; Leo Library ; ; Copyright (C) 2021 Aleo Systems Inc. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Format Note ; ----------- ; The ABNF standard requires grammars to consist of lines terminated by CR LF ; (i.e. carriage return followed by line feed, DOS/Windows-style), ; as explained in the background on ABNF later in this file. ; This file's lines are therefore terminated by CR LF. ; To avoid losing this requirement across systems, ; this file is marked as 'text eol=crlf' in .gitattributes: ; this means that the file is textual, enabling visual diffs, ; but its lines will always be terminated by CR LF on any system. ; Note that this CR LF requirement only applies to the grammar files themselves. ; It does not apply to the lines of the languages described by the grammar. ; ABNF grammars may describe any kind of languages, ; with any kind of line terminators, ; or even without line terminators at all (e.g. for "binary" languages). ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Introduction ; ------------ ; This file contains an ABNF (Augmented Backus-Naur Form) grammar of Leo. ; Background on ABNF is provided later in this file. ; This grammar provides an official definition of the syntax of Leo ; that is both human-readable and machine-readable. ; It will be part of an upcoming Leo language reference. ; It may also be used to generate parser tests at some point. ; We are also using this grammar ; as part of a mathematical formalization of the Leo language, ; which we are developing in the ACL2 theorem prover ; and which we plan to publish at some point. ; In particular, we have used a formally verified parser of ABNF grammars ; (at https://github.com/acl2/acl2/tree/master/books/kestrel/abnf; ; also see the paper at https://www.kestrel.edu/people/coglio/vstte18.pdf) ; to parse this grammar into a formal representation of the Leo concrete syntax ; and to validate that the grammar satisfies certain consistency properties. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Background on ABNF ; ------------------ ; ABNF is an Internet standard: ; see RFC 5234 at https://www.rfc-editor.org/info/rfc5234 ; and RFC 7405 at https://www.rfc-editor.org/info/rfc7405. ; It is used to specify the syntax of JSON, HTTP, and other standards. ; ABNF adds conveniences and makes slight modifications ; to Backus-Naur Form (BNF), ; without going beyond context-free grammars. ; Instead of BNF's angle-bracket notation for nonterminals, ; ABNF uses case-insensitive names consisting of letters, digits, and dashes, ; e.g. HTTP-message and IPv6address. ; ABNF includes an angle-bracket notation for prose descriptions, ; e.g. , ; usable as last resort in the definiens of a nonterminal. ; While BNF allows arbitrary terminals, ; ABNF uses only natural numbers as terminals, ; and denotes them via: ; (i) binary, decimal, or hexadecimal sequences, ; e.g. %b1.11.1010, %d1.3.10, and %x.1.3.A ; all denote the sequence of terminals '1 3 10'; ; (ii) binary, decimal, or hexadecimal ranges, ; e.g. %x30-39 denotes any singleton sequence of terminals ; 'n' with 48 <= n <= 57 (an ASCII digit); ; (iii) case-sensitive ASCII strings, ; e.g. %s"Ab" denotes the sequence of terminals '65 98'; ; and (iv) case-insensitive ASCII strings, ; e.g. %i"ab", or just "ab", denotes ; any sequence of terminals among ; '65 66', ; '65 98', ; '97 66', and ; '97 98'. ; ABNF terminals in suitable sets represent ASCII or Unicode characters. ; ABNF allows repetition prefixes n*m, ; where n and m are natural numbers in decimal notation; ; if absent, ; n defaults to 0, and ; m defaults to infinity. ; For example, ; 1*4HEXDIG denotes one to four HEXDIGs, ; *3DIGIT denotes up to three DIGITs, and ; 1*OCTET denotes one or more OCTETs. ; A single n prefix ; abbreviates n*n, ; e.g. 3DIGIT denotes three DIGITs. ; Instead of BNF's |, ABNF uses / to separate alternatives. ; Repetition prefixes have precedence over juxtapositions, ; which have precedence over /. ; Round brackets group things and override the aforementioned precedence rules, ; e.g. *(WSP / CRLF WSP) denotes sequences of terminals ; obtained by repeating, zero or more times, ; either (i) a WSP or (ii) a CRLF followed by a WSP. ; Square brackets also group things but make them optional, ; e.g. [":" port] is equivalent to 0*1(":" port). ; Instead of BNF's ::=, ABNF uses = to define nonterminals, ; and =/ to incrementally add alternatives ; to previously defined nonterminals. ; For example, the rule BIT = "0" / "1" ; is equivalent to BIT = "0" followed by BIT =/ "1". ; The syntax of ABNF itself is formally specified in ABNF ; (in Section 4 of the aforementioned RFC 5234, ; after the syntax and semantics of ABNF ; are informally specified in natural language ; (in Sections 1, 2, and 3 of the aforementioned RFC 5234). ; The syntax rules of ABNF prescribe the ASCII codes allowed for ; white space (spaces and horizontal tabs), ; line endings (carriage returns followed by line feeds), ; and comments (semicolons to line endings). ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Structure ; --------- ; This ABNF grammar consists of two (sub-)grammars: ; (i) a lexical grammar that describes how ; sequence of characters are parsed into tokens, and ; (ii) a syntactic grammar that described how ; tokens are parsed into expressions, statements, etc. ; The adjectives 'lexical' and 'syntactic' are ; the same ones used in the Java language reference, ; for instance; ; alternative terms may be used in other languages, ; but the separation into these two components is quite common ; (the situation is sometimes a bit more complex, with multiple passes, ; e.g. Unicode escape processing in Java). ; This separation enables ; concerns of white space, line endings, etc. ; to be handled by the lexical grammar, ; with the syntactic grammar focused on the more important structure. ; Handling both aspects in a single grammar may be unwieldy, ; so having two grammars provides more clarity and readability. ; ABNF is a context-free grammar notation, with no procedural interpretation. ; The two grammars conceptually define two subsequent processing phases, ; as detailed below. ; However, a parser implementation does not need to perform ; two strictly separate phases (in fact, it typically does not), ; so long as it produces the same final result. ; The grammar is accompanied by some extra-grammatical requirements, ; which are not conveniently expressible in a context-free grammar like ABNF. ; These requirements are needed to make the grammar unambiguous, ; i.e. to ensure that, for each sequence of terminals, ; there is exactly one parse tree for that sequence terminals ; that satisfies not only the grammar rules ; but also the extra-grammatical requirements. ; These requirements are expressed as comments in this file. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Operator Precedence ; ------------------- ; We formulate the grammar rules for expressions ; in a way that describes the relative precedence of operators, ; as often done in language syntax specifications. ; For instance, consider the rules ; ; multiplicative-expression = ; exponential-expression ; / multiplicative-expression "*" exponential-expression ; / multiplicative-expression "/" exponential-expression ; ; additive-expression = ; multiplicative-expression ; / additive-expression "+" multiplicative-expression ; / additive-expression "-" multiplicative-expression ; ; These rules tell us ; that the additive operators '+' and '-' have lower precedence ; than the multiplicative operators '*' and '/', ; and that both the additive and multiplicative operators associate to the left. ; This may be best understood via the examples given below. ; According to the rules, the expression ; ; x + y * z ; ; can only be parsed as ; ; + ; / \ ; x * ; / \ ; y z ; ; and not as ; ; * ; / \ ; + z ; / \ ; x y ; ; because a multiplicative expression cannot have an additive expression ; as first sub-expression, as it would in the second tree above. ; Also according to the rules, the expression ; ; x + y + z ; ; can only be parsed as ; ; + ; / \ ; + z ; / \ ; x y ; ; and not as ; ; + ; / \ ; x + ; / \ ; y z ; ; because an additive expression cannot have an additive expression ; as second sub-expression, as it would in the second tree above. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Naming Convention ; ----------------- ; This ABNF grammar uses nonterminal names ; that consist of complete English words, separated by dashes, ; and that describe the construct the way it is in English. ; For instance, we use the name 'conditional-statement' ; to describe conditional statements. ; At the same time, this grammar establishes ; a precise and official nomenclature for the Leo constructs, ; by way of the nonterminal names that define their syntax. ; For instance, the rule ; ; group-literal = product-group-literal ; / affine-group-literal ; ; tells us that there are two kinds of group literals, ; namely product group literals and affine group literals. ; This is more precise than describing them as ; integers (which are not really group elements per se), ; or points (they are all points, just differently specified), ; or being singletons vs. pairs (which is a bit generic). ; The only exception to the nomenclature-establishing role of the grammar ; is the fact that, as discussed above, ; we write the grammar rules in a way that determines ; the relative precedence and the associativity of expression operators, ; and therefore we have rules like ; ; unary-expression = primary-expression ; / "!" unary-expression ; / "-" unary-expression ; ; In order to allow the recursion of the rule to stop, ; we need to regard, in the grammar, a primary expression as a unary expression ; (i.e. a primary expression is also a unary expression in the grammar; ; but note that the opposite is not true). ; However, this is just a grammatical artifact: ; ontologically, a primary expression is not really a unary expression, ; because a unary expression is one that consists of ; a unary operator and an operand sub-expression. ; These terminological exceptions should be easy to identify in the rules. ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Lexical Grammar ; --------------- ; A Leo file is a finite sequence of Unicode characters, ; represented as Unicode code points, ; which are numbers in the range form 0 to 10FFFFh. ; These are captured by the ABNF rule 'character' below. ; The lexical grammar defines how, at least conceptually, ; the sequence of characters is turned into ; a sequence of tokens, comments, and whitespaces: ; these entities are all defined by the grammar rules below. ; As stated, the lexical grammar alone is ambiguous. ; For example, the sequence of characters '**' (i.e. two stars) ; could be equally parsed as two '*' symbol tokens or one '**' symbol token ; (see rule for 'symbol' below). ; As another example, the sequence or characters '' ; (i.e. carriage return followed by line feed) ; could be equally parsed as two line terminators or one ; (see rule for 'newline'). ; Thus, as often done in language syntax definitions, ; the lexical grammar is disambiguated by ; the extra-grammatical requirement that ; the longest possible sequence of characters is always parsed. ; This way, '**' must be parsed as one '**' symbol token, ; and '' must be parsed as one line terminator. ; As mentioned above, a character is any Unicode code point. ; This grammar does not say how those are encoded in files (e.g. UTF-8): ; it starts with a decoded sequence of Unicode code points. ; Note that we allow any value, ; even though some values may not be used according to the Unicode standard. character = %x0-10FFFF ; any Unicode code point ; We give names to certain ASCII characters. horizontal-tab = %x9 line-feed = %xA carriage-return = %xD space = %x20 double-quote = %x22 ; We give names to complements of certain ASCII characters. ; These consist of all the Unicode characters except for one or two. not-double-quote = %x0-22 / %x24-10FFFF ; anything but " not-star = %x0-29 / %x2B-10FFFF ; anything but * not-line-feed-or-carriage-return = %x0-9 / %xB-C / %xE-10FFFF ; anything but LF or CR not-star-or-slash = %x0-29 / %x2B-2E / %x30-10FFFF ; anything but * or / ; Lines in Leo may be terminated via ; a single carriage return, ; a line feed, ; or a carriage return immediately followed by a line feed. ; Note that the latter combination constitutes a single line terminator, ; according to the extra-grammatical requirement of the longest sequence, ; described above. newline = line-feed / carriage-return / carriage-return line-feed ; Line terminators form whitespace, along with spaces and horizontal tabs. whitespace = space / horizontal-tab / newline ; There are two kinds of comments in Leo, as in other languages. ; One is block comments of the form '/* ... */', ; and the other is end-of-line comments of the form '// ...'. ; The first kind start at '/*' and end at the first '*/', ; possibly spanning multiple (partial) lines; ; these do no nest. ; The second kind start at '//' and extend till the end of the line. ; The rules about comments given below are similar to ; the ones used in the Java language reference. comment = block-comment / end-of-line-comment block-comment = "/*" rest-of-block-comment rest-of-block-comment = "*" rest-of-block-comment-after-star / not-star rest-of-block-comment rest-of-block-comment-after-star = "/" / "*" rest-of-block-comment-after-star / not-star-or-slash rest-of-block-comment end-of-line-comment = "//" *not-line-feed-or-carriage-return newline ; Below are the keywords in the Leo language. ; They cannot be used as identifiers. keyword = %s"address" / %s"as" / %s"bool" / %s"circuit" / %s"console" / %s"const" / %s"else" / %s"false" / %s"field" / %s"for" / %s"function" / %s"group" / %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" / %s"if" / %s"import" / %s"in" / %s"input" / %s"let" / %s"mut" / %s"return" / %s"Self" / %s"self" / %s"static" / %s"string" / %s"true" / %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" ; The following rules define (ASCII) digits ; and (uppercase and lowercase) letters. digit = %x30-39 ; 0-9 uppercase-letter = %x41-5A ; A-Z lowercase-letter = %x61-7A ; a-z letter = uppercase-letter / lowercase-letter ; An identifier is a non-empty sequence of letters, digits, and underscores, ; starting with a letter. ; It must not be a keyword: this is an extra-grammatical constraint. identifier = letter *( letter / digit / "_" ) ; but not a keyword ; A package name consists of one or more segments separated by single dashes, ; where each segment is a non-empty sequence of lowercase letters and digits. package-name = 1*( lowercase-letter / digit ) *( "-" 1*( lowercase-letter / digit ) ) ; An address starts with 'aleo1' ; and continues with exactly 58 lowercase letters and digits. ; Thus an address always consists of 63 characters. address = %s"aleo1" 58( lowercase-letter / digit ) ; A formatted string is a sequence of characters, other than double quote, ; surrounded by double quotes. ; Within a formatted string, sub-strings '{}' are distinguished as containers ; (these are the ones that may be matched with values ; whose textual representation replaces the containers ; in the printed string). ; There is an implicit extra-grammatical requirements that ; the explicit 'formatted-string-container' instances include ; all the occurrences of '{}' in the parsed character sequence: ; that is, there may not be two contiguous 'not-double-quote' instances ; that are '{' and '}'. formatted-string-container = "{}" formatted-string = double-quote *( not-double-quote / formatted-string-container ) double-quote ; Here is (part of this ABNF comment), ; an alternative way to specify formatted strings, ; which captures the extra-grammatical requirement above in the grammar, ; but is more complicated: ; ; not-double-quote-or-open-brace = %x0-22 / %x24-7A / %x7C-10FFFF ; ; not-double-quote-or-close-brace = %x0-22 / %x24-7C / %x7E-10FFFF ; ; formatted-string-element = not-double-quote-or-open-brace ; / "{" not-double-quote-or-close-brace ; / formatted-string-container ; ; formatted-string = double-quote *formatted-string-element double-quote ; ; It is not immediately clear which approach is better; there are tradeoffs. ; We may choose to adopt this one in future revisions of the grammar. ; Annotations have names, which are identifiers immediately preceded by '@'. annotation-name = "@" identifier ; A natural (number) is a sequence of one or more digits. ; We allow leading zeros, e.g. '007'. natural = 1*digit ; An integer (number) is either a natural or its negation. ; We allow leading zeros also in negative numbers, e.g. '-007'. integer = [ "-" ] natural ; An untyped literal is just an integer. untyped-literal = integer ; Unsigned literals are naturals followed by unsigned types. unsigned-literal = natural ( %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" ) ; Signed literals are integers followed by signed types. signed-literal = integer ( %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" ) ; Field literals are integers followed by the type of field elements. field-literal = integer %s"field" ; There are two kinds of group literals. ; One is a single integer followed by the type of group elements, ; which denotes the scalar product of the generator point by the integer. ; The other kind is not a token because it allows some whitespace inside; ; therefore, it is defined in the syntactic grammar. product-group-literal = integer %s"group" ; Boolean literals are the usual two. boolean-literal = %s"true" / %s"false" ; An address literal is an address wrapped into an indication of address, ; to differentiate it from an identifier. address-literal = %s"address" "(" address ")" ; The ones above are all the atomic literals ; (in the sense that they are tokens, without whitespace allowed in them), ; as defined by the following rule. atomic-literal = untyped-literal / unsigned-literal / signed-literal / field-literal / product-group-literal / boolean-literal / address-literal ; After defining the (mostly) alphanumeric tokens above, ; it remains to define tokens for non-alphanumeric symbols such as "+" and "(". ; Different programming languages used different terminologies for these, ; e.g. operators, separators, punctuators, etc. ; Here we use 'symbol', for all of them. ; We also include a token consisting of ; a closing parenthesis immediately followed by 'group': ; as defined in the syntactic grammar, ; this is the final part of an affine group literal; ; even though it includes letters, ; it seems appropriate to still consider it a symbol, ; particularly since it starts with a proper symbol. ; We could give names to all of these symbols, ; via rules such as ; ; equality-operator = "==" ; ; and defining 'symbol' in terms of those ; ; symbol = ... / equality-operator / ... ; ; This may or may not make the grammar more readable, ; but it would help establish a terminology in the grammar, ; namely the exact names of some of these token. ; On the other hand, at least some of them are perhaps simple enough ; that they could be just described in terms of their symbols, ; e.g. 'double dot', 'question mark', etc. symbol = "!" / "&&" / "||" / "==" / "!=" / "<" / "<=" / ">" / ">=" / "+" / "-" / "*" / "/" / "**" / "=" / "+=" / "-=" / "*=" / "/=" / "**=" / "(" / ")" / "[" / "]" / "{" / "}" / "," / "." / ".." / "..." / ";" / ":" / "::" / "?" / "->" / "_" / %s")group" ; Everything defined above, other than comments and whitespace, ; is a token, as defined by the following rule. token = keyword / identifier / atomic-literal / package-name / formatted-string / annotation-name / symbol ;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;; ; Syntactic Grammar ; ----------------- ; The processing defined by the lexical grammar above ; turns the initial sequence of characters ; into a sequence of tokens, comments, and whitespaces. ; The purpose of comments and whitespaces, from a syntactic point of view, ; is just to separate tokens: ; they are discarded, leaving a sequence of tokens. ; The syntactic grammar describes how to turn ; a sequence of tokens into concrete syntax trees. ; There are unsigned and signed integer types, for five sizes. unsigned-type = %s"u8" / %s"u16" / %s"u32" / %s"u64" / %s"u128" signed-type = %s"i8" / %s"i16" / %s"i32" / %s"i64" / %s"i128" integer-type = unsigned-type / signed-type ; The integer types, along with the field and group types, ; for the arithmetic types, i.e. the ones that support arithmetic operations. field-type = %s"field" group-type = %s"group" arithmetic-type = integer-type / field-type / group-type ; The arithmetic types, along with the boolean and address types, ; form the scalar types, i.e. the ones whose values do not contain (sub-)values. boolean-type = %s"bool" address-type = %s"address" scalar-type = boolean-type / arithmetic-type / address-type ; Circuit types are denoted by identifiers and the keyword 'Self'. ; The latter is only allowed inside a circuit definition, ; to denote the circuit being defined. self-type = %s"Self" circuit-type = identifier / self-type ; A tuple type consists of zero, two, or more component types. tuple-type = "(" [ type 1*( "," type ) ] ")" ; An array type consists of an element type ; and an indication of dimensions. ; There is either a single dimension, ; or a tuple of one or more dimensions. array-type = "[" type ";" array-dimensions "]" array-dimensions = natural / "(" natural *( "," natural ) ")" ; Circuit, tuple, and array types form the aggregate types, ; i.e. types whose values contain (sub-)values ; (with the corner-case exception of the empty tuple value). aggregate-type = tuple-type / array-type / circuit-type ; Scalar and aggregate types form all the types. type = scalar-type / aggregate-type ; The lexical grammar given earlier defines product group literals. ; The other kind of group literal is a pair of integer coordinates, ; which are reduced modulo the prime to identify a point, ; which must be on the elliptic curve. ; It is also allowed to omit one coordinate (not both), ; with an indication of how to fill in the missing coordinate ; (i.e. sign high, sign low, or inferred). ; This is an affine group literal, ; because it consists of affine point coordinates. group-coordinate = integer / "+" / "-" / "_" affine-group-literal = "(" group-coordinate "," group-coordinate %s")group" ; A literal is either an atomic one or an affine group literal. literal = atomic-literal / affine-group-literal ; The following rule is not directly referenced in the rules for expressions ; (which reference 'literal' instead), ; but it is useful to establish terminology: ; a group literal is either a product group literal or an affine group literal. group-literal = product-group-literal / affine-group-literal ; As often done in grammatical language syntax specifications, ; we define rules for different kinds of expressions, ; which also defines the relative precedence ; of operators and other expression constructs, ; and the (left or right) associativity of binary operators. ; The primary expressions are self-contained in a way, ; i.e. they have clear deliminations: ; Some consist of single tokens, ; while others have explicit endings. ; Primary expressions also include parenthesized expressions, ; i.e. any expression may be turned into a primary one ; by putting parentheses around it. primary-expression = identifier / %s"self" / %s"input" / literal / "(" expression ")" / tuple-expression / array-expression / circuit-expression ; Tuple expressions construct tuples. ; Each consists of zero, two, or more component expressions. tuple-construction = "(" [ expression 1*( "," expression ) ] ")" tuple-expression = tuple-construction ; Array expressions construct arrays. ; There are two kinds: ; one lists the element expressions (at least one), ; including spreads (via '...') which are arrays being spliced in; ; the other repeats (the value of) a single expression ; across one or more dimensions. array-inline-construction = "[" array-inline-element *( "," array-inline-element ) "]" array-inline-element = expression / "..." expression array-repeat-construction = "[" expression ";" array-dimensions "]" array-construction = array-inline-construction / array-repeat-construction array-expression = array-construction ; Circuit expressions construct circuit values. ; Each lists values for all the member variables (in any order); ; there must be at least one member variable. ; A single identifier abbreviates ; a pair consisting of the same identifier separated by colon; ; note that, in the expansion, the left one denotes a member name, ; while the right one denotes an expression (a variable), ; so they are syntactically identical but semantically different. circuit-construction = circuit-type "{" circuit-inline-element *( "," circuit-inline-element ) "}" circuit-inline-element = identifier ":" expression / identifier circuit-expression = circuit-construction ; After primary expressions, postfix expressions have highest precedence. ; They apply to primary expressions, and recursively to postfix expressions. ; There are postfix expressions to access parts of aggregate values. ; A tuple access selects a component by index (zero-based). ; There are two kinds of array accesses: ; one selects a single element by index (zero-based); ; the other selects a range via two indices, ; the first inclusive and the second exclusive -- ; both are optional, ; the first defaulting to 0 and the second to the array length. ; A circuit access selects a member variable by name. ; Function calls are also postfix expressions. ; There are three kinds of function calls: ; top-level function calls, ; instance (i.e. non-static) member function calls, and ; static member function calls. ; What changes is the start, but they all end in an argument list. function-arguments = "(" [ expression *( "," expression ) ] ")" postfix-expression = primary-expression / postfix-expression "." natural / postfix-expression "." identifier / identifier function-arguments / postfix-expression "." identifier function-arguments / circuit-type "::" identifier function-arguments / postfix-expression "[" expression "]" / postfix-expression "[" [expression] ".." [expression] "]" ; Unary operators have the highest operator precedence. ; They apply to postfix expressions, ; and recursively to unary expressions. unary-expression = postfix-expression / "!" unary-expression / "-" unary-expression ; Next in the operator precedence is casting. cast-expression = unary-expression / cast-expression %s"as" type ; Next in the operator precedence is exponentiation, ; following mathematical practice. ; The current rule below makes exponentiation left-associative, ; i.e. 'a ** b ** c' must be parsed as '(a ** b) ** c'. exponential-expression = cast-expression / exponential-expression "**" cast-expression ; Next in precedence come multiplication and division, both left-associative. multiplicative-expression = exponential-expression / multiplicative-expression "*" exponential-expression / multiplicative-expression "/" exponential-expression ; Then there are addition and subtraction, both left-assocative. additive-expression = multiplicative-expression / additive-expression "+" multiplicative-expression / additive-expression "-" multiplicative-expression ; Next in the precedence order are ordering relations. ; These are not associative, because they return boolean values. ordering-expression = additive-expression / additive-expression "<" additive-expression / additive-expression ">" additive-expression / additive-expression "<=" additive-expression / additive-expression ">=" additive-expression ; Equalities return booleans but may also operate on booleans; ; the rule below makes them left-associative. equality-expression = ordering-expression / equality-expression "==" ordering-expression / equality-expression "!=" ordering-expression ; Next come conjunctive expressions, left-associative. conjunctive-expression = equality-expression / conjunctive-expression "&&" equality-expression ; Next come disjunctive expressions, left-associative. disjunctive-expression = conjunctive-expression / disjunctive-expression "||" conjunctive-expression ; Finally we have conditional expressions. conditional-expression = disjunctive-expression / conditional-expression "?" expression ":" conditional-expression ; Those above are all the expressions. ; Recall that conditional expressions ; may be disjunctive expressions, ; which may be conjunctive expressions, ; and so on all the way to primary expressions. expression = conditional-expression ; There are various kinds of statements, including blocks. ; Blocks are possibly empty sequences of statements surrounded by curly braces. statement = expression-statement / return-statement / variable-definition-statement / conditional-statement / loop-statement / assignment-statement / console-statement / block block = "{" *statement "}" ; An expression (that must return the empty tuple, as semantically required) ; can be turned into a statement by appending a semicolon. expression-statement = expression ";" ; A return statement always takes an expression, ; and does not end with a semicolon. return-statement = %s"return" expression ; There are two kinds of variable definition statements, ; which only differ in the starting keyword. ; The variables are either a single one or a tuple of two or more; ; in all cases, there is just one optional type ; and just one initializing expression. variable-definition-statement = ( %s"let" / %s"const" ) identifier-or-identifiers [ ":" type ] "=" expression ";" identifier-or-identifiers = identifier / "(" identifier 1*( "," identifier ) ")" ; A conditional statement always starts with a condition and a block ; (which together form a branch). ; It may stop there, or it may continue with an alternative block, ; or possibly with another conditional statement, forming a chain. ; Note that blocks are required in all branches, not merely statements. branch = %s"if" expression block conditional-statement = branch / branch %s"else" block / branch %s"else" conditional-statement ; A loop statement implicitly defines a loop variable ; that goes from a starting value (inclusive) to an ending value (exclusive). ; The body is a block. loop-statement = %s"for" identifier %s"in" expression ".." expression block ; An assignment statement is straightforward. ; Based on the operator, the assignment may be simple (i.e. '=') ; or compound (i.e. combining assignment with an arithmetic operation). assignment-operator = "=" / "+=" / "-=" / "*=" / "/=" / "**=" assignment-statement = expression assignment-operator expression ";" ; Console statements start with the 'console' keyword, ; followed by a console function call. ; The call may be an assertion or a print command. ; The former takes an expression (which must be boolean) as argument. ; The latter takes either no argument, ; or a formatted string followed by expressions, ; whose number must match the number of containers '{}' in the formatted string. ; Note that the console function names are identifiers, not keywords. ; There are three kinds of print commands. console-statement = %s"console" "." console-call console-call = assert-call / print-call assert-call = %s"assert" "(" expression ")" print-function = %s"debug" / %s"error" / %s"log" print-arguments = "(" [ formatted-string *( "," expression ) ] ")" print-call = print-function print-arguments ; An annotation consists of an annotation name (which starts with '@') ; with optional annotation arguments, which are identifiers. ; Note that no parentheses are used if there are no arguments. annotation = annotation-name [ "(" identifier *( "," identifier ) ")" ] ; A function declaration defines a function. ; The output type is optional, defaulting to the empty tuple type. ; In general, a function input consists of an identifier and a type, ; with an optional 'const' modifier. ; Additionally, functions inside circuits ; may start with a 'mut self' or 'const self' or 'self' parameter. ; Furthermore, any function may end with an 'input' parameter. function-declaration = *annotation %s"function" identifier "(" [ function-parameters ] ")" [ "->" type ] block function-parameters = self-parameter [ "," input-parameter ] / self-parameter "," function-inputs [ "," input-parameter ] / function-inputs [ "," input-parameter ] / input-parameter self-parameter = [ %s"mut" / %s"const" ] %s"self" function-inputs = function-input *( "," function-input ) function-input = [ %s"const" ] identifier ":" type input-parameter = %s"input" ; A circuit member variable declaration consists of an identifier and a type. ; A circuit member function declaration consists of a function declaration. member-declaration = member-variable-declaration / member-function-declaration member-variable-declaration = identifier ":" type member-function-declaration = function-declaration ; A circuit declaration defines a circuit type, ; as consisting of member variables and functions. circuit-declaration = *annotation %s"circuit" identifier "{" member-declaration *( "," member-declaration ) "}" ; An import declaration consists of the 'import' keyword ; followed by a package path, which may be one of the following: ; a single wildcard; ; an identifier, optionally followed by a local renamer; ; a package name followed by a path, recursively; ; or a parenthesized list of package paths, ; which are "fan out" of the initial path. ; Note that we allow the last element of the parenthesized list ; to be followed by a comma, for convenience. import-declaration = %s"import" package-path package-path = "*" / identifier [ %s"as" identifier ] / package-name "." package-path / "(" package-path *( "," package-path ) [","] ")" ; Finally, we define a file as a sequence of zero or more declarations. declaration = import-declaration / function-declaration / circuit-declaration file = *declaration