = ctx.parents[ncurrparent]
	ctx.parents[ncurrparent] = nil
	ctx.n_parents = ncurrparent - 1
	ctx.n_children = currsnap
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|merging_substack|pipe to
library.merging_substack = function (ctx)
	local ncurrparent = ctx.n_parents
	if ncurrparent < 1 then error(modulename ..
		', ‘merging_substack’: No substack has been created', 0) end
	local parent = ctx.parents[ncurrparent]
	local child = ctx.params
	ctx.params = parent
	ctx.parents[ncurrparent] = nil
	ctx.n_parents = ncurrparent - 1
	for key, val in pairs(child) do parent[key] = val end
	return context_iterate(ctx, 1)
end


-- Syntax:  #invoke:params|flushing|pipe to
library.flushing = function (ctx)
	if ctx.n_children < 1 then error(modulename ..
		', ‘flushing’: There are no substacks to flush', 0) end
	local parent = ctx.params
	local currsnap = ctx.n_children
	for key, val in pairs(ctx.children[currsnap]) do parent[key] = val end
	ctx.children[currsnap] = nil
	ctx.n_children = currsnap - 1
	return context_iterate(ctx, 1)
end



	--[[ Functions ]]--
	-----------------------------


-- Syntax:  #invoke:params|count
library.count = function (ctx)
	-- NOTE: `ctx.pipe` and `ctx.params` might be the original metatables!
	local retval = 0
	for _ in ctx.iterfunc(ctx.params) do retval = retval + 1 end
	if ctx.subset == -1 then retval = retval - #ctx.params end
	ctx.text = retval
	return false
end


-- Syntax:  #invoke:args|concat_and_call|template name|[prepend 1]|[prepend 2]
--            |[...]|[item n]|[named item 1=value 1]|[...]|[named item n=value
--            n]|[...]
library.concat_and_call = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable!
	local opts = ctx.pipe
	local tname
	if opts[1] ~= nil then tname = opts[1]:match'^%s*(.*%S)' end
	if tname == nil then error(modulename ..
		', ‘concat_and_call’: No template name was provided', 0) end
	remove_numeric_keys(opts, 1, 1)
	ctx.text = ctx.frame:expandTemplate{
		title = tname,
		args = concat_params(ctx)
	}
	return false
end


-- Syntax:  #invoke:args|concat_and_invoke|module name|function name|[prepend
--            1]|[prepend 2]|[...]|[item n]|[named item 1=value 1]|[...]|[named
--            item n=value n]|[...]
library.concat_and_invoke = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable!
	local opts = ctx.pipe
	local mname
	local fname
	if opts[1] ~= nil then mname = opts[1]:match'^%s*(.*%S)' end
	if mname == nil then error(modulename ..
		', ‘concat_and_invoke’: No module name was provided', 0) end
	if opts[2] ~= nil then fname = opts[2]:match'^%s*(.*%S)' end
	if fname == nil then error(modulename ..
		', ‘concat_and_invoke’: No function name was provided', 0) end
	remove_numeric_keys(opts, 1, 2)
	local mfunc = require('Module:' .. mname)[fname]
	if mfunc == nil then error(modulename ..
		', ‘concat_and_invoke’: The function ‘' .. fname ..
		'’ does not exist', 0) end
	ctx.text = mfunc(ctx.frame:newChild{
		title = 'Module:' .. fname,
		args = concat_params(ctx)
	})
	return false
end


-- Syntax:  #invoke:args|concat_and_magic|parser function|[prepend 1]|[prepend
--            2]|[...]|[item n]|[named item 1=value 1]|[...]|[named item n=
--            value n]|[...]
library.concat_and_magic = function (ctx)
	-- NOTE: `ctx.params` might be the original metatable!
	local opts = ctx.pipe
	local magic
	if opts[1] ~= nil then magic = opts[1]:match'^%s*(.*%S)' end
	if magic == nil then error(modulename ..
		', ‘concat_and_magic’: No parser function was provided', 0) end
	remove_numeric_keys(opts, 1, 1)
	ctx.text = ctx.frame:callParserFunction(magic, concat_params(ctx))
	return false
end


-- Syntax:  #invoke:params|value_of|parameter name
library.value_of = function (ctx)
	-- NOTE: `ctx.pipe` and `ctx.params` might be the original metatables!
	local opts = ctx.pipe
	local kstr
	if opts[1] ~= nil then kstr = opts[1]:match'^%s*(.*%S)' end
	if kstr == nil then error(modulename ..
		', ‘value_of’: No parameter name was provided', 0) end
	local knum = tonumber(kstr)
	local len = #ctx.params  -- No worries: unused when in first position
	local val = ctx.params[knum or kstr]
	if val ~= nil and (
		ctx.subset ~= -1 or knum == nil or knum > len or knum < 1
	) and (
		ctx.subset ~= 1 or (knum ~= nil and knum <= len and knum > 0)
	) then
		ctx.text = (ctx.header or '') .. val .. (ctx.footer or '')
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|list
library.list = function (ctx)
	-- NOTE: `ctx.pipe` might be the original metatable!
	local kvs = ctx.pairsep or ''
	local pps = ctx.itersep or ''
	local ret = {}
	local nss = 0
	flush_params(
		ctx,
		function (key, val)
			ret[nss + 1] = pps
			ret[nss + 2] = key
			ret[nss + 3] = kvs
			ret[nss + 4] = val
			nss = nss + 4
		end
	)
	if nss > 0 then
		if nss > 4 and ctx.lastsep ~= nil then
			ret[nss - 3] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|list_values
library.list_values = function (ctx)
	-- NOTE: `ctx.pipe` might be the original metatable!
	-- NOTE: `library.coins()` and `library.unique_coins()` rely on us
	local pps = ctx.itersep or ''
	local ret = {}
	local nss = 0
	flush_params(
		ctx,
		function (key, val)
			ret[nss + 1] = pps
			ret[nss + 2] = val
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|coins|[first coin = value 1]|[second coin = value
--            2]|[...]|[last coin = value N]
library.coins = function (ctx)
	-- NOTE: `ctx.pipe` might be the original metatable!
	local opts = ctx.pipe
	local tbl = ctx.params
	for key, val in pairs(tbl) do tbl[key] = opts[tonumber(val) or val] end
	return library.list_values(ctx)
end


-- Syntax:  #invoke:params|unique_coins|[first coin = value 1]|[second coin =
--            value 2]|[...]|[last coin = value N]
library.unique_coins = function (ctx)
	local opts = ctx.pipe
	local tbl = ctx.params
	local tmp
	for key, val in pairs(tbl) do
		tmp = tonumber(val) or val
		tbl[key] = opts[tmp]
		opts[tmp] = nil
	end
	return library.list_values(ctx)
end


-- Syntax:  #invoke:params|for_each|wikitext
library.for_each = function (ctx)
	-- NOTE: `ctx.pipe` might be the original metatable!
	local txt = ctx.pipe[1] or ''
	local pps = ctx.itersep or ''
	local ret = {}
	local nss = 0
	flush_params(
		ctx,
		function (key, val)
			ret[nss + 1] = pps
			ret[nss + 2] = txt:gsub('%$#', key):gsub('%$@', val)
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|call_for_each|template name|[append 1]|[append 2]
--            |[...]|[append n]|[named param 1=value 1]|[...]|[named param
--            n=value n]|[...]
library.call_for_each = function (ctx)
	local opts = ctx.pipe
	local tname
	if opts[1] ~= nil then tname = opts[1]:match'^%s*(.*%S)' end
	if tname == nil then error(modulename ..
		', ‘call_for_each’: No template name was provided', 0) end
	local model = { title = tname, args = opts }
	local ccs = ctx.itersep or ''
	local ret = {}
	local nss = 0
	table.insert(opts, 1, true)
	flush_params(
		ctx,
		function (key, val)
			opts[1] = key
			opts[2] = val
			ret[nss + 1] = ccs
			ret[nss + 2] = ctx.frame:expandTemplate(model)
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|invoke_for_each|module name|module function|[append
--            1]|[append 2]|[...]|[append n]|[named param 1=value 1]|[...]
--            |[named param n=value n]|[...]
library.invoke_for_each = function (ctx)
	local opts = ctx.pipe
	local mname
	local fname
	if opts[1] ~= nil then mname = opts[1]:match'^%s*(.*%S)' end
	if mname == nil then error(modulename ..
		', ‘invoke_for_each’: No module name was provided', 0) end
	if opts[2] ~= nil then fname = opts[2]:match'^%s*(.*%S)' end
	if fname == nil then error(modulename ..
		', ‘invoke_for_each’: No function name was provided', 0) end
	local model = { title = 'Module:' .. mname, args = opts }
	local mfunc = require(model.title)[fname]
	local ccs = ctx.itersep or ''
	local ret = {}
	local nss = 0
	flush_params(
		ctx,
		function (key, val)
			opts[1] = key
			opts[2] = val
			ret[nss + 1] = ccs
			ret[nss + 2] = mfunc(ctx.frame:newChild(model))
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|magic_for_each|parser function|[append 1]|[append 2]
--            |[...]|[append n]|[named param 1=value 1]|[...]|[named param
--            n=value n]|[...]
library.magic_for_each = function (ctx)
	local opts = ctx.pipe
	local magic
	if opts[1] ~= nil then magic = opts[1]:match'^%s*(.*%S)' end
	if magic == nil then error(modulename ..
		', ‘magic_for_each’: No parser function was provided', 0) end
	local ccs = ctx.itersep or ''
	local ret = {}
	local nss = 0
	table.insert(opts, 1, true)
	flush_params(
		ctx,
		function (key, val)
			opts[1] = key
			opts[2] = val
			ret[nss + 1] = ccs
			ret[nss + 2] = ctx.frame:callParserFunction(magic,
				opts)
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|call_for_each_value|template name|[append 1]|[append
--            2]|[...]|[append n]|[named param 1=value 1]|[...]|[named param
--            n=value n]|[...]
library.call_for_each_value = function (ctx)
	local opts = ctx.pipe
	local tname
	if opts[1] ~= nil then tname = opts[1]:match'^%s*(.*%S)' end
	if tname == nil then error(modulename ..
		', ‘call_for_each_value’: No template name was provided', 0) end
	local model = { title = tname, args = opts }
	local ccs = ctx.itersep or ''
	local ret = {}
	local nss = 0
	flush_params(
		ctx,
		function (key, val)
			opts[1] = val
			ret[nss + 1] = ccs
			ret[nss + 2] = ctx.frame:expandTemplate(model)
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|invoke_for_each_value|module name|[append 1]|[append
--            2]|[...]|[append n]|[named param 1=value 1]|[...]|[named param
--            n=value n]|[...]
library.invoke_for_each_value = function (ctx)
	local opts = ctx.pipe
	local mname
	local fname
	if opts[1] ~= nil then mname = opts[1]:match'^%s*(.*%S)' end
	if mname == nil then error(modulename ..
		', ‘invoke_for_each_value’: No module name was provided', 0) end
	if opts[2] ~= nil then fname = opts[2]:match'^%s*(.*%S)' end
	if fname == nil then error(modulename ..
		', ‘invoke_for_each_value’: No function name was provided', 0) end
	local model = { title = 'Module:' .. mname, args = opts }
	local mfunc = require(model.title)[fname]
	local ccs = ctx.itersep or ''
	local ret = {}
	local nss = 0
	remove_numeric_keys(opts, 1, 1)
	flush_params(
		ctx,
		function (key, val)
			opts[1] = val
			ret[nss + 1] = ccs
			ret[nss + 2] = mfunc(ctx.frame:newChild(model))
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|magic_for_each_value|parser function|[append 1]
--            |[append 2]|[...]|[append n]|[named param 1=value 1]|[...]|[named
--            param n=value n]|[...]
library.magic_for_each_value = function (ctx)
	local opts = ctx.pipe
	local magic
	if opts[1] ~= nil then magic = opts[1]:match'^%s*(.*%S)' end
	if magic == nil then error(modulename ..
		', ‘magic_for_each_value’: No parser function was provided', 0) end
	local ccs = ctx.itersep or ''
	local ret = {}
	local nss = 0
	flush_params(
		ctx,
		function (key, val)
			opts[1] = val
			ret[nss + 1] = ccs
			ret[nss + 2] = ctx.frame:callParserFunction(magic,
				opts)
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end


-- Syntax:  #invoke:params|call_for_each_group|template name|[append 1]|[append
--            2]|[...]|[append n]|[named param 1=value 1]|[...]|[named param
--            n=value n]|[...]
library.call_for_each_group = function (ctx)
	-- NOTE: `ctx.pipe` and `ctx.params` might be the original metatables!
	local opts = ctx.pipe
	local tmp
	if opts[1] ~= nil then tmp = opts[1]:match'^%s*(.*%S)' end
	if tmp == nil then error(modulename ..
		', ‘call_for_each_group’: No template name was provided', 0) end
	local model = { title = tmp }
	local ccs = ctx.itersep or ''
	local nss = 0
	local ret = {}
	opts = {}
	for key, val in pairs(ctx.pipe) do
		if type(key) == 'number' then opts[key - 1] = val
		else opts[key] = val end
	end
	ctx.pipe = opts
	ctx.params = make_groups(ctx.params)
	flush_params(
		ctx,
		function (gid, group)
			for key, val in pairs(opts) do group[key] = val end
			group[0] = gid
			model.args = group
			ret[nss + 1] = ccs
			ret[nss + 2] = ctx.frame:expandTemplate(model)
			nss = nss + 2
		end
	)
	if nss > 0 then
		if nss > 2 and ctx.lastsep ~= nil then
			ret[nss - 1] = ctx.lastsep
		end
		ret[1] = ctx.header or ''
		if ctx.footer ~= nil then ret[nss + 1] = ctx.footer end
		ctx.text = table.concat(ret)
		return false
	end
	ctx.text = ctx.ifngiven or ''
	return false
end



	---                                        ---
	---     PUBLIC ENVIRONMENT                 ---
	---    ________________________________    ---
	---                                        ---



	--[[ First-position-only modifiers ]]--
	---------------------------------------


-- Syntax:  #invoke:params|new|pipe to
static_iface.new = function (frame)
	local ctx = context_new(frame:getParent())
	ctx.pipe = copy_or_ref_table(frame.args, false)
	ctx.params = {}
	main_loop(ctx, context_iterate(ctx, 1))
	return ctx.text
end



	--[[ First-position-only functions ]]--
	---------------------------------------


-- Syntax:  #invoke:params|self
static_iface.self = function (frame)
	return frame:getParent():getTitle()
end



	--[[ Public metatable of functions ]]--
	---------------------------------------


return setmetatable({}, {
	__index = function (_, query)
		local fname = query:match'^%s*(.*%S)'
		if fname == nil then error(modulename ..
			': You must specify a function to call', 0) end
		local func = static_iface[fname]
		if func ~= nil then return func end
		func = library[fname]
		if func == nil then error(modulename ..
			': The function ‘' .. fname .. '’ does not exist', 0) end
		return function (frame)
			local ctx = context_new(frame:getParent())
			ctx.pipe = copy_or_ref_table(frame.args,
				refpipe[fname])
			ctx.params = copy_or_ref_table(ctx.oparams,
				refparams[fname])
			main_loop(ctx, func)
			return ctx.text
		end
	end
})