-- Rime Script >https://github.com/baopaau/rime-lua-collection/blob/master/calculator_translator.lua
-- 簡易計算器（執行任何Lua表達式）
--
-- 格式：=<exp>
-- Lambda語法糖：\<arg>.<exp>|
--
-- 例子：
-- =1+1 輸出 2
-- =floor(9^(8/7)*cos(deg(6))) 輸出 -3
-- =e^pi>pi^e 輸出 true
-- =max({1,7,2}) 輸出 7
-- =map({1,2,3},\x.x^2|) 輸出 {1, 4, 9}
-- =map(range(-5,5),\x.x*pi/4|,deriv(sin)) 輸出 {-0.7071, -1, -0.7071, 0, 0.7071, 1, 0.7071, 0, -0.7071, -1}
-- =$(range(-5,5,0.01))(map,\x.-60*x^2-16*x+20|)(max)() 輸出 21.066
-- =test(\x.trunc(sin(x),1e-3)==trunc(deriv(cos)(x),1e-3)|,range(-2,2,0.1)) 輸出 true
--
-- 安装：
-- - 將本文件保存至 <rime>/lua/
-- - 在 <rime>/rime.lua 新增一行：
--   `calculator_translator = require("calculator_translator")`
-- - 在 <rime>/<schema>.schema.yaml 新增：
--   `engine/translators/@next: lua_translator@calculator_translator`
--   `recognizer/patterns/expression: "^=.*$"`
-- 註：
-- - <rime> 替換爲RIME的共享目錄
-- - <schema> 替換爲自己的方案ID
-- - 如目錄／文件不存在，請自行創建

-- 定義全局函數、常數（注意命名空間污染）
cos = math.cos
sin = math.sin
tan = math.tan
acos = math.acos
asin = math.asin
atan = math.atan
rad = math.rad
deg = math.deg

abs = math.abs
floor = math.floor
ceil = math.ceil
mod = math.fmod
trunc = function(x, dc)
    if dc == nil then
        return math.modf(x)
    end
    return x - mod(x, dc)
end

round = function(x, dc)
    dc = dc or 1
    local dif = mod(x, dc)
    if abs(dif) > dc / 2 then
        return x < 0 and x - dif - dc or x - dif + dc
    end
    return x - dif
end

random = math.random
randomseed = math.randomseed

inf = math.huge
MAX_INT = math.maxinteger
MIN_INT = math.mininteger
pi = math.pi
sqrt = math.sqrt
exp = math.exp
e = exp(1)
ln = math.log
log = function(x, base)
    base = base or 10
    return ln(x) / ln(base)
end

min = function(arr)
    local m = inf
    for k, x in ipairs(arr) do
        m = x < m and x or m
    end
    return m
end

max = function(arr)
    local m = -inf
    for k, x in ipairs(arr) do
        m = x > m and x or m
    end
    return m
end

sum = function(t)
    local acc = 0
    for k, v in ipairs(t) do
        acc = acc + v
    end
    return acc
end

avg = function(t)
    return sum(t) / #t
end

isinteger = function(x)
    return math.fmod(x, 1) == 0
end

-- iterator . array
array = function(...)
    local arr = {}
    for v in ... do
        arr[#arr + 1] = v
    end
    return arr
end

-- iterator <- [form, to)
irange = function(from, to, step)
    if to == nil then
        to = from
        from = 0
    end
    step = step or 1
    local i = from - step
    to = to - step
    return function()
        if i < to then
            i = i + step
            return i
        end
    end
end

-- array <- [form, to)
range = function(from, to, step)
    return array(irange(from, to, step))
end

-- array . reversed iterator
irev = function(arr)
    local i = #arr + 1
    return function()
        if i > 1 then
            i = i - 1
            return arr[i]
        end
    end
end

-- array . reversed array
arev = function(arr)
    return array(irev(arr))
end

test = function(f, t)
    for k, v in ipairs(t) do
        if not f(v) then
            return false
        end
    end
    return true
end

-- # Functional
map = function(t, ...)
    local ta = {}
    for k, v in pairs(t) do
        local tmp = v
        for _, f in pairs({ ... }) do tmp = f(tmp) end
        ta[k] = tmp
    end
    return ta
end

filter = function(t, ...)
    local ta = {}
    local i = 1
    for k, v in pairs(t) do
        local erase = false
        for _, f in pairs({ ... }) do
            if not f(v) then
                erase = true
                break
            end
        end
        if not erase then
            ta[i] = v
            i = i + 1
        end
    end
    return ta
end

-- e.g: foldr({2,3},\n,x.x^n|,2) = 81
foldr = function(t, f, acc)
    for k, v in pairs(t) do
        acc = f(acc, v)
    end
    return acc
end

-- e.g: foldl({2,3},\n,x.x^n|,2) = 512
foldl = function(t, f, acc)
    for v in irev(t) do
        acc = f(acc, v)
    end
    return acc
end

-- 調用鏈生成函數（HOF for method chaining）
-- e.g: chain(range(-5,5))(map,\x.x/5|)(map,sin)(map,\x.e^x*10|)(map,floor)()
--    = floor(map(map(map(range(-5,5),\x.x/5|),sin),\x.e^x*10|))
--    = {4, 4, 5, 6, 8, 10, 12, 14, 17, 20}
-- 可以用 $ 代替 chain
chain = function(t)
    local ta = t
    local function cf(f, ...)
        if f ~= nil then
            ta = f(ta, ...)
            return cf
        else
            return ta
        end
    end
    return cf
end

-- # Statistics
fac = function(n)
    local acc = 1
    for i = 2, n do
        acc = acc * i
    end
    return acc
end

nPr = function(n, r)
    return fac(n) / fac(n - r)
end

nCr = function(n, r)
    return nPr(n, r) / fac(r)
end

MSE = function(t)
    local ss = 0
    local s = 0
    local n = #t
    for k, v in ipairs(t) do
        ss = ss + v * v
        s = s + v
    end
    return sqrt((n * ss - s * s) / (n * n))
end

-- # Linear Algebra


-- # Calculus
-- Linear approximation
lapproxd = function(f, delta)
    local delta = delta or 1e-8
    return function(x)
        return (f(x + delta) - f(x)) / delta
    end
end

-- Symmetric approximation
sapproxd = function(f, delta)
    local delta = delta or 1e-8
    return function(x)
        return (f(x + delta) - f(x - delta)) / delta / 2
    end
end

-- 近似導數
deriv = function(f, delta, dc)
    dc = dc or 1e-4
    local fd = sapproxd(f, delta)
    return function(x)
        return round(fd(x), dc)
    end
end

-- Trapezoidal rule
trapzo = function(f, a, b, n)
    local dif = b - a
    local acc = 0
    for i = 1, n - 1 do
        acc = acc + f(a + dif * (i / n))
    end
    acc = acc * 2 + f(a) + f(b)
    acc = acc * dif / n / 2
    return acc
end

-- 近似積分
integ = function(f, delta, dc)
    delta = delta or 1e-4
    dc = dc or 1e-4
    return function(a, b)
        if b == nil then
            b = a
            a = 0
        end
        local n = round(abs(b - a) / delta)
        return round(trapzo(f, a, b, n), dc)
    end
end

-- Runge-Kutta
rk4 = function(f, timestep)
    local timestep = timestep or 0.01
    return function(start_x, start_y, time)
        local x = start_x
        local y = start_y
        local t = time
        -- loop until i >= t
        for i = 0, t, timestep do
            local k1 = f(x, y)
            local k2 = f(x + (timestep / 2), y + (timestep / 2) * k1)
            local k3 = f(x + (timestep / 2), y + (timestep / 2) * k2)
            local k4 = f(x + timestep, y + timestep * k3)
            y = y + (timestep / 6) * (k1 + 2 * k2 + 2 * k3 + k4)
            x = x + timestep
        end
        return y
    end
end


-- # System
date = os.date
time = os.time
path = function()
    return debug.getinfo(1).source:match("@?(.*/)")
end


local function serialize(obj)
    local type = type(obj)
    if type == "number" then
        return isinteger(obj) and floor(obj) or obj
    elseif type == "boolean" then
        return tostring(obj)
    elseif type == "string" then
        return '"' .. obj .. '"'
    elseif type == "table" then
        local str = "{"
        local i = 1
        for k, v in pairs(obj) do
            if i ~= k then
                str = str .. "[" .. serialize(k) .. "]="
            end
            str = str .. serialize(v) .. ", "
            i = i + 1
        end
        str = str:len() > 3 and str:sub(0, -3) or str
        return str .. "}"
    elseif pcall(obj) then -- function類型
        return "callable"
    end
    return obj
end

-- greedy：隨時求值（每次變化都會求值，否則結尾爲特定字符時求值）
local greedy = true

local function calculator_translator(input, seg)
    if string.sub(input, 1, 1) ~= "C" then return end

    local expfin = greedy or string.sub(input, -1, -1) == ";"
    local exp = (greedy or not expfin) and string.sub(input, 2, -1) or string.sub(input, 2, -2)

    -- 空格輸入可能
    exp = exp:gsub("#", " ")

    yield(Candidate("number", seg.start, seg._end, exp, "表達式"))

    if not expfin then return end

    local expe = exp
    -- 鏈式調用語法糖
    expe = expe:gsub("%$", " chain ")
    -- lambda語法糖
    do
        local count
        repeat
            expe, count = expe:gsub("\\%s*([%a%d%s,_]-)%s*%.(.-)|", " (function (%1) return %2 end) ")
        until count == 0
    end
    --yield(Candidate("number", seg.start, seg._end, expe, "展開"))

    -- 防止危險操作，禁用os和io命名空間
    if expe:find("i?os?%.") then return end
    -- return語句保證了只有合法的Lua表達式才可執行
    local result = load("return " .. expe)()
    if result == nil then return end

    result = serialize(result)
    yield(Candidate("number", seg.start, seg._end, result, "答案"))
    yield(Candidate("number", seg.start, seg._end, exp .. " = " .. result, "等式"))
end

return calculator_translator
