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--- Functional helpers like composition, binding and placeholder expressions.
-- Placeholder expressions are useful for short anonymous functions, and were
-- inspired by the Boost Lambda library.
--
-- > utils.import 'pl.func'
-- > ls = List{10,20,30}
-- > = ls:map(_1+1)
-- {11,21,31}
--
-- They can also be used to _bind_ particular arguments of a function.
--
-- > p = bind(print,'start>',_0)
-- > p(10,20,30)
-- > start> 10 20 30
--
-- See @{07-functional.md.Creating_Functions_from_Functions|the Guide}
--
-- Dependencies: `pl.utils`, `pl.tablex`
-- @module pl.func
local type,setmetatable,getmetatable,rawset = type,setmetatable,getmetatable,rawset
local concat,append = table.concat,table.insert
local tostring = tostring
local utils = require 'pl.utils'
local pairs,rawget,unpack,pack = pairs,rawget,utils.unpack,utils.pack
local tablex = require 'pl.tablex'
local map = tablex.map
local _DEBUG = rawget(_G,'_DEBUG')
local assert_arg = utils.assert_arg
local func = {}
-- metatable for Placeholder Expressions (PE)
local _PEMT = {}
local function P (t)
setmetatable(t,_PEMT)
return t
end
func.PE = P
local function isPE (obj)
return getmetatable(obj) == _PEMT
end
func.isPE = isPE
-- construct a placeholder variable (e.g _1 and _2)
local function PH (idx)
return P {op='X',repr='_'..idx, index=idx}
end
-- construct a constant placeholder variable (e.g _C1 and _C2)
local function CPH (idx)
return P {op='X',repr='_C'..idx, index=idx}
end
func._1,func._2,func._3,func._4,func._5 = PH(1),PH(2),PH(3),PH(4),PH(5)
func._0 = P{op='X',repr='...',index=0}
function func.Var (name)
local ls = utils.split(name,'[%s,]+')
local res = {}
for i = 1, #ls do
append(res,P{op='X',repr=ls[i],index=0})
end
return unpack(res)
end
function func._ (value)
return P{op='X',repr=value,index='wrap'}
end
local repr
func.Nil = func.Var 'nil'
function _PEMT.__index(obj,key)
return P{op='[]',obj,key}
end
function _PEMT.__call(fun,...)
return P{op='()',fun,...}
end
function _PEMT.__tostring (e)
return repr(e)
end
function _PEMT.__unm(arg)
return P{op='unm',arg}
end
function func.Not (arg)
return P{op='not',arg}
end
function func.Len (arg)
return P{op='#',arg}
end
local function binreg(context,t)
for name,op in pairs(t) do
rawset(context,name,function(x,y)
return P{op=op,x,y}
end)
end
end
local function import_name (name,fun,context)
rawset(context,name,function(...)
return P{op='()',fun,...}
end)
end
local imported_functions = {}
local function is_global_table (n)
return type(_G[n]) == 'table'
end
--- wrap a table of functions. This makes them available for use in
-- placeholder expressions.
-- @string tname a table name
-- @tab context context to put results, defaults to environment of caller
function func.import(tname,context)
assert_arg(1,tname,'string',is_global_table,'arg# 1: not a name of a global table')
local t = _G[tname]
context = context or _G
for name,fun in pairs(t) do
import_name(name,fun,context)
imported_functions[fun] = name
end
end
--- register a function for use in placeholder expressions.
-- @func fun a function
-- @string[opt] name an optional name
-- @return a placeholder functiond
function func.register (fun,name)
assert_arg(1,fun,'function')
if name then
assert_arg(2,name,'string')
imported_functions[fun] = name
end
return function(...)
return P{op='()',fun,...}
end
end
function func.lookup_imported_name (fun)
return imported_functions[fun]
end
local function _arg(...) return ... end
function func.Args (...)
return P{op='()',_arg,...}
end
-- binary operators with their precedences (see Lua manual)
-- precedences might be incremented by one before use depending on
-- left- or right-associativity, space them out
local binary_operators = {
['or'] = 0,
['and'] = 2,
['=='] = 4, ['~='] = 4, ['<'] = 4, ['>'] = 4, ['<='] = 4, ['>='] = 4,
['..'] = 6,
['+'] = 8, ['-'] = 8,
['*'] = 10, ['/'] = 10, ['%'] = 10,
['^'] = 14
}
-- unary operators with their precedences
local unary_operators = {
['not'] = 12, ['#'] = 12, ['unm'] = 12
}
-- comparisons (as prefix functions)
binreg (func,{And='and',Or='or',Eq='==',Lt='<',Gt='>',Le='<=',Ge='>='})
-- standard binary operators (as metamethods)
binreg (_PEMT,{__add='+',__sub='-',__mul='*',__div='/',__mod='%',__pow='^',__concat='..'})
binreg (_PEMT,{__eq='=='})
--- all elements of a table except the first.
-- @tab ls a list-like table.
function func.tail (ls)
assert_arg(1,ls,'table')
local res = {}
for i = 2,#ls do
append(res,ls[i])
end
return res
end
--- create a string representation of a placeholder expression.
-- @param e a placeholder expression
-- @param lastpred not used
function repr (e,lastpred)
local tail = func.tail
if isPE(e) then
local pred = binary_operators[e.op] or unary_operators[e.op]
if pred then
-- binary or unary operator
local s
if binary_operators[e.op] then
local left_pred = pred
local right_pred = pred
if e.op == '..' or e.op == '^' then
left_pred = left_pred + 1
else
right_pred = right_pred + 1
end
local left_arg = repr(e[1], left_pred)
local right_arg = repr(e[2], right_pred)
s = left_arg..' '..e.op..' '..right_arg
else
local op = e.op == 'unm' and '-' or e.op
s = op..' '..repr(e[1], pred)
end
if lastpred and lastpred > pred then
s = '('..s..')'
end
return s
else -- either postfix, or a placeholder
local ls = map(repr,e)
if e.op == '[]' then
return ls[1]..'['..ls[2]..']'
elseif e.op == '()' then
local fn
if ls[1] ~= nil then -- was _args, undeclared!
fn = ls[1]
else
fn = ''
end
return fn..'('..concat(tail(ls),',')..')'
else
return e.repr
end
end
elseif type(e) == 'string' then
return '"'..e..'"'
elseif type(e) == 'function' then
local name = func.lookup_imported_name(e)
if name then return name else return tostring(e) end
else
return tostring(e) --should not really get here!
end
end
func.repr = repr
-- collect all the non-PE values in this PE into vlist, and replace each occurence
-- with a constant PH (_C1, etc). Return the maximum placeholder index found.
local collect_values
function collect_values (e,vlist)
if isPE(e) then
if e.op ~= 'X' then
local m = 0
for i = 1,#e do
local subx = e[i]
local pe = isPE(subx)
if pe then
if subx.op == 'X' and subx.index == 'wrap' then
subx = subx.repr
pe = false
else
m = math.max(m,collect_values(subx,vlist))
end
end
if not pe then
append(vlist,subx)
e[i] = CPH(#vlist)
end
end
return m
else -- was a placeholder, it has an index...
return e.index
end
else -- plain value has no placeholder dependence
return 0
end
end
func.collect_values = collect_values
--- instantiate a PE into an actual function. First we find the largest placeholder used,
-- e.g. _2; from this a list of the formal parameters can be build. Then we collect and replace
-- any non-PE values from the PE, and build up a constant binding list.
-- Finally, the expression can be compiled, and e.__PE_function is set.
-- @param e a placeholder expression
-- @return a function
function func.instantiate (e)
local consts,values,parms = {},{},{}
local rep, err, fun
local n = func.collect_values(e,values)
for i = 1,#values do
append(consts,'_C'..i)
if _DEBUG then print(i,values[i]) end
end
for i =1,n do
append(parms,'_'..i)
end
consts = concat(consts,',')
parms = concat(parms,',')
rep = repr(e)
local fstr = ('return function(%s) return function(%s) return %s end end'):format(consts,parms,rep)
if _DEBUG then print(fstr) end
fun,err = utils.load(fstr,'fun')
if not fun then return nil,err end
fun = fun() -- get wrapper
fun = fun(unpack(values)) -- call wrapper (values could be empty)
e.__PE_function = fun
return fun
end
--- instantiate a PE unless it has already been done.
-- @param e a placeholder expression
-- @return the function
function func.I(e)
if rawget(e,'__PE_function') then
return e.__PE_function
else return func.instantiate(e)
end
end
utils.add_function_factory(_PEMT,func.I)
--- bind the first parameter of the function to a value.
-- @function func.bind1
-- @func fn a function of one or more arguments
-- @param p a value
-- @return a function of one less argument
-- @usage (bind1(math.max,10))(20) == math.max(10,20)
func.bind1 = utils.bind1
func.curry = func.bind1
--- create a function which chains two functions.
-- @func f a function of at least one argument
-- @func g a function of at least one argument
-- @return a function
-- @usage printf = compose(io.write,string.format)
function func.compose (f,g)
return function(...) return f(g(...)) end
end
--- bind the arguments of a function to given values.
-- `bind(fn,v,_2)` is equivalent to `bind1(fn,v)`.
-- @func fn a function of at least one argument
-- @param ... values or placeholder variables
-- @return a function
-- @usage (bind(f,_1,a))(b) == f(a,b)
-- @usage (bind(f,_2,_1))(a,b) == f(b,a)
function func.bind(fn,...)
local args = pack(...)
local holders,parms,bvalues,values = {},{},{'fn'},{}
local nv,maxplace,varargs = 1,0,false
for i = 1,args.n do
local a = args[i]
if isPE(a) and a.op == 'X' then
append(holders,a.repr)
maxplace = math.max(maxplace,a.index)
if a.index == 0 then varargs = true end
else
local v = '_v'..nv
append(bvalues,v)
append(holders,v)
append(values,a)
nv = nv + 1
end
end
for np = 1,maxplace do
append(parms,'_'..np)
end
if varargs then append(parms,'...') end
bvalues = concat(bvalues,',')
parms = concat(parms,',')
holders = concat(holders,',')
local fstr = ([[
return function (%s)
return function(%s) return fn(%s) end
end
]]):format(bvalues,parms,holders)
if _DEBUG then print(fstr) end
local res = utils.load(fstr)
res = res()
return res(fn,unpack(values))
end
return func
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