Parsing

Parsing Tutorial

This document serves as an introduction to parsing text with Hoon. No prior knowledge of parsing is required, and we will explain the basic structure of how parsing works in a purely functional language such as Hoon before moving on to how it is implemented in Hoon.

What is parsing?

A program which takes a raw sequence of characters as an input and produces a data structure as an output is known as a parser. The data structure produced depends on the use case, but often it may be represented as a tree and the output is thought of as a structural representation of the input. Parsers are ubiquitous in computing, commonly used for to perform tasks such as reading files, compiling source code, or understanding commands input in a command line interface.

Parsing a string is rarely done all at once. Instead, it is usually done character-by-character, and the return contains the data structure representing what has been parsed thus far as well as the remainder of the string to be parsed. They also need to be able to fail in case the input is improperly formed. We will see each of these standard practices implemented in Hoon below.

Functional parsers

How parsers are built varies substantially depending on what sort of programming language it is written in. As Hoon is a functional programming language, we will be focused on understanding functional parsers, also known as combinator parsers. In this section we will make light use of pseudocode, as introducing the Hoon to describe functional parsers here creates a chicken-and-egg problem.

Complex functional parsers are built piece by piece from simpler parsers that are plugged into one another in various ways to perform the desired task.

The basic building blocks, or primitives, are parsers that read only a single character. There are frequently a few types of possible input characters, such as letters, numbers, and symbols. For example, (parse "1" integer) calls the parsing routine on the string "1" and looks for an integer, and so it returns the integer 1. However, taking into account what was said above about parsers returning the unparsed portion of the string as well, we should represent this return as a tuple. So we should expect something like this:

> (parse "1" integer)
[1 ""]
> (parse "123" integer)
[1 "23"]

What if we wish to parse the rest of the string? We would need to apply the parse function again:

> (parse (parse "123" integer) integer)
[12 "3"]
> (parse (parse (parse "123" integer) integer) integer)
[123 ""]

So we see that we can parse strings larger than one character by stringing together parsing functions for single characters. Thus in addition to parsing functions for single input characters, we want parser combinators that allow you to combine two or more parsers to form a more complex one. Combinators come in a few shapes and sizes, and typical operations they may perform would be to repeat the same parsing operation until the string is consumed, try a few different parsing operations until one of them works, or perform a sequence of parsing operations. We will see how all of this is done with Hoon in the Parsing in Hoon section.

Parsing in Hoon

In this section we will cover the basic types, parser functions, and parser combinators that are utilized for parsing in Hoon. This is not a complete guide to every parsing-related functionality in the standard library (of which there are quite a few), but ought to be sufficient to get started with parsing in Hoon and be equipped to discover the remainder yourself.

Basic types

In this section we discuss the types most commonly used for Hoon parsers. In short:

hair

++  hair  [p=@ud q=@ud]

A hair is a pair of @ud used to keep track of what has already been parsed for stack tracing purposes. This allows the parser to reveal where the problem is in case it hits something unexpected during parsing.

p represents the column and q represents the line.

nail

++  nail  [p=hair q=tape]

We recall from our discussion above that parsing functions must keep track of both what has been parsed and what has yet to be parsed. Thus a nail consists of both a hair, giving the line and column up to which the input sequence has already been parsed, and a tape, consisting of what remains of the original input string (i.e. everything after the location indicated by the nail, including the character at that nail).

For example, if you wish to feed the entire tape "abc" into a parser, you would pass it as the nail [[1 1] "abc"]. If the parser successfully parses the first character, the nail it returns will be [[1 2] "bc"] (though we note that parser outputs are actually edges which contain a nail, see the following). The nail only matters for book-keeping reasons - it could be any value here since it doesn't refer to a specific portion of the string being input, but only what has theoretically already been parsed up to that point.

edge

++  edge  [p=hair q=(unit [p=* q=nail])]

An edge is the output of a parser. If parsing succeeded, p is the location of the original input tape up to which the text has been parsed. If parsing failed, p will be the first hair at which parsing failed.

q may be ~, indicating that parsing has failed . If parsing did not fail, p.q is the data structure that is the result of the parse up to this point, while q.q is the nail which contains the remainder of what is to be parsed. If q is not null, p and p.q.q are identical.

rule

++  rule  _|:($:nail $:edge)

A rule is a gate which takes in a nail and returns an edge - in other words, a parser.

Parser builders

These functions are used to build rules (i.e. parsers), and thus are often called rule-builders. For a complete list of parser builders, see 4f: Parsing (Rule-Builders), but also the more specific functions in 4h: Parsing (ASCII Glyphs), 4i: Parsing (Useful Idioms), 4j: Parsing (Bases and Base Digits), 4l: Atom Parsing.

+just

The most basic rule builder, +just takes in a single char and produces a rule that attempts to match that char to the first character in the tape of the input nail.

> =edg ((just 'a') [[1 1] "abc"])
> edg
[p=[p=1 q=2] q=[~ [p='a' q=[p=[p=1 q=2] q="bc"]]]]

We note that p.edg is [p=1 q=2], indicating that the next character to be parsed is in line 1, column 2. q.edg is not null, indicating that parsing succeeded. p.q.edg is 'a', which is the result of the parse. p.q.q.edg is the same as p.edg, which is always the case for rules built using standard library functions when parsing succeeds. Lastly, q.q.edg is "bc", which is the part of the input tape that has yet to be parsed.

Now let's see what happens when parsing fails.

> =edg ((just 'b') [[1 1] "abc"])
> edg
[p=[p=1 q=1] q=~]

Now we have that p.edg is the same as the input hair, [1 1], meaning the parser has not advanced since parsing failed. q.edg is null, indicating that parsing has failed.

Later we will use +star to string together a sequence of +justs in order to parse multiple characters at once.

+jest

+jest is a rule builder used to match a cord. It takes an input cord and produces a rule that attempts to match that cord against the beginning of the input.

Let's see what happens when we successfully parse the entire input tape.

> =edg ((jest 'abc') [[1 1] "abc"])
> edg
[p=[p=1 q=4] q=[~ [p='abc' q=[p=[p=1 q=4] q=""]]]]

p.edg is [p=1 q=4], indicating that the next character to be parsed is at line 1, column 4. Of course, this does not exist since the input tape was only 3 characters long, so this actually indicates that the entire tape has been successfully parsed (since the hair does not advance in the case of failure). p.q.edg is 'abc', as expected. q.q.edg is "", indicating that nothing remains to be parsed.

What happens if we only match some of the input tape?

> =edg ((jest 'ab') [[1 1] "abc"])
> edg
[p=[p=1 q=3] q=[~ [p='ab' q=[p=[p=1 q=3] q="c"]]]]

Now we have that the result, p.q.edg, is 'ab', while the remainder q.q.q.edg is "c". So +jest has successfully parsed the first two characters, while the last character remains. Furthermore, we still have the information that the remaining character was in line 1 column 3 from p.edg and p.q.q.edg.

What happens when +jest fails?

> ((jest 'bc') [[1 1] "abc"])
[p=[p=1 q=1] q=~]

Despite the fact that 'bc' appears in "abc", because it was not at the beginning the parse failed. We will see in parser combinators how to modify this rule so that it finds bc successfully.

+shim

+shim is used to parse characters within a given range. It takes in two atoms and returns a rule.

> ((shim 'a' 'z') [[1 1] "abc"])
[p=[p=1 q=2] q=[~ [p='a' q=[p=[p=1 q=2] q="bc"]]]]

+cold

+cold is a rule builder that takes in a constant noun we'll call cus and a rule we'll call sef. It returns a rule identical to the sef except it replaces the parsing result with cus.

Here we see that p.q of the edge returned by the rule created with +cold is %foo.

> ((cold %foo (just 'a')) [[1 1] "abc"])
[p=[p=1 q=2] q=[~ u=[p=%foo q=[p=[p=1 q=2] q="bc"]]]]

One common scenario where +cold sees play is when writing command line interface (CLI) apps. We usher the reader there to find an example where +cold is used.

+knee

Another important function in the parser builder library is +knee, used for building recursive parsers. We delay discussion of +knee to the section below as more context is needed to explain it properly.

Outside callers

Since hairs, nails, etc. are only utilized within the context of writing parsers, we'd like to hide them from the rest of the code of a program that utilizes parsers. That is to say, you'd like the programmer to only worry about passing tapes to the parser, and not have to dress up the tape as a nail themselves. Thus we have several functions for exactly this purpose.

These functions take in either a tape or a cord, alongside a rule, and attempt to parse the input with the rule. If the parse succeeds, it returns the result. There are crashing and unitized versions of each caller, corresponding to what happens when a parse fails.

For additional information including additional examples see 4g: Parsing (Outside Caller).

Parsing tapes

+scan takes in a tape and a rule and attempts to parse the tape with the rule.

> (scan "hello" (jest 'hello'))
'hello'
> (scan "hello zod" (jest 'hello'))
{1 6}
'syntax-error'

+rust is the unitized version of +scan.

> (rust "a" (just 'a'))
[~ 'a']
> (rust "a" (just 'b'))
~

For the remainder of this tutorial we will make use of +scan so that we do not need to deal directly with nails except where it is ilustrative to do so.

Parsing atoms

Recall that cords are atoms with the aura @t and are typically used to represent strings internally as data, as atoms are faster for the computer to work with than tapes, which are lists of @tD atoms. +rash and +rush are for parsing atoms, with +rash being analogous to +scan and +rush being analogous to rust. Under the hood, +rash calls +scan after converting the input atom to a tape, and +rush does similary for +rust.

Parser modifiers

The standard library provides a number of gates that take a rule and produce a new modified rule according to some process. We call these parser modifiers. These are documented among the parser builders.

+ifix

+ifix modifies a rule so that it matches that rule only when it is surrounded on both sides by text that matches a pair of rules, which is discarded.

> (scan "(42)" (ifix [lit rit] (jest '42')))
'42'

+lit and +rit are shorthand for (just '(') and (just ')'), respectively. All ASCII glyphs have counterparts of this sort, documented here.

+star

+star is used to apply a rule repeatedly. Recall that +just only parses the first character in the input tape.

> ((just 'a') [[1 1] "aaaa"])
[p=[p=1 q=2] q=[~ [p='a' q=[p=[p=1 q=2] q="aaa"]]]]

We can use +star to get the rest of the tape:

> ((star (just 'a')) [[1 1] "aaa"])
[p=[p=1 q=4] q=[~ [p=[i='a' t=<|a a|>] q=[p=[p=1 q=4] q=""]]]]

and we note that the parsing ceases when it fails.

> ((star (just 'a')) [[1 1] "aaab"])
[p=[p=1 q=4] q=[~ [p=[i='a' t=<|a a|>] q=[p=[p=1 q=4] q="b"]]]]

Parser combinators

Building complex parsers from simpler parsers is accomplished in Hoon with the use of two tools: the monadic applicator rune ;~ and parsing combinators. First we introduce a few combinators, then we examine more closely how ;~ is used to chain them together.

The syntax to combine rules is

;~(combinator rule1 rule2 ... ruleN)

The rules are composed together using the combinator as an intermediate function, which takes product of a rule (an edge) and a rule and turns it into a sample (a nail) for the next rule to handle. We elaborate on this behavior below.

+plug

+plug simply takes the nail in the edge produced by one rule and passes it to the next rule, forming a cell of the results as it proceeds.

> (scan "starship" ;~(plug (jest 'star') (jest 'ship')))
['star' 'ship']

+pose

+pose tries each rule you hand it successively until it finds one that works.

> (scan "a" ;~(pose (just 'a') (just 'b')))
'a'
> (scan "b" ;~(pose (just 'a') (just 'b')))
'b'

+glue

+glue parses a delimiter in between each rule and forms a cell of the results of each rule.

> (scan "a,b" ;~((glue com) (just 'a') (just 'b')))
['a' 'b']
> (scan "a,b,a" ;~((glue com) (just 'a') (just 'b')))
{1 4}
syntax error

;~

Understanding the rune ;~ is essential to building parsers with Hoon. Let's take this opportunity to think about it carefully.

The rule created by ;~(combinator [list rule]) may be understood inductively. To do this, let's consider the base case where our [list rule] has only a single entry.

> (scan "star" ;~(plug (jest 'star')))
'star'

Our output is identical to that given by scan "star" (jest 'star'). This is to be expected. The combinator +plug is specifically used for chaining together rules in the [list rule], but if there is only one rule, there is nothing to chain. Thus, swapping out +plug for another combinator makes no difference here:

> (scan "star" ;~(pose (jest 'star')))
'star'
> (scan "star" ;~((glue com) (jest 'star')))
'star'

;~ and the combinator only begin to play a role once the [list rule] has at least two elements. So let's look at an example done with +plug, the simplest combinator.

> (scan "star" ;~(plug (jest 'st') (jest 'ar')))
['st' 'ar']

Our return suggests that we first parsed "star" with the rule (jest 'st') and passed the resulting edge to (jest 'ar') - in other words, we called +plug on (jest 'st') and the edge returned once it had been used to parse "star". Thus +plug was the glue that allowed us to join the two rules, and ;~ performed the gluing operation. And so, swapping +plug for +pose results in a crash, which clues us into the fact that the combinator now has an effect since there is more than one rule.

> (scan "star" ;~(pose (jest 'st') (jest 'ar')))
{1 3}
syntax error

Parsing numbers

Functions for parsing numbers are documented in 4j: Parsing (Bases and Base Digits). In particualr, dem is a rule for parsing decimal numbers.

> (scan "42" dem)
42
> (add 1 (scan "42" dem))
43

Recursive parsers

Naively attempting to write a recursive rule, i.e. like

> |-(;~(pose den ;~(pose $ (easy ~))))

results in an error.

-find.,.+6
-find.,.+6
rest-loop

Thus some special sauce is required, the +knee function.

+knee takes in a noun that is the default value of the parser, typically given as the bunt value of the type that the rule produces, as well as a gate that accepts a rule. +knee produces a rule that implements any recursive calls in the rule in a manner acceptable to the compiler. Thus the preferred manner to write the above rule is as follows:

++  pars
  |-
  ;~  plug  prn
    ;~  pose
      (knee *tape |.(^$))
      (easy ~)
    ==
  ==

You may want to utilize the ~+ rune when writing recursive parsers to cache the parser to improve performance. In parsing arithmetic expressions we will be writing a recursive parser making use of +knee and ~+ throughout.

Parsing arithmetic expressions

In this section we will be applying what we have learned to write a parser for arithmetic expressions in Hoon. That is, we will make a rule that takes in tapes of the form "(2+3)*4" and returns 20 as a @ud.

We call a tape consisting of some consistent arithmetic string of numbers, +, *, (, and ) an expression. We wish to build a rule that takes in an expression and returns the result of the arithmetic computation described by the expression as a @ud.

To build a parser it is a helpful exercise to first describe its grammar. This has a formal mathematical definition, but we will manage to get by here describing the grammar for arithmetic expressions informally.

First lets look at the code we're going to use, and then dive into explaining it. If you'd like to follow along, save the following as expr-parse.hoon in your gen/ folder.

::  expr-parse: parse arithmetic expressions
::
|=  xprs=tape
|^  (scan xprs tape)
++  factor
  %+  knee  *@ud
  |.  ~+
  ;~  pose
    dem
    (ifix [lit rit] expr)
  ==
++  turm
  %+  knee  *@ud
  |.  ~+
  ;~  pose
    ((slug mul) tar ;~(pose factor turm))
    factor
  ==
++  expr
  %+  knee  *@ud
  |.  ~+
  ;~  pose
    ((slug add) lus ;~(pose turm expr))
    turm
  ==
--

Informally, the grammar here is:

Factors, terms, and expressions

Our grammar consists of three rules: one for factors, one for terms, and one for expressions.

Factors

++  factor
  %+  knee  *@ud
  |.  ~+
  ;~  pose
    dem
    (ifix [lit rit] expr)
  ==

A factor is either a decimal number or an expression surrounded by parentheses. Put into Hoon terms, a decimal number is parsed by the rule +dem and an expression is parsed by removing the surrounding parentheses and then passing the result to the expression parser arm +expr, given by the rule (ifix [lit rit] expr). Since we want to parse our expression with one or the other, we chain these two rules together using the monadic applicator rune ;~ along with +pose, which says to try each rule in succession until one of them works.

Since expressions ultimately reduce to factors, we are actually building a recursive rule. Thus we need to make use of +knee. The first argument for +knee is *@ud, since our final answer should be a @ud.

Then follows the definition of the gate utilized by +knee:

  |.  ~+
  ;~  pose
    dem
    (ifix [lit rit] expr)
  ==

~+ is used to cache the parser, so that it does not need to be computed over and over again. Then it follows the rule we described above.

Parsing expressions

An expression is either a term plus an expression or a term.

In the case of a term plus an expression, we actually must compute what that equals. Thus we will make use of +slug, which parses a delimited list into tapes separated by a given delimiter and then composes them by folding with a binary gate. In this case, our delimiter is + and our binary gate is +add. That is to say, we will split the input string into terms and expressions separated by luses, parse each term and expression until they reduce to a @ud, and then add them together. This is accomplished with the rule ((slug add) lus ;~(pose turm expr)).

If the above rule does not parse the expression, it must be a turm, so the tape is automatically passed to +turm to be evaluated. Again we use ;~ and pose to accomplish this:

;~  pose
  ((slug add) lus ;~(pose turm expr))
  turm
==

The rest of the +expr arm is structured just like how +factor is, and for the same reasons.

Parsing terms

A term is either a factor times a term or a factor. This is handled similarly for expressions, we just need to swap lus for tar, add for mul, and ;~(pose factor turm) instead of ;~(pose turm expr).

++  expr
  %+  knee  *@ud
  |.  ~+
  ;~  pose
    ((slug add) lus ;~(pose turm expr))
    turm
  ==

Try it out

Let's feed some expressions to +expr-parse and see how it does.

> +expr-parse "3"
3
> +expr-parse "3+3"
6
> +expr-parse "3+3+(2*3)+(4+2)*(4+1)"
42
> +expr-parse "3+3+2*3"
12

As an exercise, add exponentiation (e.g. 2^3 = 8) to +expr-parse.