Wolfram/Parser | Paclet Repository

Wolfram`Parser`

ParseOperatorTable

ParseOperatorTable [unit,levels]
	returns the ParserCombinator that parses an operator-precedence expression grammar — operands separated by prefix, infix, and postfix operators — in a single linear left-to-right pass.

unit parses one operand (an atom, or a parenthesised sub-expression via

ParseRecursive

). levels is a list of precedence levels, tightest-binding first; each level is a list of operator specs

{fixity,opParser}

It is the

Pratt / top-down-operator-precedence

("precedence climbing") engine, exposed as a combinator: precedence becomes data (the table) instead of structure (a hand-cascaded tower of

ParseChainLeft

ParseChainRight

nonterminals).

Details and Options

▪

fixity is one of the strings

"InfixL"

(left-associative),

"InfixR"

(right-associative),

"Prefix"

, or

"Postfix"

▪

Operator parsers return their combining function — the same convention as

ParseChainLeft

. opParser matches the operator token and yields a function: binary

f[left,right]

for infix, unary

f[operand]

for prefix / postfix. Use

ParseAction

to attach the function, e.g.

ParseAction[ParseLiteral["+"],(Plus&)]

▪

Precedence is the level position. The first level binds tightest; the last binds loosest. Operators that share a level share a precedence (e.g.

and

▪

A lone spec stands in for a one-operator level:

{"InfixL",op}

is accepted as shorthand for

▪

Recursion is via

ParseRecursive

: a parenthesised-expression branch inside unit refers back to the symbol the table is bound to, so the engine re-enters at binding power 0 inside brackets.

▪

Linear time. The leading operand is parsed once; operators are then consumed while their binding power exceeds the caller's. A

ParseChoice

over

or|and|apply

re-parses the shared leading operand once per alternative and backtracks exponentially (the TPTP THF blow-up);