leo/docs/rfc/001-initial-strings.md

Leo RFC 001: Initial String Support

Authors

• Max Bruce
• Collin Chin
• Alessandro Coglio
• Eric McCarthy
• Pratyush Mishra
• Jon Pavlik
• Damir Shamanaev
• Damon Sicore
• Howard Wu

Status

DRAFT

Summary

The purpose of this proposal is to provide initial support for strings in Leo. Since strings are sequences of characters, the proposal inextricably also involves characters. This proposal is described as initial, because it provides some basic features that we may extend in the future; the initial features should be sufficiently simple and conservative that they should not limit the design of the future features.

This proposal adds a new scalar type for characters, along with a new kind of literals to denote characters. A string is then simply an array of characters, but this proposal also adds a new kind of literals to denote strings more directly than via character array construction expressions. Along with equality and inequality, which always apply to every Leo type, this proposal also introduces some operations on characters and strings that can be implemented over time.

By not prescribing a new type for strings, this initial proposal leaves the door open to a future more flexible type of resizable strings.

Motivation

Strings (and characters) are common in programming languages. Use cases for Leo include simple ones like URLs and token ticker symbols, and more complex ones like Bech32 encoding, edit distance in strings representing proteins, and zero-knowledge proofs of occurrences or absences of patterns in textual logs.

Design

Since strings are sequences of characters, a design for strings inextricably also involves a design for characters. Thus, we first present a design for both characters and strings.

Characters

We add a new scalar type, char for characters. In accord with Leo's strong typing, this new type is separate from all the other scalar types. Type casts (a future feature of Leo) will be needed to convert between char and other types.

The set of values of type char is isomorphic to the set of Unicode code points from 0 to 10FFFF (both inclusive). That is, we support Unicode characters, more precisely code points (this may include some invalid code points, but it is simpler to allow every code point in that range). A character is an atomic entity: there is no notion of Unicode encoding (e.g. UTF-8) that applies here.

We add a new kind of literals for characters, consisting of single characters or escapes, surrounded by single quotes. Any single Unicode character except a single quote is allowed, e.g. 'a', '*', and '"'. Single quotes must be escaped with a backslash, i.e. '\''; backslashes must be escaped as well, i.e. '\\' We allow other backslash escapes for commonly used characters that are not otherwise easily denoted. This is the complete list of single-character backslash escapes:

• \' for code point 39 (single quote)
• \" for code point 34 (double quote)
• \\ for code point 92 (backslash)
• \n for code point 10 (line feed)
• \r for code point 13 (carriage return)
• \t for core point 9 (horizontal tab)
• \0 for code point 0 (the null character)

We also allow ASCII escapes of the form \xOH, where O is an octal digit and H is a hexadecimal digit (both uppercase and lowercase are allowed). These represent ASCII code points, i.e. from 0 to 127 (both inclusive).

We also allow Unicode escapes of the form '\u{X}', where X is a sequence of one to six hex digits (both uppercase and lowercase letters are allowed) whose value must be between 0 and 10FFFF, inclusive.

Note that the literal character is assembled by the compiler---for creating literals, there is no need for the circuit to know which code points are disallowed.

The equality operators == and != are automatically available for char. Given that characters are essentially code points, we may also support the ordering operators <, <=, >, and >=; these may be useful to check whether a character is in certain range.

Below is a list of possible operations we could support on characters. It should be fairly easy to add more.

• is_alphabetic - Returns true if the char has the Alphabetic property.
• is_ascii - Returns true if the char is in the ASCII range.
• is_ascii_alphabetic - Returns true if the char is in the ASCII Alphabetic range.
• is_lowercase - Returns true if the char has the Lowercase property.
• is_numeric - Returns true if the char has one of the general categories for numbers.
• is_uppercase - Returns true if the char has the Uppercase property.
• is_whitespace - Returns true if the char has the White_Space property.
• to_digit - Converts the char to the given radix format.
• from_digit - Inverse of to_digit.
• to_uppercase - Converts lowercase to uppercase, leaving others unchanged.
• to_lowercase - Converts uppercase to lowercase, leaving others unchanged.

It seems natural to convert between char values and u8 or u16 or u32 values, under suitable range conditions; perhaps also between char values and (non-negative) i8 or i16 or i32 values. This will be accomplished as part of the type casting extension of Leo.

The following code sample illustrates three ways of defining characters: character literal, single-character escapes, and Unicode escapes.

function main() -> [char; 5] {

    // using char literals to form an array
    const world: [char; 5] = ['w', 'o', 'r', 'l', 'd'];

    // escaped characters
    const escaped: [char; 4] = ['\n', '\t', '\\', '\''];

    // unicode escapes - using emoji character 😊
    const smiling_face: char = '\u{1F60A}';

    return [smiling_face, ...escaped];
}

Strings

In this initial design proposal, we do not introduce any new type for strings. Instead, we rely on the fact that Leo already has arrays and that arrays of characters can be regarded as strings. Existing array operations, such as element and range access, apply to these strings without the need of language extensions.

To ease the common use case of writing a string value in the code, we add a new kind of literal for strings (i.e. character arrays), consisting of a sequence of one or more single characters or escapes surrounded by double quotes; this is just syntactic sugar. Any single Unicode character except double quote is allowed, e.g. "", "Aleo", "it's", and "x + y". Double quotes must be escaped with a backslash, e.g. "say \"hi\""; backslashes must be escaped as well, e.g. "c:\\dir". We allow the same backslash escapes allowed for character literals (see the section on characters above). We also allow the same Unicode escapes allowed in character literals (described in the section on characters above). In any case, the type of a string literal is [char; N], where N is the length of the string measured in characters, i.e. the size of the array. Note that there is no notion of Unicode encoding (e.g. UTF-8) that applies to string literals.

The rationale for not introducing a new type for strings initially, and instead, piggyback on the existing array types and operations, is twofold. First, it is an economical design that lets us reuse the existing array machinery, both at the language level (e.g. readily use array operations) and at the R1CS compilation level (see the section on compilation to R1CS below). Second, it leaves the door open to providing, in a future design iteration, a richer type for strings, as discussed in the section about future extensions below.

Recall that empty arrays are disallowed in Leo. (The reason is that arrays, which must have a size known at compile time and are not resizable, are flattened into their elements when compiling to R1CS; thus, an empty array would be flattened into nothing.) Therefore, in this initial design empty strings must be disallowed as well. A future type of resizable strings will support empty strings.

Because array, and therefore string, sizes must be known at compile time, there is no point to having an operation to return the length of a string. This operation will be supported for a future type of resizable strings.

Below are some examples of array operations that are also common for strings in other programming languages:

• [...s1, ...s2] concatenates the strings s1 and s2.
• [c, ...s] adds the character c in front of the string s.
• s[i] extracts the i-th character from the string s.
• s[1..] removes the first character from the string s.

Below is a list of possible operations we could support on strings. It should be fairly easy to add more.

• u8 to [char; 2] hexstring, .., u128 to [char; 32] hexstring.
• Field element to [char; 64] hexstring. (Application can test leading zeros and slice them out if it needs to return, say, a 40-hex-digit string.)
• Apply to_uppercase (see above) to every character.
• Apply to_lowercase (see above) to every character.

Note that the latter two could be also realize via simple loops through the string.

Given the natural conversions between char values and integer values discussed earlier, it may be natural to also support element-wise conversions between strings and arrays of integers. This may be accomplished as part of the type casting extensions of Leo.

The following code shows a string literal and its actual transformation into an array of characters as well as possible array-like operations on strings: concatenation and comparison.

function main() -> bool {
    // double quotes create char array from string
    let hello: [char; 5] = "hello";
    let world: [char; 5] = ['w','o','r','l','d'];

    // string concatenation can be performed using array syntax
    let hello_world: [char; 11] = [...hello, ' ', ...world];

    // string comparison is also implemented via array type
    return hello_world == "hello world";
}

Format Strings

Leo currently supports format strings as their own entity, usable exclusively as first arguments of console print calls. This proposal eliminates this very specific notion, which is subsumed by the string literals described above. In other words, a console print call will take a string literal as the first argument, which will be interpreted as a format string according to the semantics of console print calls. The internal UTF-32 string will be translated to UTF-8 for output.

Circuit Types for Character and String Operations

The operations on characters and lists described earlier, e.g. is_ascii, are provided as static member functions of two new built-in or library circuit types Char and String. Thus, an example call is Char::is_ascii(c). This seems a general good way to organize built-in or library operations, and supports the use of the same name with different circuit types, e.g. Char::to_uppercase and String::to_uppercase.

These circuit types could also include constants, e.g. for certain ASCII characters. However, currently Leo does not support constants in circuit types, so that would have to be added separately first.

Input and Output of Literal Characters and Strings

Since UTF-8 is a standard encoding, it would make sense for the literal characters and strings in the .in file to be automatically converted to UTF-32 by the Leo compiler. However, the size of a string can be confusing since multiple Unicode code points can be composed into a single glyph which then appears to be a single character. If a parameter of type [char; 10] [if that is the syntax we decide on] is passed a literal string of a different size, the error message should explain that the size must be the number of codepoints needed to encode the string.

Compilation to R1CS

So far, the discussion has been independent from R1CS (except for a brief reference when discussing the rationale behind the design). This is intentional because the syntax and semantics of Leo should be understandable independently from the compilation of Leo to R1CS. However, compilation to R1CS is a critical consideration that affects the design of Leo. This section discusses R1CS compilation considerations for this proposal for characters and strings.

Values of type char can be represented directly as field elements, since the prime of the field is (much) larger than 10FFFF. This is more efficient than using a bit representation of characters. By construction, field elements that represent char values are never above 10FFFF. Note that field and char remain separate types in Leo: it is only in the compilation to R1CS that everything is reduced to field elements.

Since strings are just arrays of characters, there is nothing special about compiling strings to R1CS, compared to other types of arrays. In particular, the machinery to infer array sizes at compile time, necessary for the flattening to R1CS, applies to strings without exception. String literals are just syntactic sugar for suitable array inline construction expressions.

There are at least two approaches to implementing ordering operations < and <= on char values. Recalling that characters are represented as field values that are (well) below (p-1)/2 where p is the prime, we can compare two field values x and y, both below (p-1)/2, via the constraints

(2) (x - y) = (b0 + 2*b1 + 4*b2 + ...)
(b0) (1 - b0) = 0
(b1) (1 - b1) = 0
(b2) (1 - b2) = 0
...

that take the difference, double it, and convert to bits. If x >= y, the difference is below (p-1)/2, and doubling results in an even number below p, with therefore b0 = 0. If x < y, the difference is above (p-1)/2 (when reduced modulo p), and doubling results in an odd number when reduced modulo p, with therefore b0 = 1. Note that we need one variable and one constraint for every bit of p. The other approach is to convert the x and y to bits and compare them as integers; in this case we only need 21 bits for each. We need more analysis to determine which approach is more efficient.

The details of implementing other character and string operations in R1CS will be fleshed out as each operation is added.

Future Extensions

As alluded to in the section about design above, for now, we are avoiding the introduction of a string type, isomorphic to but separate from character arrays, because we may want to introduce later a more flexible type of strings, in particular, one that supports resizing. This may be realized via a built-in or library circuit type that includes a character array and a fill index. This may be a special case of a built-in or library circuit type for resizable vectors, possibly realized via an array and a fill index. This hypothetical type of resizable vectors may have to be parameterized over the element type, requiring an extension of the Leo type system that is much more general than strings.

Because of the above considerations, it seems premature to design a string type at this time, provided that the simple initial design described in the section above suffices to cover the initial use cases that motivate this RFC.

Drawbacks

This proposal does not appear to bring any real drawbacks, other than making the language inevitably slightly more complex. But the need to support characters and strings justifies the extra complexity.

Effect on Ecosystem

With the ability of Leo programs to process strings, it may be useful to have external tools that convert Leo strings to/from common formats, e.g. UTF-8. See the discussion of input files in the design section.

Alternatives

We could avoid the new char type altogether, and instead, rely on the existing u32 to represent Unicode code points, and provide character-oriented operations on u32 values. (Note that both u8 and u16 are too small for 10FFFF, and that signed integer types include negative integers which are not Unicode code points: this makes u32 the obvious choice.) However, many values of type u32 are above 10FFFF, and many operations on u32 do not really make sense on code points. We would probably want a notation for character literals anyhow, which could be (arguably mis)used for non-character unsigned integers. All in all, introducing a new type for characters is consistent with Leo's strong typing approach. Furthermore, for compilation to R1CS, u32, even if restricted to the number of bits needed for Unicode code points, is less efficient than the field representation described earlier because u32 requires a field element for each bit.

Instead of representing strings as character arrays, we could introduce a new type string whose values are finite sequences of zero or more characters. These strings would be isomorphic to, but distinct form, character arrays. However, for compilation to R1CS, it would be necessary to perform the same kind of known-size analysis on strings that is already performed on arrays, possibly necessitating to include size as part of the type, i.e. string(N), which is obviously isomorphic to [char; N]. Thus, using character arrays avoids duplication. Furthermore, as noted in the section on future extensions, this leaves the door open to introducing a future type string for resizable strings.

Yet another option could be to use directly field to represent characters and [field; N] to represent strings of N characters. However, many values of type field are not valid Unicode code points, and many field operations do not make sense for characters. Thus, having a separate type char for characters seems better, and more in accordance with Leo's strong typing.