About

      Loogle searches of Lean and Mathlib definitions and theorems.

      Usage

      Loogle finds definitions and lemmas in various ways:

      1. By constant:
        Real.sin finds all lemmas whose statement somehow mentions the sinefunction.

      2. By lemma name substring:
        "differ" finds all lemmas that have "differ" somewhere in their lemma name.

      3. By subexpression:
        _ * (_ ^ _) finds all lemmas whose statements somewhere include a product where the second argument is raised to some power.

        The pattern can also be non-linear, as in Real.sqrt ?a * Real.sqrt ?a

        If the pattern has parameters, they are matched in any order. Both of these will find List.map:
        (?a -> ?b) -> List ?a -> List ?b
        List ?a -> (?a -> ?b) -> List ?b

      4. By main conclusion:
        |- tsum _ = _ * tsum _ finds all lemmas where the conclusion (the subexpression to the right of all → and ∀) has the given shape.

        As before, if the pattern has parameters, they are matched against the hypotheses of the lemma in any order; for example, |- _ < _ → tsum _ < tsum _ will find tsum_lt_tsum even though the hypothesis f i < g i is not the last.

      If you pass more than one such search filter, separated by commas Loogle will return lemmas which match all of them. The search Real.sin, "two", tsum, _ * _, _ ^ _, |- _ < _ → _ would find all lemmas which mention the constants Real.sin and tsum, have "two" as a substring of the lemma name, include a product and a power somewhere in the type, and have a hypothesis of the form _ < _ (if there were any such lemmas). Metavariables (?a) are assigned independently in each filter.

      Source code

      You can find the source code for this service at https://github.com/nomeata/loogle. The https://loogle.lean-lang.org/ service is currently provided by Joachim Breitner <mail@joachim-breitner.de>.