INST_TYPE : (hol_type,hol_type) subst -> thm -> thm

SYNOPSIS

Instantiates types in a theorem.

DESCRIBE

INST_TYPE is a primitive rule in the HOL logic, which allows instantiation of type variables.

              A |- t
  ----------------------------------- INST_TYPE[vty1|->ty1,..., vtyn|->tyn]
   A |- t[ty1,...,tyn/vty1,...,vtyn]

where none of the types vtyi are free in the assumption list. Variables will be renamed if necessary to prevent distinct variables becoming identical after the instantiation.

FAILURE

INST_TYPE fails if any of the type variables occurs free in the hypotheses of the theorem, or if upon instantiation two distinct variables (with the same name) become equal.

USES

INST_TYPE is employed to make use of polymorphic theorems.

EXAMPLE

Suppose one wanted to specialize the theorem EQ_SYM_EQ for particular values, the first attempt could be to use SPECL as follows:

   - SPECL [``a:num``, ``b:num``] EQ_SYM_EQ;
   uncaught exception HOL_ERR

The failure occurred because EQ_SYM_EQ contains polymorphic types. The desired specialization can be obtained by using INST_TYPE:

   - load "numTheory";
   > val it = () : unit

   - SPECL [(--`a:num`--), (--`b:num`--)]
           (INST_TYPE [``:'a`` |-> ``:num``] EQ_SYM_EQ);

   > val it = |- (a = b) = (b = a) : thm

SEEALSO  INST,   INST_TY_TERM