package pratter

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package pratter
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Module PratterSource

Transform 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

  • how to concatenate two expressions with a function of type '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);
  • how to determine whether a value of 'i should be considered an operator;
  • how to parse tokens of 'i that aren't operators.

The algorithm implemented is an extension of the Pratt parser. The Shunting Yard algorithm could also be used.

Sourcetype associativity =
  1. | Left
    (*

    If + is a left associative operator, x + y + z is parsed (x + y) + z.

    *)
  2. | Right
    (*

    If + is a right associative operator, x + y + z is parsed x + (y + z).

    *)
  3. | Neither
    (*

    If + is not associative, then (x + y) + z is not x + (y + z) and x + y + z results in a syntax error.

    *)

Associativity of an operator.

Sourcetype fixity =
  1. | Infix of associativity
    (*

    Infix operator like + in x + y.

    *)
  2. | Prefix
    (*

    Prefix operator like ! in ! x.

    *)
  3. | Postfix
    (*

    Postfix operator like ^ in x ^.

    *)

The fixity of an operator

Sourcetype 't error = [
  1. | `Op_conflict of 't
    (*

    Priority or associativiy conflict between two operators. In `OpConflict o, o is an operator which generates a conflict.

    *)
  2. | `Too_few_arguments
    (*

    More 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.

Sourcetype ('a, 'b) result = ('a, 'b error) result

A specialised error type.

Sourcetype ('tok, 'out) parser

Values of that type are parsers from sequences of 'tok to values of type 'out.

Sourceval expression : appl:('b -> 'b -> 'b) -> token:('a -> 'b) -> ops:('a -> (fixity * float * 'b) list) -> ('a, 'b) parser

expression 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. A token t can be used as an operator if ops t isn't empty. Each value (f, p, s) of ops t means that token t can be parsed as token s with fixity f and priority p.

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.

Sourceval run : ('tok, 'out) parser -> 'tok Seq.t -> ('out, 'tok) result

Run the given parser on a sequence of tokens.