lex_xl: Parse Excel formulas into tokens
In nacnudus/lexl: Tokenise 'Excel' Formulas

Description Usage Arguments Details Value See Also Examples

lex_xl takes an Excel formula and separates it into tokens. It returns a dataframe, one row per token, giving the token itself, its type (e.g. number, or error), and its level.

The level is a number to show the depth of a token within nested function calls. The token A2 in the formula IF(A1=1,A2,MAX(A3,A4)) is at level 1. Tokens A3 and A4 are at level 2. The token IF is at level 0, which is the outermost level.

The output isn't enough to enable computation or validation of formulas, but it is enough to investigate the structure of formulas and spreadsheets. It has been tested on millions of formulas in the Enron corpus.

lex_xl(x)

`x`	Character vector of length 1, giving the formula.

The different types of tokens are:

ref A cell reference/address e.g. A1 or $B2:C$14.
sheetA sheet name, e.g. Sheet1! or 'My Sheet'!. If the sheet is from a different file, then the file is included in this token – usually it has been normalized to the form [0].
name A named range, or more properly a named formula.
function An Excel or user-defined function, e.g. MAX or _xll.MY_CUSTOM_FUNCTION. A complete list of official Excel functions is available in the vector excel_functions.
error An error, e.g. #N/A or #REF!.
bool TRUE or FALSE – note that there are also functions TRUE() and FALSE().
number All forms of numbers, e.g. 1, 1.1, -1, 1.2E3.
text Strings inside double quotes, e.g. "Hello, World!".
operator The usual infix operators, +, -, *, /, ^, <, <=, <>, etc. and also the range operator : when it is used with ranges that aren't cell addresses, e.g. INDEX(something):A1. The union operator , is the same symbol that is used to separate function arguments and array columns, so it is only tagged operator when it is inside parentheses that are not function parentheses or array curly braces (see the examples).
paren_open An open parenthesis ( indicating an increase in the level of nesting, but not directly enclosing function arguments.
paren_close As open, but reducing the level of nesting.
open_array An open curly brace '{' indicating the start of an array of constants, and an increase in the level of nesting.
close_array As open_array, but ending the array of constants
fun_open An open parenthesis ( immediately after a function name, directly enclosing the function arguments.
fun_close As fun_open but immediately after the function arguments.
separator A comma , separating function arguments or array columns, or a semicolon ; separating array rows.
DDE A call to a Dynamic Data Exchange server, usually normalized to the form [1]!'DDE_parameter=1', but the full form is 'ABCD'|'EFGH'!'IJKL'.
space Some old files haven't stripped formulas of meaningless spaces. They are returned as space tokens so that the original formula can always be reconstructed by concatenating all tokens.
other If you see this, then something has gone wrong – please report it at https://github.com/nacnudus/lexl/issues with a reproducible example (e.g. using the reprex package).

Every part of the original formula is returned as a token, so the original formula can be reconstructed by concatenating the tokens. If that doesn't work, please report it at https://github.com/nacnudus/lexl/issues with a reproducible example (e.g. using the reprex package).

The XLParser project was a great help in creating the grammar. https://github.com/spreadsheetlab/XLParser.

A data frame (a tibble, if you use the tidyverse) one row per token, giving the token itself, its type (e.g. number, or error), and its level.

plot.lexl(), lexl::lexl_igraph(), lexl::demo_lexl()

# All explicit cell references/addresses are returned as a single 'ref'
# token.
lex_xl("A1")
lex_xl("A$1")
lex_xl("$A1")
lex_xl("$A$1")
lex_xl("A1:B2")
lex_xl("1:1") # Whole row
lex_xl("A:B") # Whole column

# If one part of an address is a name or a function, then the colon ':' is
# regarded as a 'range operator', so is tagged 'operator'.
lex_xl("A1:SOME.NAME")
lex_xl("SOME_FUNCTION():B2")
lex_xl("SOME_FUNCTION():SOME.NAME")

# Sheet names are recognised by the terminal exclamation mark '!'.
lex_xl("Sheet1!A1")
lex_xl("'Sheet 1'!A1")       # Quoted names may contain some punctuation
lex_xl("'It''s a sheet'!A1") # Quotes are escaped by doubling

# Sheets can be ranged together in so-called 'three-dimensional formulas'.
# Both sheets are returned in a single 'sheet' token.
lex_xl("Sheet1:Sheet2!A1")
lex_xl("'Sheet 1:Sheet 2'!A1") # Quotes surround both sheets (not each)

# Sheets from other files are prefixed by the filename, which Excel
# normalizes the filenames into indexes.  Either way, lex_xl() includes the
# file/index in the 'sheet' token.
lex_xl("[1]Sheet1!A1")
lex_xl("'[1]Sheet 1'!A1") # Quotes surround both the file index and the sheet
lex_xl("'C:\\My Documents\\[file.xlsx]Sheet1'!A1")

# Function names are recognised by the terminal open-parenthesis '('.  There
# is no distinction between custom functions and built-in Excel functions.
# The open-parenthesis is tagged 'fun_open', and the corresponding
# close-parenthesis at the end of the arguments is tagged 'fun_close'.
lex_xl("MAX(1,2)")
lex_xl("_xll.MY_CUSTOM_FUNCTION()")

# Named ranges (properly called 'named formulas') are a last resort after
# attempting to match a function (ending in an open parenthesis '(') or a
# sheet (ending in an exclamation mark '!')
lex_xl("MY_NAMED_RANGE")

# Some cell addresses/references, functions and names can look alike, but
# lex_xl() should always make the right choice.
lex_xl("XFD1")     # A cell in the maximum column in Excel
lex_xl("XFE1")     # Beyond the maximum column, must be a named range/formula
lex_xl("A1048576") # A cell in the maximum row in Excel
lex_xl("A1048577") # Beyond the maximum row, must be a named range/formula
lex_xl("LOG10")    # A cell address
lex_xl("LOG10()")  # A log function
lex_xl("LOG:LOG")  # The whole column 'LOG'
lex_xl("LOG")      # Not a cell address, must be a named range/formula
lex_xl("LOG()")    # Another log function
lex_xl("A1.2!A1")  # A sheet called 'A1.2'

# Text is surrounded by double-quotes.
lex_xl("\"Some text\"")
lex_xl("\"Some \"\"text\"\"\"") # Double-quotes within text are escaped by

# Numbers are signed where it makes sense, and can be scientific
lex_xl("1")
lex_xl("1.2")
lex_xl("-1")
lex_xl("-1-1")
lex_xl("-1+-1")
lex_xl("MAX(-1-1)")
lex_xl("-1.2E-3")

# Booleans can be constants or functions, and names can look like booleans,
# but lex_xl() should always make the right choice.
lex_xl("TRUE")
lex_xl("TRUEISH")
lex_xl("TRUE!A1")
lex_xl("TRUE()")

# Errors are tagged 'error'
lex_xl("#DIV/0!")
lex_xl("#N/A")
lex_xl("#NAME?")
lex_xl("#NULL!")
lex_xl("#NUM!")
lex_xl("#REF!")
lex_xl("#VALUE!")

# Operators with more than one character are treated as single tokens
lex_xl("1<>2")
lex_xl("1<=2")
lex_xl("1<2")
lex_xl("1=2")
lex_xl("1&2")
lex_xl("1 2")
lex_xl("(1,2)")
lex_xl("1%")   # postfix operator

# The union operator is a comma ',', which is the same symbol that is used
# to separate function arguments or array columns.  It is tagged 'operator'
# only when it is inside parentheses that are not function parentheses or
# array curly braces.  The curly braces are tagged 'array_open' and
# 'array_close'.
lex_xl("A1,B2") # invalid formula, defaults to 'union' to avoid a crash
lex_xl("(A1,B2)")
lex_xl("MAX(A1,B2)")
lex_xl("SMALL((A1,B2),1)")

# Function arguments are separated by commas ',', which are tagged
# 'separator'.
lex_xl("MAX(1,2)")

# Nested functions are marked by an increase in the 'level'.  The level
# increases inside parentheses, rather than at the parentheses.  Curly
# braces, for arrays, have the same behaviour, as do subexpressions inside
# ordinary parenthesis, tagged 'paren_open' and 'paren_close'.
lex_xl("MAX(MIN(1,2),3)")
lex_xl("{1,2;3,4}")
lex_xl("1*(2+3)")

# Arrays are marked by opening and closing curly braces, with comma ','
# between columns, and semicolons ';' between rows  Commas and semicolons are
# both tagged 'separator'.  Arrays contain only constants, which are
# booleans, numbers, text, and errors.
lex_xl("MAX({1,2;3,4})")
lex_xl("=MAX({-1E-2,TRUE;#N/A,\"Hello, World!\"})")

# Structured references are surrounded by square brackets.  Subexpressions
# may also be surrounded by square brackets, but lex_xl() returns the whole
# expression in a single 'structured_ref' token.
lex_xl("[@col2]")
lex_xl("SUM([col22])")
lex_xl("Table1[col1]")
lex_xl("Table1[[col1]:[col2]]")
lex_xl("Table1[#Headers]")
lex_xl("Table1[[#Headers],[col1]]")
lex_xl("Table1[[#Headers],[col1]:[col2]]")

# DDE calls (Dynamic Data Exchange) are normalized by Excel into indexes.
# Either way, lex_xl() includes everything in one token.
lex_xl("[1]!'DDE_parameter=1'")
lex_xl("'Quote'|'NYSE'!ZAXX")
# Meaningless spaces that appear in some old files are returned as 'space'
# tokens, so that the original formula can still be recovered by
# concatenating all the tokens.  Spaces between function names and their open
# parenthesis have not been observed, so are not permitted.
lex_xl(" MAX( A1 ) ")