Footnote:
a variant which lists files under UTI group headings:
use AppleScript version "2.4"
use framework "Foundation"
use framework "Appkit"
use scripting additions
on run
    
    set fldr to filePath("~/Desktop")
    script nameAndUTI
        on |λ|(strName)
            if strName starts with "." then
                {}
            else
                {{name:strName, uti:fileUTI(fldr & "/" & strName)}}
            end if
        end |λ|
    end script
    
    script groupListing
        on |λ|(a, gp)
            script indented
                on |λ|(x)
                    tab & "- " & (name of x)
                end |λ|
            end script
            
            a & uti of item 1 of gp & ":" & linefeed & ¬
                unlines(map(indented, gp)) & ¬
                linefeed & linefeed
        end |λ|
    end script
    
    fldr & linefeed & linefeed & ¬
        foldl(groupListing, "", ¬
            groupBy(|on|(my eq, fpUTI), ¬
                sortBy(mappendComparing({fpUTI, fpName}), ¬
                    concatMap(nameAndUTI, getDirectoryContents(fldr)))))
end run
on fpUTI(x)
    uti of x
end fpUTI
on fpName(x)
    name of x
end fpName
on label(x)
    (name of x) -- & tab & (uti of x)
end label
-- GENERIC FUNCTIONS ----------------------------------------------------
-- https://github.com/RobTrew/prelude-applescript
-- Left :: a -> Either a b
on |Left|(x)
    {type:"Either", |Left|:x, |Right|:missing value}
end |Left|
-- Right :: b -> Either a b
on |Right|(x)
    {type:"Either", |Left|:missing value, |Right|:x}
end |Right|
-- Tuple (,) :: a -> b -> (a, b)
on Tuple(a, b)
    {type:"Tuple", |1|:a, |2|:b, length:2}
end Tuple
-- bindLR (>>=) :: Either a -> (a -> Either b) -> Either b
on bindLR(m, mf)
    if missing value is not |Right| of m then
        mReturn(mf)'s |λ|(|Right| of m)
    else
        m
    end if
end bindLR
-- Ordering  :: (-1 | 0 | 1)
-- compare :: a -> a -> Ordering
on compare(a, b)
    if a < b then
        -1
    else if a > b then
        1
    else
        0
    end if
end compare
-- concatMap :: (a -> [b]) -> [a] -> [b]
on concatMap(f, xs)
    set lng to length of xs
    if 0 < lng and class of xs is string then
        set acc to ""
    else
        set acc to {}
    end if
    tell mReturn(f)
        repeat with i from 1 to lng
            set acc to acc & |λ|(item i of xs, i, xs)
        end repeat
    end tell
    return acc
end concatMap
-- eq :: a -> a -> Bool
on eq(a, b)
    a = b
end eq
-- filePath :: String -> FilePath
on filePath(s)
    ((current application's ¬
        NSString's stringWithString:s)'s ¬
        stringByStandardizingPath()) as string
end filePath
-- fileStatus :: FilePath -> Either String Dict
on fileStatus(fp)
    set e to reference
    set {v, e} to current application's NSFileManager's defaultManager's ¬
        attributesOfItemAtPath:fp |error|:e
    if v is not missing value then
        |Right|(v as record)
    else
        |Left|((localizedDescription of e) as string)
    end if
end fileStatus
-- fileUTI :: FilePath -> String
on fileUTI(fp)
    set {uti, e} to (current application's ¬
        NSWorkspace's sharedWorkspace()'s ¬
        typeOfFile:fp |error|:(reference)) as list
    if uti is missing value then
        e's localizedDescription() as text
    else
        uti as text
    end if
end fileUTI
-- foldl :: (a -> b -> a) -> a -> [b] -> a
on foldl(f, startValue, xs)
    tell mReturn(f)
        set v to startValue
        set lng to length of xs
        repeat with i from 1 to lng
            set v to |λ|(v, item i of xs, i, xs)
        end repeat
        return v
    end tell
end foldl
-- getDirectoryContents :: FilePath -> IO [FilePath]
on getDirectoryContents(strPath)
    set ca to current application
    (ca's NSFileManager's defaultManager()'s ¬
        contentsOfDirectoryAtPath:(stringByStandardizingPath of ¬
            (ca's NSString's stringWithString:(strPath))) ¬
            |error|:(missing value)) as list
end getDirectoryContents
-- Typical usage: groupBy(on(eq, f), xs)
-- groupBy :: (a -> a -> Bool) -> [a] -> [[a]]
on groupBy(f, xs)
    set mf to mReturn(f)
    
    script enGroup
        on |λ|(a, x)
            if length of (active of a) > 0 then
                set h to item 1 of active of a
            else
                set h to missing value
            end if
            
            if h is not missing value and mf's |λ|(h, x) then
                {active:(active of a) & {x}, sofar:sofar of a}
            else
                {active:{x}, sofar:(sofar of a) & {active of a}}
            end if
        end |λ|
    end script
    
    if length of xs > 0 then
        set dct to foldl(enGroup, {active:{item 1 of xs}, sofar:{}}, tail(xs))
        if length of (active of dct) > 0 then
            sofar of dct & {active of dct}
        else
            sofar of dct
        end if
    else
        {}
    end if
end groupBy
-- map :: (a -> b) -> [a] -> [b]
on map(f, xs)
    tell mReturn(f)
        set lng to length of xs
        set lst to {}
        repeat with i from 1 to lng
            set end of lst to |λ|(item i of xs, i, xs)
        end repeat
        return lst
    end tell
end map
-- mappendComparing :: [(a -> b)] -> (a -> a -> Ordering)
on mappendComparing(fs)
    script
        on |λ|(x, y)
            script
                on |λ|(ordr, f)
                    if ordr ≠ 0 then
                        ordr
                    else
                        tell mReturn(f)
                            compare(|λ|(x), |λ|(y))
                        end tell
                    end if
                end |λ|
            end script
            foldl(result, 0, fs)
        end |λ|
    end script
end mappendComparing
-- Lift 2nd class handler function into 1st class script wrapper 
-- mReturn :: First-class m => (a -> b) -> m (a -> b)
on mReturn(f)
    if class of f is script then
        f
    else
        script
            property |λ| : f
        end script
    end if
end mReturn
-- e.g. sortBy(|on|(compare, |length|), ["epsilon", "mu", "gamma", "beta"])
-- on :: (b -> b -> c) -> (a -> b) -> a -> a -> c
on |on|(f, g)
    script
        on |λ|(a, b)
            tell mReturn(g) to set {va, vb} to {|λ|(a), |λ|(b)}
            tell mReturn(f) to |λ|(va, vb)
        end |λ|
    end script
end |on|
-- partition :: predicate -> List -> (Matches, nonMatches)
-- partition :: (a -> Bool) -> [a] -> ([a], [a])
on partition(f, xs)
    tell mReturn(f)
        set ys to {}
        set zs to {}
        repeat with x in xs
            set v to contents of x
            if |λ|(v) then
                set end of ys to v
            else
                set end of zs to v
            end if
        end repeat
    end tell
    Tuple(ys, zs)
end partition
-- Enough for small scale sorts.
-- Use instead sortOn :: Ord b => (a -> b) -> [a] -> [a]
-- which is equivalent to the more flexible sortBy(comparing(f), xs)
-- and uses a much faster ObjC NSArray sort method
-- sortBy :: (a -> a -> Ordering) -> [a] -> [a]
on sortBy(f, xs)
    if length of xs > 1 then
        set h to item 1 of xs
        set f to mReturn(f)
        script
            on |λ|(x)
                f's |λ|(x, h) ≤ 0
            end |λ|
        end script
        set lessMore to partition(result, rest of xs)
        sortBy(f, |1| of lessMore) & {h} & ¬
            sortBy(f, |2| of lessMore)
    else
        xs
    end if
end sortBy
-- tail :: [a] -> [a]
on tail(xs)
    if xs = {} then
        missing value
    else
        rest of xs
    end if
end tail
-- unlines :: [String] -> String
on unlines(xs)
    set {dlm, my text item delimiters} to ¬
        {my text item delimiters, linefeed}
    set str to xs as text
    set my text item delimiters to dlm
    str
end unlines