+ Penlight

1 files changed, 999 insertions, 0 deletions

diff --git a/Data/Libraries/Penlight/lua/pl/tablex.lua b/Data/Libraries/Penlight/lua/pl/tablex.lua
new file mode 100644
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+++ b/Data/Libraries/Penlight/lua/pl/tablex.lua
@@ -0,0 +1,999 @@
+--- Extended operations on Lua tables.
+--
+-- See @{02-arrays.md.Useful_Operations_on_Tables|the Guide}
+--
+-- Dependencies: `pl.utils`, `pl.types`
+-- @module pl.tablex
+local utils = require ('pl.utils')
+local types = require ('pl.types')
+local getmetatable,setmetatable,require = getmetatable,setmetatable,require
+local tsort,append,remove = table.sort,table.insert,table.remove
+local min = math.min
+local pairs,type,unpack,select,tostring = pairs,type,utils.unpack,select,tostring
+local function_arg = utils.function_arg
+local assert_arg = utils.assert_arg
+
+local tablex = {}
+
+-- generally, functions that make copies of tables try to preserve the metatable.
+-- However, when the source has no obvious type, then we attach appropriate metatables
+-- like List, Map, etc to the result.
+local function setmeta (res,tbl,pl_class)
+    local mt = getmetatable(tbl) or pl_class and require('pl.' .. pl_class)
+    return mt and setmetatable(res, mt) or res
+end
+
+local function makelist(l)
+    return setmetatable(l, require('pl.List'))
+end
+
+local function makemap(m)
+    return setmetatable(m, require('pl.Map'))
+end
+
+local function complain (idx,msg)
+    error(('argument %d is not %s'):format(idx,msg),3)
+end
+
+local function assert_arg_indexable (idx,val)
+    if not types.is_indexable(val) then
+        complain(idx,"indexable")
+    end
+end
+
+local function assert_arg_iterable (idx,val)
+    if not types.is_iterable(val) then
+        complain(idx,"iterable")
+    end
+end
+
+local function assert_arg_writeable (idx,val)
+    if not types.is_writeable(val) then
+        complain(idx,"writeable")
+    end
+end
+
+--- copy a table into another, in-place.
+-- @within Copying
+-- @tab t1 destination table
+-- @tab t2 source (actually any iterable object)
+-- @return first table
+function tablex.update (t1,t2)
+    assert_arg_writeable(1,t1)
+    assert_arg_iterable(2,t2)
+    for k,v in pairs(t2) do
+        t1[k] = v
+    end
+    return t1
+end
+
+--- total number of elements in this table.
+-- Note that this is distinct from `#t`, which is the number
+-- of values in the array part; this value will always
+-- be greater or equal. The difference gives the size of
+-- the hash part, for practical purposes. Works for any
+-- object with a __pairs metamethod.
+-- @tab t a table
+-- @return the size
+function tablex.size (t)
+    assert_arg_iterable(1,t)
+    local i = 0
+    for k in pairs(t) do i = i + 1 end
+    return i
+end
+
+--- make a shallow copy of a table
+-- @within Copying
+-- @tab t an iterable source
+-- @return new table
+function tablex.copy (t)
+    assert_arg_iterable(1,t)
+    local res = {}
+    for k,v in pairs(t) do
+        res[k] = v
+    end
+    return res
+end
+
+local function cycle_aware_copy(t, cache)
+    if type(t) ~= 'table' then return t end
+    if cache[t] then return cache[t] end
+    assert_arg_iterable(1,t)
+    local res = {}
+    cache[t] = res
+    local mt = getmetatable(t)
+    for k,v in pairs(t) do
+        k = cycle_aware_copy(k, cache)
+        v = cycle_aware_copy(v, cache)
+        res[k] = v
+    end
+    setmetatable(res,mt)
+    return res
+end
+
+--- make a deep copy of a table, recursively copying all the keys and fields.
+-- This supports cycles in tables; cycles will be reproduced in the copy.
+-- This will also set the copied table's metatable to that of the original.
+-- @within Copying
+-- @tab t A table
+-- @return new table
+function tablex.deepcopy(t)
+    return cycle_aware_copy(t,{})
+end
+
+local abs = math.abs
+
+local function cycle_aware_compare(t1,t2,ignore_mt,eps,cache)
+    if cache[t1] and cache[t1][t2] then return true end
+    local ty1 = type(t1)
+    local ty2 = type(t2)
+    if ty1 ~= ty2 then return false end
+    -- non-table types can be directly compared
+    if ty1 ~= 'table' then
+        if ty1 == 'number' and eps then return abs(t1-t2) < eps end
+        return t1 == t2
+    end
+    -- as well as tables which have the metamethod __eq
+    local mt = getmetatable(t1)
+    if not ignore_mt and mt and mt.__eq then return t1 == t2 end
+    for k1 in pairs(t1) do
+        if t2[k1]==nil then return false end
+    end
+    for k2 in pairs(t2) do
+        if t1[k2]==nil then return false end
+    end
+    cache[t1] = cache[t1] or {}
+    cache[t1][t2] = true
+    for k1,v1 in pairs(t1) do
+        local v2 = t2[k1]
+        if not cycle_aware_compare(v1,v2,ignore_mt,eps,cache) then return false end
+    end
+    return true
+end
+
+--- compare two values.
+-- if they are tables, then compare their keys and fields recursively.
+-- @within Comparing
+-- @param t1 A value
+-- @param t2 A value
+-- @bool[opt] ignore_mt if true, ignore __eq metamethod (default false)
+-- @number[opt] eps if defined, then used for any number comparisons
+-- @return true or false
+function tablex.deepcompare(t1,t2,ignore_mt,eps)
+    return cycle_aware_compare(t1,t2,ignore_mt,eps,{})
+end
+
+--- compare two arrays using a predicate.
+-- @within Comparing
+-- @array t1 an array
+-- @array t2 an array
+-- @func cmp A comparison function; `bool = cmp(t1_value, t2_value)`
+-- @return true or false
+-- @usage
+-- assert(tablex.compare({ 1, 2, 3 }, { 1, 2, 3 }, "=="))
+--
+-- assert(tablex.compare(
+--    {1,2,3, hello = "world"},  -- fields are not compared!
+--    {1,2,3}, function(v1, v2) return v1 == v2 end)
+function tablex.compare (t1,t2,cmp)
+    assert_arg_indexable(1,t1)
+    assert_arg_indexable(2,t2)
+    if #t1 ~= #t2 then return false end
+    cmp = function_arg(3,cmp)
+    for k = 1,#t1 do
+        if not cmp(t1[k],t2[k]) then return false end
+    end
+    return true
+end
+
+--- compare two list-like tables using an optional predicate, without regard for element order.
+-- @within Comparing
+-- @array t1 a list-like table
+-- @array t2 a list-like table
+-- @param cmp A comparison function (may be nil)
+function tablex.compare_no_order (t1,t2,cmp)
+    assert_arg_indexable(1,t1)
+    assert_arg_indexable(2,t2)
+    if cmp then cmp = function_arg(3,cmp) end
+    if #t1 ~= #t2 then return false end
+    local visited = {}
+    for i = 1,#t1 do
+        local val = t1[i]
+        local gotcha
+        for j = 1,#t2 do
+            if not visited[j] then
+                local match
+                if cmp then match = cmp(val,t2[j]) else match = val == t2[j] end
+                if match then
+                    gotcha = j
+                    break
+                end
+            end
+        end
+        if not gotcha then return false end
+        visited[gotcha] = true
+    end
+    return true
+end
+
+
+--- return the index of a value in a list.
+-- Like string.find, there is an optional index to start searching,
+-- which can be negative.
+-- @within Finding
+-- @array t A list-like table
+-- @param val A value
+-- @int idx index to start; -1 means last element,etc (default 1)
+-- @return index of value or nil if not found
+-- @usage find({10,20,30},20) == 2
+-- @usage find({'a','b','a','c'},'a',2) == 3
+function tablex.find(t,val,idx)
+    assert_arg_indexable(1,t)
+    idx = idx or 1
+    if idx < 0 then idx = #t + idx + 1 end
+    for i = idx,#t do
+        if t[i] == val then return i end
+    end
+    return nil
+end
+
+--- return the index of a value in a list, searching from the end.
+-- Like string.find, there is an optional index to start searching,
+-- which can be negative.
+-- @within Finding
+-- @array t A list-like table
+-- @param val A value
+-- @param idx index to start; -1 means last element,etc (default `#t`)
+-- @return index of value or nil if not found
+-- @usage rfind({10,10,10},10) == 3
+function tablex.rfind(t,val,idx)
+    assert_arg_indexable(1,t)
+    idx = idx or #t
+    if idx < 0 then idx = #t + idx + 1 end
+    for i = idx,1,-1 do
+        if t[i] == val then return i end
+    end
+    return nil
+end
+
+
+--- return the index (or key) of a value in a table using a comparison function.
+--
+-- *NOTE*: the 2nd return value of this function, the value returned
+-- by the comparison function, has a limitation that it cannot be `false`.
+-- Because if it is, then it indicates the comparison failed, and the
+-- function will continue the search. See examples.
+-- @within Finding
+-- @tab t A table
+-- @func cmp A comparison function
+-- @param arg an optional second argument to the function
+-- @return index of value, or nil if not found
+-- @return value returned by comparison function (cannot be `false`!)
+-- @usage
+-- -- using an operator
+-- local lst = { "Rudolph", true, false, 15 }
+-- local idx, cmp_result = tablex.rfind(lst, "==", "Rudolph")
+-- assert(idx == 1)
+-- assert(cmp_result == true)
+--
+-- local idx, cmp_result = tablex.rfind(lst, "==", false)
+-- assert(idx == 3)
+-- assert(cmp_result == true)       -- looking up 'false' works!
+--
+-- -- using a function returning the value looked up
+-- local cmp = function(v1, v2) return v1 == v2 and v2 end
+-- local idx, cmp_result = tablex.rfind(lst, cmp, "Rudolph")
+-- assert(idx == 1)
+-- assert(cmp_result == "Rudolph")  -- the value is returned
+--
+-- -- NOTE: this fails, since 'false' cannot be returned!
+-- local idx, cmp_result = tablex.rfind(lst, cmp, false)
+-- assert(idx == nil)               -- looking up 'false' failed!
+-- assert(cmp_result == nil)
+function tablex.find_if(t,cmp,arg)
+    assert_arg_iterable(1,t)
+    cmp = function_arg(2,cmp)
+    for k,v in pairs(t) do
+        local c = cmp(v,arg)
+        if c then return k,c end
+    end
+    return nil
+end
+
+--- return a list of all values in a table indexed by another list.
+-- @tab tbl a table
+-- @array idx an index table (a list of keys)
+-- @return a list-like table
+-- @usage index_by({10,20,30,40},{2,4}) == {20,40}
+-- @usage index_by({one=1,two=2,three=3},{'one','three'}) == {1,3}
+function tablex.index_by(tbl,idx)
+    assert_arg_indexable(1,tbl)
+    assert_arg_indexable(2,idx)
+    local res = {}
+    for i = 1,#idx do
+        res[i] = tbl[idx[i]]
+    end
+    return setmeta(res,tbl,'List')
+end
+
+--- apply a function to all values of a table.
+-- This returns a table of the results.
+-- Any extra arguments are passed to the function.
+-- @within MappingAndFiltering
+-- @func fun A function that takes at least one argument
+-- @tab t A table
+-- @param ... optional arguments
+-- @usage map(function(v) return v*v end, {10,20,30,fred=2}) is {100,400,900,fred=4}
+function tablex.map(fun,t,...)
+    assert_arg_iterable(1,t)
+    fun = function_arg(1,fun)
+    local res = {}
+    for k,v in pairs(t) do
+        res[k] = fun(v,...)
+    end
+    return setmeta(res,t)
+end
+
+--- apply a function to all values of a list.
+-- This returns a table of the results.
+-- Any extra arguments are passed to the function.
+-- @within MappingAndFiltering
+-- @func fun A function that takes at least one argument
+-- @array t a table (applies to array part)
+-- @param ... optional arguments
+-- @return a list-like table
+-- @usage imap(function(v) return v*v end, {10,20,30,fred=2}) is {100,400,900}
+function tablex.imap(fun,t,...)
+    assert_arg_indexable(1,t)
+    fun = function_arg(1,fun)
+    local res = {}
+    for i = 1,#t do
+        res[i] = fun(t[i],...) or false
+    end
+    return setmeta(res,t,'List')
+end
+
+--- apply a named method to values from a table.
+-- @within MappingAndFiltering
+-- @string name the method name
+-- @array t a list-like table
+-- @param ... any extra arguments to the method
+-- @return a `List` with the results of the method (1st result only)
+-- @usage
+-- local Car = {}
+-- Car.__index = Car
+-- function Car.new(car)
+--   return setmetatable(car or {}, Car)
+-- end
+-- Car.speed = 0
+-- function Car:faster(increase)
+--   self.speed = self.speed + increase
+--   return self.speed
+-- end
+--
+-- local ferrari = Car.new{ name = "Ferrari" }
+-- local lamborghini = Car.new{ name = "Lamborghini", speed = 50 }
+-- local cars = { ferrari, lamborghini }
+--
+-- assert(ferrari.speed == 0)
+-- assert(lamborghini.speed == 50)
+-- tablex.map_named_method("faster", cars, 10)
+-- assert(ferrari.speed == 10)
+-- assert(lamborghini.speed == 60)
+function tablex.map_named_method (name,t,...)
+    utils.assert_string(1,name)
+    assert_arg_indexable(2,t)
+    local res = {}
+    for i = 1,#t do
+        local val = t[i]
+        local fun = val[name]
+        res[i] = fun(val,...)
+    end
+    return setmeta(res,t,'List')
+end
+
+--- apply a function to all values of a table, in-place.
+-- Any extra arguments are passed to the function.
+-- @func fun A function that takes at least one argument
+-- @tab t a table
+-- @param ... extra arguments passed to `fun`
+-- @see tablex.foreach
+function tablex.transform (fun,t,...)
+    assert_arg_iterable(1,t)
+    fun = function_arg(1,fun)
+    for k,v in pairs(t) do
+        t[k] = fun(v,...)
+    end
+end
+
+--- generate a table of all numbers in a range.
+-- This is consistent with a numerical for loop.
+-- @int start  number
+-- @int finish number
+-- @int[opt=1] step  make this negative for start < finish
+function tablex.range (start,finish,step)
+    local res
+    step = step or 1
+    if start == finish then
+        res = {start}
+    elseif (start > finish and step > 0) or (finish > start and step < 0) then
+        res = {}
+    else
+        local k = 1
+        res = {}
+        for i=start,finish,step do res[k]=i; k=k+1 end
+    end
+    return makelist(res)
+end
+
+--- apply a function to values from two tables.
+-- @within MappingAndFiltering
+-- @func fun a function of at least two arguments
+-- @tab t1 a table
+-- @tab t2 a table
+-- @param ... extra arguments
+-- @return a table
+-- @usage map2('+',{1,2,3,m=4},{10,20,30,m=40}) is {11,22,23,m=44}
+function tablex.map2 (fun,t1,t2,...)
+    assert_arg_iterable(1,t1)
+    assert_arg_iterable(2,t2)
+    fun = function_arg(1,fun)
+    local res = {}
+    for k,v in pairs(t1) do
+        res[k] = fun(v,t2[k],...)
+    end
+    return setmeta(res,t1,'List')
+end
+
+--- apply a function to values from two arrays.
+-- The result will be the length of the shortest array.
+-- @within MappingAndFiltering
+-- @func fun a function of at least two arguments
+-- @array t1 a list-like table
+-- @array t2 a list-like table
+-- @param ... extra arguments
+-- @usage imap2('+',{1,2,3,m=4},{10,20,30,m=40}) is {11,22,23}
+function tablex.imap2 (fun,t1,t2,...)
+    assert_arg_indexable(2,t1)
+    assert_arg_indexable(3,t2)
+    fun = function_arg(1,fun)
+    local res,n = {},math.min(#t1,#t2)
+    for i = 1,n do
+        res[i] = fun(t1[i],t2[i],...)
+    end
+    return res
+end
+
+--- 'reduce' a list using a binary function.
+-- @func fun a function of two arguments
+-- @array t a list-like table
+-- @array memo optional initial memo value. Defaults to first value in table.
+-- @return the result of the function
+-- @usage reduce('+',{1,2,3,4}) == 10
+function tablex.reduce (fun,t,memo)
+    assert_arg_indexable(2,t)
+    fun = function_arg(1,fun)
+    local n = #t
+    if n == 0 then
+        return memo
+    end
+    local res = memo and fun(memo, t[1]) or t[1]
+    for i = 2,n do
+        res = fun(res,t[i])
+    end
+    return res
+end
+
+--- apply a function to all elements of a table.
+-- The arguments to the function will be the value,
+-- the key and _finally_ any extra arguments passed to this function.
+-- Note that the Lua 5.0 function table.foreach passed the _key_ first.
+-- @within Iterating
+-- @tab t a table
+-- @func fun a function on the elements; `function(value, key, ...)`
+-- @param ... extra arguments passed to `fun`
+-- @see tablex.transform
+function tablex.foreach(t,fun,...)
+    assert_arg_iterable(1,t)
+    fun = function_arg(2,fun)
+    for k,v in pairs(t) do
+        fun(v,k,...)
+    end
+end
+
+--- apply a function to all elements of a list-like table in order.
+-- The arguments to the function will be the value,
+-- the index and _finally_ any extra arguments passed to this function
+-- @within Iterating
+-- @array t a table
+-- @func fun a function with at least one argument
+-- @param ... optional arguments
+function tablex.foreachi(t,fun,...)
+    assert_arg_indexable(1,t)
+    fun = function_arg(2,fun)
+    for i = 1,#t do
+        fun(t[i],i,...)
+    end
+end
+
+--- Apply a function to a number of tables.
+-- A more general version of map
+-- The result is a table containing the result of applying that function to the
+-- ith value of each table. Length of output list is the minimum length of all the lists
+-- @within MappingAndFiltering
+-- @func fun a function of n arguments
+-- @tab ... n tables
+-- @usage mapn(function(x,y,z) return x+y+z end, {1,2,3},{10,20,30},{100,200,300}) is {111,222,333}
+-- @usage mapn(math.max, {1,20,300},{10,2,3},{100,200,100}) is    {100,200,300}
+-- @param fun A function that takes as many arguments as there are tables
+function tablex.mapn(fun,...)
+    fun = function_arg(1,fun)
+    local res = {}
+    local lists = {...}
+    local minn = 1e40
+    for i = 1,#lists do
+        minn = min(minn,#(lists[i]))
+    end
+    for i = 1,minn do
+        local args,k = {},1
+        for j = 1,#lists do
+            args[k] = lists[j][i]
+            k = k + 1
+        end
+        res[#res+1] = fun(unpack(args))
+    end
+    return res
+end
+
+--- call the function with the key and value pairs from a table.
+-- The function can return a value and a key (note the order!). If both
+-- are not nil, then this pair is inserted into the result: if the key already exists, we convert the value for that
+-- key into a table and append into it. If only value is not nil, then it is appended to the result.
+-- @within MappingAndFiltering
+-- @func fun A function which will be passed each key and value as arguments, plus any extra arguments to pairmap.
+-- @tab t A table
+-- @param ... optional arguments
+-- @usage pairmap(function(k,v) return v end,{fred=10,bonzo=20}) is {10,20} _or_ {20,10}
+-- @usage pairmap(function(k,v) return {k,v},k end,{one=1,two=2}) is {one={'one',1},two={'two',2}}
+function tablex.pairmap(fun,t,...)
+    assert_arg_iterable(1,t)
+    fun = function_arg(1,fun)
+    local res = {}
+    for k,v in pairs(t) do
+        local rv,rk = fun(k,v,...)
+        if rk then
+            if res[rk] then
+                if type(res[rk]) == 'table' then
+                    table.insert(res[rk],rv)
+                else
+                    res[rk] = {res[rk], rv}
+                end
+            else
+                res[rk] = rv
+            end
+        else
+            res[#res+1] = rv
+        end
+    end
+    return res
+end
+
+local function keys_op(i,v) return i end
+
+--- return all the keys of a table in arbitrary order.
+-- @within Extraction
+--  @tab t A table
+function tablex.keys(t)
+    assert_arg_iterable(1,t)
+    return makelist(tablex.pairmap(keys_op,t))
+end
+
+local function values_op(i,v) return v end
+
+--- return all the values of the table in arbitrary order
+-- @within Extraction
+--  @tab t A table
+function tablex.values(t)
+    assert_arg_iterable(1,t)
+    return makelist(tablex.pairmap(values_op,t))
+end
+
+local function index_map_op (i,v) return i,v end
+
+--- create an index map from a list-like table. The original values become keys,
+-- and the associated values are the indices into the original list.
+-- @array t a list-like table
+-- @return a map-like table
+function tablex.index_map (t)
+    assert_arg_indexable(1,t)
+    return makemap(tablex.pairmap(index_map_op,t))
+end
+
+local function set_op(i,v) return true,v end
+
+--- create a set from a list-like table. A set is a table where the original values
+-- become keys, and the associated values are all true.
+-- @array t a list-like table
+-- @return a set (a map-like table)
+function tablex.makeset (t)
+    assert_arg_indexable(1,t)
+    return setmetatable(tablex.pairmap(set_op,t),require('pl.Set'))
+end
+
+--- combine two tables, either as union or intersection. Corresponds to
+-- set operations for sets () but more general. Not particularly
+-- useful for list-like tables.
+-- @within Merging
+-- @tab t1 a table
+-- @tab t2 a table
+-- @bool dup true for a union, false for an intersection.
+-- @usage merge({alice=23,fred=34},{bob=25,fred=34}) is {fred=34}
+-- @usage merge({alice=23,fred=34},{bob=25,fred=34},true) is {bob=25,fred=34,alice=23}
+-- @see tablex.index_map
+function tablex.merge (t1,t2,dup)
+    assert_arg_iterable(1,t1)
+    assert_arg_iterable(2,t2)
+    local res = {}
+    for k,v in pairs(t1) do
+        if dup or t2[k] then res[k] = v end
+    end
+    if dup then
+      for k,v in pairs(t2) do
+        res[k] = v
+      end
+    end
+    return setmeta(res,t1,'Map')
+end
+
+--- the union of two map-like tables.
+-- If there are duplicate keys, the second table wins.
+-- @tab t1 a table
+-- @tab t2 a table
+-- @treturn tab
+-- @see tablex.merge
+function tablex.union(t1, t2)
+    return tablex.merge(t1, t2, true)
+end
+
+--- the intersection of two map-like tables.
+-- @tab t1 a table
+-- @tab t2 a table
+-- @treturn tab
+-- @see tablex.merge
+function tablex.intersection(t1, t2)
+    return tablex.merge(t1, t2, false)
+end
+
+--- a new table which is the difference of two tables.
+-- With sets (where the values are all true) this is set difference and
+-- symmetric difference depending on the third parameter.
+-- @within Merging
+-- @tab s1 a map-like table or set
+-- @tab s2 a map-like table or set
+-- @bool symm symmetric difference (default false)
+-- @return a map-like table or set
+function tablex.difference (s1,s2,symm)
+    assert_arg_iterable(1,s1)
+    assert_arg_iterable(2,s2)
+    local res = {}
+    for k,v in pairs(s1) do
+        if s2[k] == nil then res[k] = v end
+    end
+    if symm then
+        for k,v in pairs(s2) do
+            if s1[k] == nil then res[k] = v end
+        end
+    end
+    return setmeta(res,s1,'Map')
+end
+
+--- A table where the key/values are the values and value counts of the table.
+-- @array t a list-like table
+-- @func cmp a function that defines equality (otherwise uses ==)
+-- @return a map-like table
+-- @see seq.count_map
+function tablex.count_map (t,cmp)
+    assert_arg_indexable(1,t)
+    local res,mask = {},{}
+    cmp = function_arg(2,cmp or '==')
+    local n = #t
+    for i = 1,#t do
+        local v = t[i]
+        if not mask[v] then
+            mask[v] = true
+            -- check this value against all other values
+            res[v] = 1  -- there's at least one instance
+            for j = i+1,n do
+                local w = t[j]
+                local ok = cmp(v,w)
+                if ok then
+                    res[v] = res[v] + 1
+                    mask[w] = true
+                end
+            end
+        end
+    end
+    return makemap(res)
+end
+
+--- filter an array's values using a predicate function
+-- @within MappingAndFiltering
+-- @array t a list-like table
+-- @func pred a boolean function
+-- @param arg optional argument to be passed as second argument of the predicate
+function tablex.filter (t,pred,arg)
+    assert_arg_indexable(1,t)
+    pred = function_arg(2,pred)
+    local res,k = {},1
+    for i = 1,#t do
+        local v = t[i]
+        if pred(v,arg) then
+            res[k] = v
+            k = k + 1
+        end
+    end
+    return setmeta(res,t,'List')
+end
+
+--- return a table where each element is a table of the ith values of an arbitrary
+-- number of tables. It is equivalent to a matrix transpose.
+-- @within Merging
+-- @usage zip({10,20,30},{100,200,300}) is {{10,100},{20,200},{30,300}}
+-- @array ... arrays to be zipped
+function tablex.zip(...)
+    return tablex.mapn(function(...) return {...} end,...)
+end
+
+local _copy
+function _copy (dest,src,idest,isrc,nsrc,clean_tail)
+    idest = idest or 1
+    isrc = isrc or 1
+    local iend
+    if not nsrc then
+        nsrc = #src
+        iend = #src
+    else
+        iend = isrc + min(nsrc-1,#src-isrc)
+    end
+    if dest == src then -- special case
+        if idest > isrc and iend >= idest then -- overlapping ranges
+            src = tablex.sub(src,isrc,nsrc)
+            isrc = 1; iend = #src
+        end
+    end
+    for i = isrc,iend do
+        dest[idest] = src[i]
+        idest = idest + 1
+    end
+    if clean_tail then
+        tablex.clear(dest,idest)
+    end
+    return dest
+end
+
+--- copy an array into another one, clearing `dest` after `idest+nsrc`, if necessary.
+-- @within Copying
+-- @array dest a list-like table
+-- @array src a list-like table
+-- @int[opt=1] idest where to start copying values into destination
+-- @int[opt=1] isrc where to start copying values from source
+-- @int[opt=#src] nsrc number of elements to copy from source
+function tablex.icopy (dest,src,idest,isrc,nsrc)
+    assert_arg_indexable(1,dest)
+    assert_arg_indexable(2,src)
+    return _copy(dest,src,idest,isrc,nsrc,true)
+end
+
+--- copy an array into another one.
+-- @within Copying
+-- @array dest a list-like table
+-- @array src a list-like table
+-- @int[opt=1] idest where to start copying values into destination
+-- @int[opt=1] isrc where to start copying values from source
+-- @int[opt=#src] nsrc number of elements to copy from source
+function tablex.move (dest,src,idest,isrc,nsrc)
+    assert_arg_indexable(1,dest)
+    assert_arg_indexable(2,src)
+    return _copy(dest,src,idest,isrc,nsrc,false)
+end
+
+function tablex._normalize_slice(self,first,last)
+  local sz = #self
+  if not first then first=1 end
+  if first<0 then first=sz+first+1 end
+  -- make the range _inclusive_!
+  if not last then last=sz end
+  if last < 0 then last=sz+1+last end
+  return first,last
+end
+
+--- Extract a range from a table, like  'string.sub'.
+-- If first or last are negative then they are relative to the end of the list
+-- eg. sub(t,-2) gives last 2 entries in a list, and
+-- sub(t,-4,-2) gives from -4th to -2nd
+-- @within Extraction
+-- @array t a list-like table
+-- @int first An index
+-- @int last An index
+-- @return a new List
+function tablex.sub(t,first,last)
+    assert_arg_indexable(1,t)
+    first,last = tablex._normalize_slice(t,first,last)
+    local res={}
+    for i=first,last do append(res,t[i]) end
+    return setmeta(res,t,'List')
+end
+
+--- set an array range to a value. If it's a function we use the result
+-- of applying it to the indices.
+-- @array t a list-like table
+-- @param val a value
+-- @int[opt=1] i1 start range
+-- @int[opt=#t] i2 end range
+function tablex.set (t,val,i1,i2)
+    assert_arg_indexable(1,t)
+    i1,i2 = i1 or 1,i2 or #t
+    if types.is_callable(val) then
+        for i = i1,i2 do
+            t[i] = val(i)
+        end
+    else
+        for i = i1,i2 do
+            t[i] = val
+        end
+    end
+end
+
+--- create a new array of specified size with initial value.
+-- @int n size
+-- @param val initial value (can be `nil`, but don't expect `#` to work!)
+-- @return the table
+function tablex.new (n,val)
+    local res = {}
+    tablex.set(res,val,1,n)
+    return res
+end
+
+--- clear out the contents of a table.
+-- @array t a list
+-- @param istart optional start position
+function tablex.clear(t,istart)
+    istart = istart or 1
+    for i = istart,#t do remove(t) end
+end
+
+--- insert values into a table.
+-- similar to `table.insert` but inserts values from given table `values`,
+-- not the object itself, into table `t` at position `pos`.
+-- @within Copying
+-- @array t the list
+-- @int[opt] position (default is at end)
+-- @array values
+function tablex.insertvalues(t, ...)
+    assert_arg(1,t,'table')
+    local pos, values
+    if select('#', ...) == 1 then
+        pos,values = #t+1, ...
+    else
+        pos,values = ...
+    end
+    if #values > 0 then
+        for i=#t,pos,-1 do
+            t[i+#values] = t[i]
+        end
+        local offset = 1 - pos
+        for i=pos,pos+#values-1 do
+            t[i] = values[i + offset]
+        end
+    end
+    return t
+end
+
+--- remove a range of values from a table.
+-- End of range may be negative.
+-- @array t a list-like table
+-- @int i1 start index
+-- @int i2 end index
+-- @return the table
+function tablex.removevalues (t,i1,i2)
+    assert_arg(1,t,'table')
+    i1,i2 = tablex._normalize_slice(t,i1,i2)
+    for i = i1,i2 do
+        remove(t,i1)
+    end
+    return t
+end
+
+local _find
+_find = function (t,value,tables)
+    for k,v in pairs(t) do
+        if v == value then return k end
+    end
+    for k,v in pairs(t) do
+        if not tables[v] and type(v) == 'table' then
+            tables[v] = true
+            local res = _find(v,value,tables)
+            if res then
+                res = tostring(res)
+                if type(k) ~= 'string' then
+                    return '['..k..']'..res
+                else
+                    return k..'.'..res
+                end
+            end
+        end
+    end
+end
+
+--- find a value in a table by recursive search.
+-- @within Finding
+-- @tab t the table
+-- @param value the value
+-- @array[opt] exclude any tables to avoid searching
+-- @return a fieldspec, e.g. 'a.b' or 'math.sin'
+-- @usage search(_G,math.sin,{package.path}) == 'math.sin'
+function tablex.search (t,value,exclude)
+    assert_arg_iterable(1,t)
+    local tables = {[t]=true}
+    if exclude then
+        for _,v in pairs(exclude) do tables[v] = true end
+    end
+    return _find(t,value,tables)
+end
+
+--- return an iterator to a table sorted by its keys
+-- @within Iterating
+-- @tab t the table
+-- @func f an optional comparison function (f(x,y) is true if x < y)
+-- @usage for k,v in tablex.sort(t) do print(k,v) end
+-- @return an iterator to traverse elements sorted by the keys
+function tablex.sort(t,f)
+    local keys = {}
+    for k in pairs(t) do keys[#keys + 1] = k end
+    tsort(keys,f)
+    local i = 0
+    return function()
+        i = i + 1
+        return keys[i], t[keys[i]]
+    end
+end
+
+--- return an iterator to a table sorted by its values
+-- @within Iterating
+-- @tab t the table
+-- @func f an optional comparison function (f(x,y) is true if x < y)
+-- @usage for k,v in tablex.sortv(t) do print(k,v) end
+-- @return an iterator to traverse elements sorted by the values
+function tablex.sortv(t,f)
+    f = function_arg(2, f or '<')
+    local keys = {}
+    for k in pairs(t) do keys[#keys + 1] = k end
+    tsort(keys,function(x, y) return f(t[x], t[y]) end)
+    local i = 0
+    return function()
+        i = i + 1
+        return keys[i], t[keys[i]]
+    end
+end
+
+--- modifies a table to be read only.
+-- This only offers weak protection. Tables can still be modified with
+-- `table.insert` and `rawset`.
+--
+-- *NOTE*: for Lua 5.1 length, pairs and ipairs will not work, since the
+-- equivalent metamethods are only available in Lua 5.2 and newer.
+-- @tab t the table
+-- @return the table read only (a proxy).
+function tablex.readonly(t)
+    local mt = {
+        __index=t,
+        __newindex=function(t, k, v) error("Attempt to modify read-only table", 2) end,
+        __pairs=function() return pairs(t) end,
+        __ipairs=function() return ipairs(t) end,
+        __len=function() return #t end,
+        __metatable=false
+    }
+    return setmetatable({}, mt)
+end
+
+return tablex