Home · Blog · Games · Resume

2020-07-03
GitHub:
https://github.com/ambuc/latis

# Background

I wrote a command-line spreadsheet toy in C++. It renders as a TUI and implements an Excel-like grammar for defining formulae. The full source is here.

# Design

In-scope for this project:

• Designing an ABNF grammar
• Writing a system for lexing, parsing, and evaluating user input.
• Writing a TUI for rendering spreadsheets interactively.
• Using C++. (Mostly to learn about OSS Bazel, absl, and protobuffers.

Out-of-scope:

• A fully-featured spreadsheet app which is easy to use or interoperates with other spreadsheet formats.

## Design Overview

A spreadsheet program needs to have individual cells, each of which either has:

• a typed value (a string value, a numeric value, or a monetary value, to name a few) or
• a formula which is dependent on zero or more cells and which returns a typed value.

User input must be lexed (broken up into a series of meaningful tokens), parsed, (turned from a series of tokens into a data structure via a formal grammar), and evaluated (rendered to a typed value). The degenerate case of this lex-parse-evaluate pipeline is a single typed value.

The program must also maintain a graph of cells and their dependencies on each other. If cell A depends on cell B, and cell B is updated, the rendering of cell A (but not its underlying formula) must also be updated. Furthermore, cells depending on A must be updated, and so on and so forth.

Finally, there should be some decoupling between the spreadsheet data structure and the onscreen contents. This design problem is often solved using the MVC pattern, and was far and away the most complex part of this project, since I foolishly insisted on using C++ and writing myself not only the spreadsheet but the underlying MVC tools and frameworks.

## ABNF Grammar

As mentioned above, a spreadsheet which can lex, parse, and evaluate user input must attempt to understand that input according to a grammar. I chose to design a grammar using ABNF, which is a manner of specifying grammar using some rules. ABNF already defines some bottom-level terminal values (numerics, literals, etc.) which make defining a grammar easier. Here is the grammar I ended up with:

### Notes on ABNF:

• Anything in double quotes is a literal, i.e. - might mean a range of values, but "-" means the literal - character.
• Anything on a line after ; is a comment.
• %c means a single text character.
• %d means a decimal digit.
• 0-9 means a range of values.
• <a>*<b>e means between a and b instances of e. If a is not specified, the default lower bound is 0. If b is not specified, the default upper bound is infinity. So 1*e means one or more instances of e.
• <a>e means e exactly a times.
• X / Y means either X or Y.
• [e] means that e is optional, i.e. shorthand for 0*1e.
DIGIT            = %d0-9

DATE_FULLYEAR    = 4DIGIT
DATE_MONTH       = 2DIGIT  ; 01-12
DATE_MDAY        = 2DIGIT  ; 01-28, 01-29, 01-30, 01-31 based on month/year
TIME_HOUR        = 2DIGIT  ; 00-23
TIME_MINUTE      = 2DIGIT  ; 00-59
TIME_SECOND      = 2DIGIT  ; 00-58, 00-59, 00-60 based on leap second rules
TIME_SECFRAC     = "." 1*DIGIT
TIME_NUMOFFSET   = ("+" / "-") TIME_HOUR ":" TIME_MINUTE
TIME_OFFSET      = "Z" / time_numoffset
DATE_TIME        = DATE_FULLYEAR "-" DATE_MONTH "-" DATE_MDAY "T"
TIME_HOUR ":" TIME_MINUTE ":" TIME_SECOND [TIME_SECFRAC]
TIME_OFFSET

UPPERCASE        = %c"A"-"Z"
ALPHANUMERIC     = 1*(UPPERCASE / DIGIT)

INT_NUMERIC      = 1*DIGIT
DOUBLE_NUMERIC   = *DIGIT "." *DIGIT
NUM_VAL          = INT_NUMERIC |
DOUBLE_NUMERIC

CURRENCY_ENUM    = "USD" / "SEK" / ...
CURRENCY_VAL     = NUM_VAL CURRENCY_ENUM

STR_VAL          = "\"" *e "\""

ROW_INDICATOR    = 1*DIGIT
COL_INDICATOR    = 1*UPPERCASE

LOCATION_VAL     = COL_INDICATOR ROW_INDICATOR     ; A1
RANGE_VAL        = COL_INDICATOR ":" COL_INDICATOR ; A:B
/ LOCATION_VAL ":" ROW_INDICATOR  ; A1:3
/ LOCATION_VAL ":" LOCATION_VAL   ; A1:B3

BOOL_VAL         = "True" / "False"

VAL              = CURRENCY_VAL / DATE_TIME / NUM_VAL / STR_VAL
/ LOCATION_VAL / RANGE_VAL / BOOL_VAL

FN               = 1*(ALPHANUMERIC / "_")

EXPR             = VAL ; 4
/ "(" EXPR ")" ; (5)
/ "(" EXPR FN EXPR ")" ; (1+1)
/ FN "(" EXPR *( "," EXPR) ")" ; POW(2,4,6)
/ EXPR "?" EXPR ":" EXPR ; cond ?  val1 : val2

GRAMMAR          = "=" EXPR


## Lexing

When lexing, we convert a string of user input into a linear sequence of meaningful tokens. Things get very verbose at this stage. We define an enum T of possible lex types, and store tokens as:

struct Token {
enum T {
equals, //  =
period, //  .
...
};
T type
std::string_view value;


where each Token holds a reference to the substring of user input it represents.

For example, lexing might turn a string like:

=POW(4.605, 2)
00000000001111
01234567890123


into a sequence of tokens like:

substring type start length
= T::equals 0 1
POW T::alpha 1 3
( T::lparen 4 1
4.605 T::numeric 5 5
, T::comma 10 1
2 T::numeric 12 1
) T::rparen 13 1

By passing around types and underlying substrings, we can parse the contents of alphanumeric tokens lazily, i.e. only when necessary.

### Note on std::string_view

std::string_view represents a read-only view into an existing character buffer. So long as the underlying string doesn’t vanish, the constructed string_view is a small data structure suitable for passing by-value (or mutating in-place) without the overhead of copying an arbitrary-length string.

## Parsing

Parsing is the process of taking a series of lexical tokens (as described above) and generating a useful data structure (read: tree) which can be stored, traversed, evaluated, manipulated, and displayed. This process happens hand-in-hand with the grammar defined above, and some tools can read ABNF grammars or other regular grammars and spit out parsers. I chose to hand-roll my own. This was the most challenging and educational aspect of this project by far.

### Parser combinators

I used the parser-combinator style; that is, I wrote a set of low-level parsers (one which parses into a character, one which parses into a number, etc.) and then a set of higher-order parsers, which combine two or more parsers and return a new parser.

Before we get into how this works, we need some background on absl::Status, StatusOr<T>, absl::Span, absl::variant, and absl::bind_front.

#### absl::Status

absl::Status is a C++ error handling class which encapsulates a typed error (kInvalidArgument, kPermissionDenied, etc.) and a human-readable string payload.

#### ???::StatusOr<T>

::StatusOr<T> is the sum type of a value of type T and an absl::Status. It doesn’t exist (yet!) in absl, but other OSS libraries hint at its existence. Since my project already imported "google/protobuf", I decided to use "google/protobuf/stubs/statusor.h", which exposes ::google::protobuf::util::StatusOr<T>. One day this may be a part of absl.

#### absl::Span

absl::Span is the same idea as std::string_view, only it applies to other containers beyond strings. Think of it as a read-only view into a container. Notably, it can be passed by-reference or mutated in-place.

#### absl::variant

absl::variant is a union type of one or more typed values. It holds exactly one value of one of its types. So a value of type absl::Variant<int, double> numeric could hold either an integer or a double.

One could use std::get<int>(numeric) to access the underlying integer type, but std::get excepts (std::bad_variant_access) if the underlying variant holds a type other than the one specified. Instead it is idiomatic to use the visitor pattern:

struct Visitor {
void operator()(const int& i) const {
std::cout << "Int: " << i;
}
void operator()(const double& i) const {
std::cout << "Double: " << i;
}
};

absl::variant<int, double> numeric = 123.456;
Visitor visitor;
absl::visit(visitor, numeric); // Prints "double: 123.456";


This is a little complicated, but the benefits outweigh the costs.

#### absl::bind_front

Finally, absl::bind_front and std::bind_front both implement partial function application. Here is an example:

// |minus| is a function with two arguments.
int minus(int a, int b) {
return a - b;
}

// But |fifty_minus| is a function with only one argument;
auto fifty_minus = std::bind_front(minus, 50);

int fifty_minus_three = fifty_minus(3); // outputs 47.


We can use this to stage partially-evaluated methods which already have their first n arguments and are waiting on their last m arguments, and can be thunked later.

### What is a Parser?

If a lexer spits out a vector of tokens, define a using TSpan = absl::Span<const Token>, where a TSpan is a mutable span of immutable tokens. That is, it is a sliding window which can be slid to any starting node and length, but there is no risk of mutating the underlying tokens.

In Latis, a parser has this type:

template <typename T>
using Prsr = std::function<StatusOr<T>(TSpan *)>;


that is, a parser takes a pointer to a TSpan, may mutate that TSpan in-place, and returns either a value of type T or an absl::Status explaining why it was unable to parse the input.

NB: This parser definition attempts to parse the head of some input, not the entire body. A successful parse will truncate the token span, leaving a shorter span suitable for running through anothe parser.

### What is a Parser combinator?

A parser combinator is a higher-order function; it accepts as arguments one or more function(s) and returns another function.

Here are some existing parsers:

StatusOr<int> ConsumeInt(TSpan *tspan);
StatusOr<double> ConsumeDouble(TSpan *tspan);


And here is a parser combinator:

template <typename... O>
static std::function<StatusOr<absl::variant<O...>>(TSpan *)>
AnyVariant(StatusOr<O>(TSpan *)>... ls);


This parser combinator (named AnyVariant) uses variadic templates to accept a series of any number of parsers (i.e. any number of inputs of type StatusOr<O>(TSpan *), and returns a parser whose return type is absl::variant<O...>.

We can use a parser combinator like AnyVariant to write a parser which attempts to parse the input as either an int or a double:

StatusOr<absl::Variant<double, int>> ConsumeNumeric(TSpan *tspan) {
return AnyVariant<double, int>(
absl::bind_front(&ConsumeDouble, this),
absl::bind_front(&ConsumeInt, this))(tspan);
}


NB: Recall that AnyVariant<O...>(...) itself returns a parser. So we need to call it like so: AnyVariant<O...>(...)(...).

### Other useful parser combinators:

In addition to AnyVariant, I also wrote:

• Any<T>, which takes one or more parsers of type T and returns one parser returning type T, which atempts to match the parsers in priority order.
• Maybe<T>, which takes exactly one parser and returns another lenient parser, which reads from TSpan but does not fail if it fails to match. This is useful for implementing optional aspects of the grammar, such as TIME_SECFRAC in the timespec.
• WithRestriction<T>, which takes exactly one parser and an filtering function, and returns a parser which only returns a value of type T if it passes that filtering function. This is useful for introducing logic into our parser, such as recognizing a numeric value as representing a number of hours if and only if it is in the range [0-24].
• InSequence<std::tuple<O...>>(Prsr<O>...), which takes a sequence of parsers and attempts to match them all, in-sequence, returning a std::tuple<> of their outputs. This is useful for matching all-or-nothing of a subgrammar, such as datetime specifications, which are only valid if they match the entire DATE_FULLYEAR-DATE_MONTH-DATE_MDAY... grammar. Otherwise this returns Status, and we do not truncate the TSpan.
• WithTransformation, which is like WithRestriction, except it takes exactly one parser and exactly one transformation function which can convert the parsed value to some other value of some other type.
• WithLookup, which accepts exactly one parser and exactly one lookup function. It is useful for looking up the returned value as the key in some map and returning its value instead. It can be thought of as a synonym for WithRestriction where the restriction is being-in-the-map, and WithTransformation where the transformation is to-the-matching-value-in-the-map.

The full list of combinators (and their implementations) lives here: https://github.com/ambuc/latis/blob/master/src/formula/parser_combinators.h.

### Parsing, altogether.

In the end we compose many parser combinators and parsers into one big function, which accepts user input and outputs a data structure (actually a protobuffer) which contains nested formulae, expressions, values, string literals, and table lookup locations.

### Evaluation

Evaluation is comparatively simple: we walk the data structure described above and “crunch” the component parts. If a node is a table lookup, we perform that lookup (or fail). If a node is a mathematical expression, we evaluate that expression.

In practice this means translating MINUS(A4, A3) -> 3.4 - 1.2 -> 2.2. This is relatively simple.