search : term list -> (string * thm) list

SYNOPSIS

Search the database of theorems according to query patterns.

DESCRIPTION

The search function is intended to locate a desired theorem by searching based on term patterns or names. The database of theorems to be searched is held in theorems, which initially contains all theorems individually bound to OCaml identifiers in the main system, and can be augmented or otherwise modified by the user. (See in particular the update script in update_database.ml which creates a database according to the current OCaml environment.) The input to search is a list of terms that are treated as patterns. Normally, a term pat is interpreted as a search for `a theorem with any subterm of the form pat', e.g. a pattern x + y for any subterm of the form s + t. However, several syntax functions create composite terms that are interpreted specially by search:

omit pat --- Search for theorems not satisfying pat
exactly `t` --- Search for theorems with subterms alpha-equivalent to t (not just of the general form t)
name "str" --- Search for theorems whose name contains str as a substring.

FAILURE CONDITIONS

Never fails.

EXAMPLE

Search for theorems with a subterm of the form s <= t / u:

  # search [`x <= y / z`];;
  val it : (string * thm) list =
    [("RAT_LEMMA4",
      |- &0 < y1 /\ &0 < y2 ==> (x1 / y1 <= x2 / y2 <=> x1 * y2 <= x2 * y1));
     ("REAL_LE_DIV", |- !x y. &0 <= x /\ &0 <= y ==> &0 <= x / y);
     ("REAL_LE_DIV2_EQ", |- !x y z. &0 < z ==> (x / z <= y / z <=> x <= y));
     ("REAL_LE_RDIV_EQ", |- !x y z. &0 < z ==> (x <= y / z <=> x * z <= y));
     ("SUM_BOUND_GEN",
      |- !s t b.
             FINITE s /\ ~(s = {}) /\ (!x. x IN s ==> f x <= b / &(CARD s))
             ==> sum s f <= b)]

Search for theorems whose name contains "CROSS" and whose conclusion involves the cardinality function CARD:

  # search [name "CROSS"; `CARD`];;
  Warning: inventing type variables
  val it : (string * thm) list =
    [("CARD_CROSS",
      |- !s t. FINITE s /\ FINITE t ==> CARD (s CROSS t) = CARD s * CARD t)]

Search for theorems that involve finiteness of the image of a set under a function, but also do not involve logical equivalence:

  # search [`FINITE(IMAGE f s)`; omit `(<=>)`];;
  Warning: inventing type variables
  val it : (string * thm) list =
    [("FINITE_IMAGE", |- !f s. FINITE s ==> FINITE (IMAGE f s))]

SEE ALSO

theorems.