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Lark Grammar for M2 language

Frédéric Chapoton edited this page Apr 26, 2024 · 10 revisions

This is related to issue #2889.

It would be convenient to have a formal model for the M2 language. This would in particular allow syntax checks of all files in the common library and packages.

Here is the Lark documentation:

https://lark-parser.readthedocs.io/en/stable/

A basic tentative was started in #2893, stuck at a preliminary stage.

This is remotely related to the question of highliting code, as allowed by

https://github.com/mahrud/language-macaulay2

How to use

Here is a sample ipython session:

from lark import Lark
with open("macaulay2.lark") as f:
 w = f.read()
m2parser = Lark(w, start='start')
tree = m2parser.parse(open("M2/M2/Macaulay2/packages/DiffAlg.m2").read())
print(tree.pretty())

and here the tentative grammar:

// this entry point is for a file input
start: (_NEWLINE | expr)*
SYMBOL: WORD ("'" WORD?)?
 | WORD "." WORD
COMMENT: /--[^\n]*/
 | /--.*\n/
 | /-\*.*\*-/
FUNCTION: "sin" | "cos" | "tan" | "abs" | "acos"
 | "agm" | "asin" | "atan" | "atan2"
 | "zeta" | "tanh" | "sqrt" | "sec" | "sech"
 | "erf" | "erfc" | "coth" | "csc" | "eint"
token: SYMBOL
 | string
 | SIGNED_NUMBER
 | operator_exp
 | command
 | timing
 | assignment
 | lists_and_sequences
 | hash_table
 | matrix
 | branching
 | bool
 | symbols
 | make_function
 | function_call
 | function_def
 | table_access
 | mapping
expr: token (";" token)* (";")?
string: STRING
 | "toString" expr
 | (string "|")+ string
mapping: expr "=>" expr
// functions
typing: ":=" mapping
wrapped_symbol: "(" SYMBOL ")"
function_call: (SYMBOL | FUNCTION | wrapped_symbol) "(" expr ("," expr)* ")"
	 | SYMBOL expr
function_def: function_call typing? "->" expr
make_function: (lists_and_sequences|SYMBOL) typing? "->" expr
command: "newPackage" "(" string ("," mapping)* ")" -> new_package
 | "select" "(" lists_and_sequences "," expr ")"
 | "position(" expr ("," expr) ")"
 | "needs" string -> needs_package
 | "method" "(" mapping? ")"
 | "instance" "(" expr "," SYMBOL ")"
 | "class" expr
// operators
unary_pre_op: "-" -> minus
 | "+" -> plus
	 | "#" -> cardinality
unary_post_op: "(*)"
 | "^*"
	 | "^!"
 | "_*"
	 | "_!"
 | "~"
 | "!"
binary_op: "+" -> plus
	 | "-" -> minus
 | "*" -> times
	 | "/" -> div
	 | "//" -> floordiv
	 | "\\" -> applied_to
 | "**" -> power
	 | "++" -> doubleplus
 | "^"
	 | "^^"
	 | "^**"
 | "<<" | ">>"
 | "<==>" -> equiv
 | "<=="
	 | "<==="
 | "==>"
	 | "===>"
 | "@" | "@@"
 | "&" | "%"
 | "|" | "|-" | "||"
 | ".." | "..<" | ":" | "_"
 | "."
operator_exp: unary_pre_op expr
 | expr unary_post_op
 | expr binary_op expr
// boolean and comparison tests
comparison: expr "==" expr -> equal
 | expr "!=" expr -> unequal
 | expr "===" expr -> strict_equal
 | expr "=!=" expr -> strict_unequal
 | expr "<" expr -> less
 | expr "<=" expr -> less_or_equal
 | expr ">" expr -> greater
 | expr ">=" expr -> greater_or_equal
BOOLEAN: "true" | "false"
bool: expr "and" expr -> and
 | bool "or" bool -> or
 | bool "xor" bool -> xor
 | "not" bool -> not
 | BOOLEAN
 | comparison
 | "all" "(" expr "," expr")" -> all
// new and symbols
// new: "new" hash_table ["of" hash_table] "from" hash_table ":=" (A,B,c) "->" expr
symbols: "global" SYMBOL
 | "local" SYMBOL
 | "symbol" SYMBOL
 | "protect" SYMBOL
 | "threadVariable" SYMBOL
// assignment
assignment: expr "=" expr
 | (expr|SYMBOL) ":=" expr
 | expr "<-" expr
comparison_operator: "?"
// subscripting and object access
accessing: "_" expr -> subscript
 | "." expr -> access_via_key
 | "#" expr? -> length_or_access
 | ".?" expr -> check_for_key
 | "#?" SYMBOL -> check_value
	 | "[" bare_range "]" -> get_range
 
table_access: expr accessing
configuration: expr "'" expr
// branching
bare_for: "for" expr ["from" expr] ["to" expr] ["when" bool]
branching: "if" expr "then" expr ["else" expr]
 | "while" expr "do" expr
 | bare_for "do" expr
 | "break" expr?
 | "continue" expr?
 | "return" expr?
// exceptions and errors
exception: "error" string
 | "try" expr ["then" expr] ["else" expr]
 | "catch" expr
 | "throw" expr
 | "shield" expr
// timing and alarms
timing: "alarm" NN
 | "time" expr
 | "timing" expr
 | "sleep" NN
 | "nanosleep" NN
 | "elapsedTime" expr
 | "elapsedTiming" expr
// lists, sets, sequences, arrays
bare_sequence: expr ("," expr)* (",")?
bare_range: expr (".."|"..<") expr
lists_and_sequences: ("{" bare_sequence "}" | "{" "}")
 | "(" bare_sequence ")"
 | "[" bare_sequence "]"
 | "<|" bare_sequence "|>"
		 | "set" ("{" bare_sequence "}" | "{" "}")
		 | bare_for "list" expr
		 | bare_range
		 | "while" bool "list" expr
matrix: "matrix" lists_and_sequences
// mapping over hash tables
hash_table: "{" mapping ("," mapping)* "}"
hash_table_operation: "applyValues(" hash_table "," expr ")"
 | "applyKeys(" hash_table "," expr ")"
 | "applyPairs(" hash_table "," expr ")"
 | "scanValues(" hash_table "," expr ")"
 | "scanKeys(" hash_table "," expr ")"
 | "scanPairs(" hash_table "," expr ")"
 | "scan(" hash_table "," expr ")"
// "merge(" A B C ")"
// combine: "combine(" A B C D E")"
_NEWLINE: ( /\r?\n[\t ]*/ | COMMENT )+
%import common.ESCAPED_STRING -> STRING
%import common.SIGNED_NUMBER
%import common.WORD
%import common.LETTER
%import common.NEWLINE
%import common.INT -> NN
%import common.SIGNED_INT -> ZZ
%import common.SIGNED_FLOAT -> RR
%import common.WS
%ignore WS
%ignore COMMENT

Too bad that one cannot store that as a file in the wiki..

OLD FILE:

// this entry point is for a file input
start: (_NEWLINE | expr)*
SYMBOL: WORD
COMMENT: /--[^\n]*/
 | /--.*\n/
 | /-\*.*\*-/
 | ";"
FUNCTION: "sin" | "cos" | "tan" | "abs" | "acos"
 | "agm" | "asin" | "atan" | "atan2"
 | "zeta" | "tanh" | "sqrt" | "sec" | "sech"
 | "erf" | "erfc" | "coth" | "csc" | "eint"
expr: SYMBOL
 | string
 | SIGNED_NUMBER
 | operator_exp
 | command
 | timing
 | assignment
 | lists_and_sequences
 | hash_table
 | branching
 | bool
 | symbols
 | make_function
 | function_call
 | function_def
 | table_access
string: STRING
 | "toString" expr
 | (string "|")+ string
mapping: expr "=>" expr
// functions
typing: ":=" mapping
function_call: (SYMBOL | FUNCTION) "(" expr ("," expr)* ")"
	 | SYMBOL expr
function_def: function_call typing? "->" expr
make_function: (lists_and_sequences|SYMBOL) typing? "->" expr
command: "newPackage" "(" string ("," mapping)* ")" -> new_package
 | "select" "(" lists_and_sequences "," expr ")"
 | "position(" expr ("," expr) ")"
 | "needs" string -> needs_package
 | "method" "(" mapping? ")"
 | "instance" "(" expr "," SYMBOL ")"
 | "class" expr
// operators
unary_pre_op: "-" -> minus
 | "+" -> plus
	 | "#" -> cardinality
unary_post_op: "(*)"
 | "^*"
	 | "^!"
 | "_*"
	 | "_!"
 | "~"
 | "!"
binary_op: "+" -> plus
	 | "-" -> minus
 | "*" -> times
	 | "/" -> div
	 | "//" -> floordiv
 | "**" -> power
	 | "++" -> doubleplus
 | "^"
	 | "^^"
	 | "^**"
 | "<<" | ">>"
 | "<==>" -> equiv
 | "<=="
	 | "<==="
 | "==>"
	 | "===>"
 | "@" | "@@"
 | "&" | "%"
 | "|" | "|-" | "||"
 | ".." | "..<" | ":" | "_"
 | "."
operator_exp: unary_pre_op expr
 | expr unary_post_op
 | expr binary_op expr
// boolean and comparison tests
comparison: expr "==" expr -> equal
 | expr "!=" expr -> unequal
 | expr "===" expr -> strict_equal
 | expr "=!=" expr -> strict_unequal
 | expr "<" expr -> less
 | expr "<=" expr -> less_or_equal
 | expr ">" expr -> greater
 | expr ">=" expr -> greater_or_equal
BOOLEAN: "true" | "false"
bool: bool "and" bool -> and
 | bool "or" bool -> or
 | bool "xor" bool -> xor
 | "not" bool -> not
 | BOOLEAN
 | comparison
 | "all" "(" expr "," expr")" -> all
// new and symbols
// new: "new" hash_table ["of" hash_table] "from" hash_table ":=" (A,B,c) "->" expr
symbols: "global" SYMBOL
 | "local" SYMBOL
 | "symbol" SYMBOL
 | "protect" SYMBOL
 | "threadVariable" SYMBOL
// assignment
assignment: expr "=" expr
 | (expr|SYMBOL) ":=" expr
 | expr "<-" expr
comparison_operator: "?"
// subscripting and object access
accessing: "_" expr -> subscript
 | "." expr -> access_via_key
 | "#" expr? -> length_or_access
 | ".?" expr -> check_for_key
 | "#?" -> check_value
 
table_access: expr accessing
// branching
branching: "if" bool "then" expr ["else" expr]
 | "while" bool ["list" expr] ["do" expr]
 | "for" expr ["from" expr] ["to" expr] ["when" bool] ["list" expr] ["do" expr]
 | "break" expr?
 | "continue" expr?
 | "return" expr?
// exceptions and errors
exception: "error" string
 | "try" expr ["then" expr] ["else" expr]
 | "catch" expr
 | "throw" expr
 | "shield" expr
// timing and alarms
timing: "alarm" NN
 | "time" expr
 | "timing" expr
 | "sleep" NN
 | "nanosleep" NN
 | "elapsedTime" expr
 | "elapsedTiming" expr
// lists, sets, sequences, arrays
bare_sequence: expr ("," expr)*
lists_and_sequences: ("{" bare_sequence "}" | "{" "}")
 | "(" bare_sequence ")"
 | "[" bare_sequence "]"
 | "<|" bare_sequence "|>"
		 | "set" ("{" bare_sequence "}" | "{" "}")
// mapping over hash tables
hash_table: "{" mapping ("," mapping)* "}"
hash_table_operation: "applyValues(" hash_table "," expr ")"
 | "applyKeys(" hash_table "," expr ")"
 | "applyPairs(" hash_table "," expr ")"
 | "scanValues(" hash_table "," expr ")"
 | "scanKeys(" hash_table "," expr ")"
 | "scanPairs(" hash_table "," expr ")"
 | "scan(" hash_table "," expr ")"
// "merge(" A B C ")"
// combine: "combine(" A B C D E")"
_NEWLINE: ( /\r?\n[\t ]*/ | COMMENT )+
%import common.ESCAPED_STRING -> STRING
%import common.SIGNED_NUMBER
%import common.WORD
%import common.LETTER
%import common.NEWLINE
%import common.INT -> NN
%import common.SIGNED_INT -> ZZ
%import common.SIGNED_FLOAT -> RR
%import common.WS
%ignore WS
%ignore COMMENT

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