PratterSourceTransform strings of tokens and mixfix operators into full binary trees. Operators are characterised by their associativity and their fixity.
To parse expressions from type 'i to type 'o, you need to tell the parser
'o -> 'o -> 'o; this function can be seen as the concatenation of two binary trees (and in that case, the input of the parser is a string of leaves);'i should be considered an operator;'i that aren't operators.The algorithm implemented is an extension of the Pratt parser. The Shunting Yard algorithm could also be used.
Associativity of an operator.
type 't error = [ | `Op_conflict of 'tPriority or associativiy conflict between two operators. In `OpConflict o, o is an operator which generates a conflict.
| `Too_few_argumentsMore arguments are expected. It is raised for instance on partial application of operators, such as x +; or when an empty input is given to the parser.
]Errors that can be encountered while parsing a stream of terms.
Values of that type are parsers from sequences of 'tok to values of type 'out.
val expression :
appl:('b -> 'b -> 'b) ->
token:('a -> 'b) ->
ops:('a, 'b) Operators.t ->
('a, 'b) parserexpression appl token ops is a parser from sequences of 'a to structured values of type 'b. The parser is driven by the operator parser ops which determines which tokens are operators. Tokens that aren't operators are parsed using the token function.
If tokens are seen as leaves of binary trees, the function appl is the concatenation of two binary trees. If tokens are seen as terms, appl is the application.
For instance, assuming that + is declared infix and we're working with numbers, it can transform 3 + 5 × 2 encoded as the stream of terms 3, +, 5, ×, 2 into the binary tree @(@(×,@(@(+,3),5)),2) where @ denotes application nodes.