if not modules then modules = { } end modules ['back-exp-imp-mth'] = {
    version   = 1.001,
    comment   = "companion to back-exp.mkiv",
    author    = "Hans Hagen, PRAGMA-ADE, Hasselt NL",
    copyright = "PRAGMA ADE / ConTeXt Development Team",
    license   = "see context related readme files"
}

local sub = string.sub
local utfchar, utfvalues = utf.char, utf.values
local setmetatableindex, concat = table.setmetatableindex, table.concat

local structurestags = structures.tags
local specifications = structurestags.specifications
local locatedtag     = structurestags.locatedtag

local backend        = structurestags.backend

local setattribute   = backend.setattribute
local extras         = backend.extras
local checks         = backend.checks
local finalizers     = backend.finalizers

----- bpfactor       = number.dimenfactors.bp
----- f_points       = string.formatters["%p"]
local f_em           = string.formatters["%.6Nem"]

local implement      = interfaces.implement

do

    local automathrows   = true  directives.register("export.math.autorows",   function(v) automathrows   = v end)
    local automathapply  = true  directives.register("export.math.autoapply",  function(v) automathapply  = v end)
    local automathnumber = true  directives.register("export.math.autonumber", function(v) automathnumber = v end)
    local automathstrip  = true  directives.register("export.math.autostrip",  function(v) automathstrip  = v end)

    local functions      = mathematics.categories.functions

    local function collapse(di,i,data,ndata,detail,element)
        local collapsing = di.data
        if data then
            di.element = element
            di.detail = nil
            i = i + 1
            while i <= ndata do
                local dn = data[i]
                if dn.detail == detail then
                    collapsing[#collapsing+1] = dn.data[1]
                    dn.skip = "ignore"
                    i = i + 1
                else
                    break
                end
            end
        end
        return i
    end

    local function collapse_mn(di,i,data,ndata)
        -- this is tricky ... we need to make sure that we wrap in mrows if we want
        -- to bypass this one
        local collapsing = di.data
        if data then
            i = i + 1
            while i <= ndata do
                local dn = data[i]
                local tg = dn.tg
                if tg == "mn" then
                    collapsing[#collapsing+1] = dn.data[1]
                    dn.skip = "ignore"
                    i = i + 1
                elseif tg == "mo" then
                    local d = dn.data[1]
                    if d == "." then
                        collapsing[#collapsing+1] = d
                        dn.skip = "ignore"
                        i = i + 1
                    else
                        break
                    end
                else
                    break
                end
            end
        end
        return i
    end

    -- maybe delay __i__ till we need it

    local apply_function = {
        {
            element = "mo",
         -- comment = "apply function",
         -- data    = { utfchar(0x2061) },
            data    = { "&#x2061;" },
            nature  = "mixed",
        }
    }

    local functioncontent = { }

    setmetatableindex(functioncontent,function(t,k)
        local v = { { content = k } }
        t[k] = v
        return v
    end)

    local dummy_nucleus = {
        element   = "mtext",
        data      = { content = "" },
        nature    = "inline",
        comment   = "dummy nucleus",
        fulltag   = "mtext>0"
    }

    local function accentchar(d) -- see mkiv for old one
        local detail = tonumber(d.detail)
        if detail then
            local d1 = d.data[1]
            if d1 and d1.tg == "mrow" then
                --
                d.element = "mrow" -- used
                d.detail = nil
                local s = specifications[d.fulltag] -- hm, used when not set
                s.detail = nil
                --
                d1.element = "mo" -- used
             -- d1.detail = nil
                d1.nature = "mixed"
                d1.data = { { content = utfchar(detail) } }
                return d
            end
        end
    end

    local no_mrow = {
        mrow     = true,
        mfenced  = true,
        mfrac    = true,
        mroot    = true,
        msqrt    = true,
        mtable   = true,
        mi       = true,
        mo       = true,
        mn       = true,
        mspace   = true,

     -- mstacker    = true,
     -- mextensible = true,
    }

    local function checkmath(root) -- we can provide utf.toentities as an option
        local data = root.data
        if data then
            local ndata = #data
            local roottg = root.tg
            if roottg == "mo" then
                local s = specifications[root.fulltag]
                local c = s.class
                if c == "open" or c == "close" or c == "middle" then
                    root.attributes = {
                        maxsize = 1
                    }
                end
            elseif roottg == "msubsup" then
                -- kind of tricky: we have a different order in display mode
                local nucleus, superscript, subscript
                if ndata > 3 then
                    -- error
                else
                    for i=1,ndata do
                        local di = data[i]
                        if not di then
                            -- weird
                        elseif di.content then
                            -- text
                        else
                            local s = specifications[di.fulltag]
                            if s.subscript then
                                subscript = i
                            elseif s.superscript then
                                superscript = i
                            else
                                nucleus = i
                            end
                        end
                    end
                    if superscript or subscript then
                        -- we probably always have 3 anyway ... needs checking
                        local nuc = nucleus     and data[nucleus]
                        local sub = subscript   and data[subscript]
                        local sup = superscript and data[superscript]
                        local n = 0 -- play safe
                        if nuc then n = n + 1 ; data[n] = nuc end
                        if sub then n = n + 1 ; data[n] = sub end
                        if sup then n = n + 1 ; data[n] = sup end
                    end
                end
         -- elseif roottg == "msup" or roottg == "msub" then
         --     -- m$^2$
         --     if ndata == 1 then
         --         local d = data[1]
         --         data[2] = d
         --         d.__i__ = 2
         --         data[1] = dummy_nucleus
         --     end
            elseif roottg == "mfenced" then
                local s = specifications[root.fulltag]
                local o = s.operator
                if o then
                    root.skip = "comment"
                 -- root.content = utfchar(o) -- use embedded for now
                else
                    local l = s.left
                    local m = s.middle
                    local r = s.right
                    if l then
                        l = utfchar(l)
                    end
                    if m then
                        local t = { }
                        for i=1,#m do
                            t[i] = utfchar(m[i])
                        end
                        m = concat(t)
                    end
                    if r then
                        r = utfchar(r)
                    end
                    root.attributes = {
                        open       = l,
                        separators = m,
                        close      = r,
                    }
                end
            elseif roottg == "mstacker" then
            end
            if ndata == 0 then
                root.skip = "comment" -- get rid of weird artefacts
                root.nota = "weird"
                return
            elseif ndata == 1 then
                local d = data[1]
                if not d or d == "" then
                    root.skip = "comment"
                    return
                elseif d.content then
                    return
                else -- if ndata == 1 then
                    local tg = d.tg
                    if automathrows and (roottg == "mrow" or roottg == "mtext") then
                        -- maybe just always ! check spec first
                        -- or we can have checks.* for each as we then can flatten
                        if no_mrow[tg] then
                            root.skip = "comment"
                        end
                    elseif roottg == "mo" then
                        if tg == "mo" then
                            root.skip = "comment"
                        end
                    end
                end
            end
            local i = 1
            while i <= ndata do                   -- -- -- TOO MUCH NESTED CHECKING -- -- --
                local di = data[i]
                if di and not di.content then
                    local tg = di.tg
                    if tg == "math" then
                     -- di.element = "mrow" -- when properties
                        di.skip = "comment"
                        checkmath(di)
                        i = i + 1
                    elseif tg == "mover" then
                        local s = specifications[di.fulltag]
                        if s.accent then
                            local t = s.top
                            local d = di.data
                            -- todo: accent = "false" (for scripts like limits)
                            di.attributes = {
                                accent = "true",
                            }
                            -- todo: p.topfixed
                            if t then
                                -- mover
                                if true then -- we don't go here any more
                                    local dd = d[1].data
                                    if dd then
                                        dd[1].content = utfchar(t)
                                    end
                                end
                                --
                                di.data = { d[2], d[1] }
                            end
                        else
                            -- can't happen
                        end
                        checkmath(di)
                        i = i + 1
                    elseif tg == "munder" then
                        local s = specifications[di.fulltag]
                        if s.accent then
                            local b = s.bottom
                            local d = di.data
                            -- todo: accent = "false" (for scripts like limits)
                            di.attributes = {
                                accent = "true",
                            }
                         -- todo: p.bottomfixed
                            if b then
                                -- munder
                                if true then -- we don't go here any more
                                    local dd = d[2].data
                                    if dd then
                                        dd[1].content = utfchar(b)
                                    end
                                end
                            end
                        else
                            -- can't happen
                        end
                        checkmath(di)
                        i = i + 1
                    elseif tg == "munderover" then
                        local s = specifications[di.fulltag]
                        if s.accent then
                            local t = s.top
                            local b = s.bottom
                            local d = di.data
                            -- todo: accent      = "false" (for scripts like limits)
                            -- todo: accentunder = "false" (for scripts like limits)
                            di.attributes = {
                                accent      = "true",
                                accentunder = "true",
                            }
                         -- todo: p.topfixed
                         -- todo: p.bottomfixed
                            if t and b then
                                -- munderover
                                if true then -- we don't go here any more
                                    local dd = d[1].data
                                    if dd then
                                        dd[1].content = utfchar(t)
                                    end
                                    local dd = d[3].data
                                    if dd then
                                        dd[1].content = utfchar(b)
                                    end
                                end
                                di.data = { d[2], d[3], d[1] }
                            else
                                -- can't happen
                            end
                        else
                            -- can't happen
                        end
                        checkmath(di)
                        i = i + 1
                    elseif tg == "mstacker" then
--                     inspect(di)
                        local d = di.data
                        local d1 = d[1]
                        local d2 = d[2]
                        local d3 = d[3]
                        local t1 = d1 and d1.tg
                        local t2 = d2 and d2.tg
                        local t3 = d3 and d3.tg
                        local m  = nil -- d1.data[1]
                        local t  = nil
                        local b  = nil
                        -- only accent when top / bot have stretch
                        -- normally we flush [base under over] which is better for tagged pdf
                        if t1 == "mstackermid" then
                            m = accentchar(d1) -- or m
                            if t2 == "mstackertop" then
                                if t3 == "mstackerbot" then
                                    t = accentchar(d2)
                                    b = accentchar(d3)
                                    di.element = "munderover"
                                    di.data    = { m or d1.data[1], b or d3.data[1], t or d2.data[1] }
                                else
                                    t = accentchar(d2)
                                    di.element = "mover"
                                    di.data    = { m or d1.data[1], t or d2.data[1] }
                                end
                            elseif t2 == "mstackerbot" then
                                if t3 == "mstackertop" then
                                    b = accentchar(d2)
                                    t = accentchar(d3)
                                    di.element = "munderover"
                                    di.data    = { m or d1.data[1], t or d3.data[1], m, b or d2.data[1] }
                                else
                                    b = accentchar(d2)
                                    di.element = "munder"
                                    di.data    = { m or d1.data[1], b or d2.data[1] }
                                end
                            else
-- di.element = "mweird"
                                -- can't happen
                            end
                        else
                            -- can't happen
                        end
                        if t or b then
                            di.attributes = {
                                accent      = t and "true" or nil,
                                accentunder = b and "true" or nil,
                            }
                            di.detail = nil
                        end
-- inspect(di)
                        checkmath(di)
                        i = i + 1
                    elseif tg == "mroot" then
                        local data = di.data
                        local size = #data
                        if size == 1 then
                            -- else firefox complains ... code in math-tag (for pdf tagging)
                            di.element = "msqrt"
                        elseif size == 2 then
                            data[1], data[2] = data[2], data[1]
                        end
                        checkmath(di)
                        i = i + 1
                    elseif tg == "break" then
                        di.skip = "comment"
                        i = i + 1
                    elseif tg == "mspace" then
                     -- di.empty = true
                        local s = specifications[di.fulltag]
                        local e = s and s.emfactor
                        if e and e ~= 0 then
                            di.element = "mspace"
                            di.attributes = {
                                width = f_em(e),
                            }
                        end
                        i = i + 1
                    elseif tg == "mtext" then
                        -- this is only needed for unboxed mtexts ... all kind of special
                        -- tex border cases and optimizations ... trial and error
                        local data = di.data
                        if #data > 1 then
                            for i=1,#data do
                                local di = data[i]
                                local content = di.content
                                if content then
                                    data[i] = {
                                        element = "mtext",
                                        nature  = "inline",
                                        data    = { di },
                                        n       = 0,
                                    }
                                elseif di.tg == "math" then
                                    local di = di.data[1]
                                    if di then
                                        data[i] = di
                                        checkmath(di)
                                    end
                                end
                            end
                            di.element = "mrow"
                         -- di.tg = "mrow"
                         -- di.nature  = "inline"
                        end
                        checkmath(di)
                        i = i + 1
                    elseif tg == "mrow" and detail then -- hm, falls through
                        di.detail = nil
                        checkmath(di)
                        di = {
                            element    = "maction",
                            nature     = "display",
                            attributes = { actiontype = detail },
                            data       = { di },
                            n          = 0,
                        }
                        data[i] = di
                        i = i + 1
                    else
                        local category = di.mathcategory
                        if category then
                         -- no checkmath(di) here
                            if category == 1 then -- mo
                                i = collapse(di,i,data,ndata,detail,"mo")
                            elseif category == 2 then -- mi
                                i = collapse(di,i,data,ndata,detail,"mi")
                            elseif category == 3 then -- mn
                                i = collapse(di,i,data,ndata,detail,"mn")
                            elseif category == 4 then -- ms
                                i = collapse(di,i,data,ndata,detail,"ms")
                            elseif category >= 1000 then
                                local apply = category >= 2000
                                if apply then
                                    category = category - 1000
                                end
                                if tg == "mi" then -- function
                                    if roottg == "mrow" then
                                        root.skip = "comment"
                                        root.element = "function"
                                    end
                                    i = collapse(di,i,data,ndata,detail,"mi")
                                    local tag = functions[category]
                                    if tag then
                                        di.data = functioncontent[tag]
                                    end
                                    if apply then
                                        di.after = apply_function
                                    elseif automathapply then -- make function
                                        local following
                                        if i <= ndata then
                                            -- normally not the case
                                            following = data[i]
                                        else
                                            local parent = di.__p__ -- == root
                                            if parent.tg == "mrow" then
                                                parent = parent.__p__
                                            end
                                            local index = parent.__i__
                                            following = parent.data[index+1]
                                        end
                                        if following then
                                            local tg = following.tg
                                            if tg == "mrow" or tg == "mfenced" then -- we need to figure out the right condition
                                                di.after = apply_function
                                            end
                                        end
                                    end
                                else -- some problem
                                    checkmath(di)
                                    i = i + 1
                                end
                            else
                                checkmath(di)
                                i = i + 1
                            end
                        elseif automathnumber and tg == "mn" then
                            checkmath(di)
                            i = collapse_mn(di,i,data,ndata)
                        else
                            checkmath(di)
                            i = i + 1
                        end
                    end
                else -- can be string or boolean
                    if parenttg ~= "mtext" and di == " " then
                        data[i] = false
                    end
                    i = i + 1
                end
            end
        end
    end

    local function stripmath(di)
        if not di then
            --
        elseif di.content then
            return di
        else
            local tg = di.tg
            if tg == "mtext" or tg == "ms" then
                return di
            elseif tg == "mspace" then
                return di
            else
                local data = di.data
                local ndata = #data
                local n = 0
                for i=1,ndata do
                    local d = data[i]
                    if d and not d.content then
                        d = stripmath(d)
                    end
                    if d then
                        local content = d.content
                        if d.tg == "mspace" then
                            n = n + 1
                            data[n] = d
                            d.data = { }
                        elseif not content then
--                      if not content then
                            n = n + 1
                            d.__i__ = n
                            data[n] = d
--                        elseif content == " " or content == "" then
--                            if d.tg == "mspace" then
--                             -- we append or prepend a space to a preceding or following mtext
--                                local parent = di.__p__
--                                local index  = di.__i__ -- == i
--                                local data   = parent.data
--                                if index > 1 then
--                                    local d = data[index-1]
--                                    if d.tg == "mtext" then
--                                        local dd = d.data
--                                        local dn = dd[#dd]
--                                        local dc = dn.content
--                                        if dc then
--                                            dn.content = dc .. content
--                                        end
--                                    end
--                                elseif index < ndata then
--                                    local d = data[index+1]
--                                    if d.tg == "mtext" then
--                                        local dd = d.data
--                                        local dn = dd[1]
--                                        local dc = dn.content
--                                        if dc then
--                                            dn.content = content .. dc
--                                        end
--                                    end
--                                end
--                            end
                        else
                            n = n + 1
                            data[n] = d
                        end
                    end
                end
                for i=ndata,n+1,-1 do
                    data[i] = nil
                end
                if #data > 0 then
                    return di
                end
            end
        end
    end

    function checks.math(di)
        if di.skip == "comment" then
            -- already done, kind of weird, happens in mathmatrix, maybe some collapse
            -- issue that i need to look into
        else
            local specification = specifications[di.fulltag]
            local mode = specification and specification.mode == "display" and "block" or "inline"
            di.attributes = {
                ["display"]    = mode,
                ["xmlns:m"]    = mathmlns,
                ["xmlns:math"] = mathmlns,
            }
            -- can be option if needed:
            if mode == "inline" then
             -- di.nature = "mixed"  -- else spacing problem (maybe inline)
                di.nature = "inline" -- we need to catch x$X$x and x $X$ x
            else
                di.nature = "display"
            end
            if automathstrip then
                stripmath(di)
            end
            checkmath(di)
        end
    end

    -- this one can replace some of the previous code .. todo (test on mathmatrix)

    -- ignore with no data can be removed

    local function checked(d)
        local n = #d
        if n == 1 then
            local di = d[1]
            local tg = di.tg
            if tg == "ignore" then
                -- todo: we can move ignore's data one level up
                return 1
            elseif di.content then
                return 1
            else
                local dd = di.data
                if #dd > 0 and checked(dd) > 0 then
                    return 1
                else
                    return 0
                end
            end
        else
            local m = 0
            for i=1,n do
                local di = d[i]
                local tg = di.tg
                if tg == "ignore" then
                    -- skip
                elseif di.content then
                    m = m + 1
                    d[m] = di
                else
                    local dd = di.data
                    if #dd > 0 and checked(dd) > 0 then
                        m = m + 1
                        d[m] = di
                    end
                end
            end
            if m < n then
                for i=n,m+1,-1 do
                    d[i] = nil
                end
            end
            return m
        end
    end

    function checks.mrow(di)
     -- local d = di.data
     -- if d then
     --     checked(d)
     -- end
    end

    -- we can move more checks here

    local function flatten(di)
        local r = di.__p__
        while r do
            local d = r.data
            local n = #d
            if d and n > 1 then
                n = checked(d)
            end
            local tg = r.tg
            if n == 1 and (tg == "mtext" or tg == "mrow") then
                r.skip = "comment" -- weird error
                r = r.__p__
            else
                break
            end
        end
    end

    function checks.mtable(di)
        flatten(di)
        local d = di.data
        for i=1,#d do
            local d = d[i]
            if d.tg == "mtr" then
                local d = d.data
                for i=1,#d do
                    local d = d[i]
                    if d.tg == "mtd" then
                        -- okay
                    elseif d.content then
                        d.content = ""
                    else
                        d.skip = "comment" -- weird error
                    end
                end
            elseif d.content then
                d.content = ""
            else
                d.skip = "comment" -- weird error
            end
        end
    end

    do

        local a, z, A, Z = 0x61, 0x7A, 0x41, 0x5A

        function extras.mi(di,element,n,fulltag) -- check with content
            local str = di.data[1].content
            if str and sub(str,1,1) ~= "&" then -- hack but good enough (maybe gsub op eerste)
                for v in utfvalues(str) do
                    if (v >= a and v <= z) or (v >= A and v <= Z) then
                        local a = di.attributes
                        if a then
                            a.mathvariant = "normal"
                        else
                            di.attributes = { mathvariant = "normal" }
                        end
                    end
                end
            end
        end

    end

    function extras.msub(di,element,n,fulltag)
        -- m$^2$
        local data = di.data
        if #data == 1 then
            local d = data[1]
            data[2] = d
            d.__i__ = 2
            data[1] = dummy_nucleus
        end
    end

    extras.msup = extras.msub

end