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--- List comprehensions implemented in Lua.
--
-- See the [wiki page](http://lua-users.org/wiki/ListComprehensions)
--
-- local C= require 'pl.comprehension' . new()
--
-- C ('x for x=1,10') ()
-- ==> {1,2,3,4,5,6,7,8,9,10}
-- C 'x^2 for x=1,4' ()
-- ==> {1,4,9,16}
-- C '{x,x^2} for x=1,4' ()
-- ==> {{1,1},{2,4},{3,9},{4,16}}
-- C '2*x for x' {1,2,3}
-- ==> {2,4,6}
-- dbl = C '2*x for x'
-- dbl {10,20,30}
-- ==> {20,40,60}
-- C 'x for x if x % 2 == 0' {1,2,3,4,5}
-- ==> {2,4}
-- C '{x,y} for x = 1,2 for y = 1,2' ()
-- ==> {{1,1},{1,2},{2,1},{2,2}}
-- C '{x,y} for x for y' ({1,2},{10,20})
-- ==> {{1,10},{1,20},{2,10},{2,20}}
-- assert(C 'sum(x^2 for x)' {2,3,4} == 2^2+3^2+4^2)
--
-- (c) 2008 David Manura. Licensed under the same terms as Lua (MIT license).
--
-- Dependencies: `pl.utils`, `pl.luabalanced`
--
-- See @{07-functional.md.List_Comprehensions|the Guide}
-- @module pl.comprehension
local utils = require 'pl.utils'
local status,lb = pcall(require, "pl.luabalanced")
if not status then
lb = require 'luabalanced'
end
local math_max = math.max
local table_concat = table.concat
-- fold operations
-- http://en.wikipedia.org/wiki/Fold_(higher-order_function)
local ops = {
list = {init=' {} ', accum=' __result[#__result+1] = (%s) '},
table = {init=' {} ', accum=' local __k, __v = %s __result[__k] = __v '},
sum = {init=' 0 ', accum=' __result = __result + (%s) '},
min = {init=' nil ', accum=' local __tmp = %s ' ..
' if __result then if __tmp < __result then ' ..
'__result = __tmp end else __result = __tmp end '},
max = {init=' nil ', accum=' local __tmp = %s ' ..
' if __result then if __tmp > __result then ' ..
'__result = __tmp end else __result = __tmp end '},
}
-- Parses comprehension string expr.
-- Returns output expression list <out> string, array of for types
-- ('=', 'in' or nil) <fortypes>, array of input variable name
-- strings <invarlists>, array of input variable value strings
-- <invallists>, array of predicate expression strings <preds>,
-- operation name string <opname>, and number of placeholder
-- parameters <max_param>.
--
-- The is equivalent to the mathematical set-builder notation:
--
-- <opname> { <out> | <invarlist> in <invallist> , <preds> }
--
-- @usage "x^2 for x" -- array values
-- @usage "x^2 for x=1,10,2" -- numeric for
-- @usage "k^v for k,v in pairs(_1)" -- iterator for
-- @usage "(x+y)^2 for x for y if x > y" -- nested
--
local function parse_comprehension(expr)
local pos = 1
-- extract opname (if exists)
local opname
local tok, post = expr:match('^%s*([%a_][%w_]*)%s*%(()', pos)
local pose = #expr + 1
if tok then
local tok2, posb = lb.match_bracketed(expr, post-1)
assert(tok2, 'syntax error')
if expr:match('^%s*$', posb) then
opname = tok
pose = posb - 1
pos = post
end
end
opname = opname or "list"
-- extract out expression list
local out; out, pos = lb.match_explist(expr, pos)
assert(out, "syntax error: missing expression list")
out = table_concat(out, ', ')
-- extract "for" clauses
local fortypes = {}
local invarlists = {}
local invallists = {}
while 1 do
local post = expr:match('^%s*for%s+()', pos)
if not post then break end
pos = post
-- extract input vars
local iv; iv, pos = lb.match_namelist(expr, pos)
assert(#iv > 0, 'syntax error: zero variables')
for _,ident in ipairs(iv) do
assert(not ident:match'^__',
"identifier " .. ident .. " may not contain __ prefix")
end
invarlists[#invarlists+1] = iv
-- extract '=' or 'in' (optional)
local fortype, post = expr:match('^(=)%s*()', pos)
if not fortype then fortype, post = expr:match('^(in)%s+()', pos) end
if fortype then
pos = post
-- extract input value range
local il; il, pos = lb.match_explist(expr, pos)
assert(#il > 0, 'syntax error: zero expressions')
assert(fortype ~= '=' or #il == 2 or #il == 3,
'syntax error: numeric for requires 2 or three expressions')
fortypes[#invarlists] = fortype
invallists[#invarlists] = il
else
fortypes[#invarlists] = false
invallists[#invarlists] = false
end
end
assert(#invarlists > 0, 'syntax error: missing "for" clause')
-- extract "if" clauses
local preds = {}
while 1 do
local post = expr:match('^%s*if%s+()', pos)
if not post then break end
pos = post
local pred; pred, pos = lb.match_expression(expr, pos)
assert(pred, 'syntax error: predicated expression not found')
preds[#preds+1] = pred
end
-- extract number of parameter variables (name matching "_%d+")
local stmp = ''; lb.gsub(expr, function(u, sin) -- strip comments/strings
if u == 'e' then stmp = stmp .. ' ' .. sin .. ' ' end
end)
local max_param = 0; stmp:gsub('[%a_][%w_]*', function(s)
local s = s:match('^_(%d+)$')
if s then max_param = math_max(max_param, tonumber(s)) end
end)
if pos ~= pose then
assert(false, "syntax error: unrecognized " .. expr:sub(pos))
end
--DEBUG:
--print('----\n', string.format("%q", expr), string.format("%q", out), opname)
--for k,v in ipairs(invarlists) do print(k,v, invallists[k]) end
--for k,v in ipairs(preds) do print(k,v) end
return out, fortypes, invarlists, invallists, preds, opname, max_param
end
-- Create Lua code string representing comprehension.
-- Arguments are in the form returned by parse_comprehension.
local function code_comprehension(
out, fortypes, invarlists, invallists, preds, opname, max_param
)
local op = assert(ops[opname])
local code = op.accum:gsub('%%s', out)
for i=#preds,1,-1 do local pred = preds[i]
code = ' if ' .. pred .. ' then ' .. code .. ' end '
end
for i=#invarlists,1,-1 do
if not fortypes[i] then
local arrayname = '__in' .. i
local idx = '__idx' .. i
code =
' for ' .. idx .. ' = 1, #' .. arrayname .. ' do ' ..
' local ' .. invarlists[i][1] .. ' = ' .. arrayname .. '['..idx..'] ' ..
code .. ' end '
else
code =
' for ' ..
table_concat(invarlists[i], ', ') ..
' ' .. fortypes[i] .. ' ' ..
table_concat(invallists[i], ', ') ..
' do ' .. code .. ' end '
end
end
code = ' local __result = ( ' .. op.init .. ' ) ' .. code
return code
end
-- Convert code string represented by code_comprehension
-- into Lua function. Also must pass ninputs = #invarlists,
-- max_param, and invallists (from parse_comprehension).
-- Uses environment env.
local function wrap_comprehension(code, ninputs, max_param, invallists, env)
assert(ninputs > 0)
local ts = {}
for i=1,max_param do
ts[#ts+1] = '_' .. i
end
for i=1,ninputs do
if not invallists[i] then
local name = '__in' .. i
ts[#ts+1] = name
end
end
if #ts > 0 then
code = ' local ' .. table_concat(ts, ', ') .. ' = ... ' .. code
end
code = code .. ' return __result '
--print('DEBUG:', code)
local f, err = utils.load(code,'tmp','t',env)
if not f then assert(false, err .. ' with generated code ' .. code) end
return f
end
-- Build Lua function from comprehension string.
-- Uses environment env.
local function build_comprehension(expr, env)
local out, fortypes, invarlists, invallists, preds, opname, max_param
= parse_comprehension(expr)
local code = code_comprehension(
out, fortypes, invarlists, invallists, preds, opname, max_param)
local f = wrap_comprehension(code, #invarlists, max_param, invallists, env)
return f
end
-- Creates new comprehension cache.
-- Any list comprehension function created are set to the environment
-- env (defaults to caller of new).
local function new(env)
-- Note: using a single global comprehension cache would have had
-- security implications (e.g. retrieving cached functions created
-- in other environments).
-- The cache lookup function could have instead been written to retrieve
-- the caller's environment, lookup up the cache private to that
-- environment, and then looked up the function in that cache.
-- That would avoid the need for this <new> call to
-- explicitly manage caches; however, that might also have an undue
-- performance penalty.
if not env then
env = utils.getfenv(2)
end
local mt = {}
local cache = setmetatable({}, mt)
-- Index operator builds, caches, and returns Lua function
-- corresponding to comprehension expression string.
--
-- Example: f = comprehension['x^2 for x']
--
function mt:__index(expr)
local f = build_comprehension(expr, env)
self[expr] = f -- cache
return f
end
-- Convenience syntax.
-- Allows comprehension 'x^2 for x' instead of comprehension['x^2 for x'].
mt.__call = mt.__index
cache.new = new
return cache
end
local comprehension = {}
comprehension.new = new
return comprehension
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