prove_rec_fn_exists : (thm -> term -> thm)

SYNOPSIS

Proves the existence of a primitive recursive function over a concrete recursive type.

DESCRIBE

prove_rec_fn_exists is a version of new_recursive_definition which proves only that the required function exists; it does not make a constant specification. The first argument is a theorem of the form returned by define_type, and the second is a user-supplied primitive recursive function definition. The theorem which is returned asserts the existence of the recursively-defined function in question (if it is primitive recursive over the type characterized by the theorem given as the first argument). See the entry for new_recursive_definition for details.

FAILURE

As for new_recursive_definition.

EXAMPLE

Given the following primitive recursion theorem for labelled binary trees:

   |- !f0 f1.
        ?! fn.
        (!x. fn(LEAF x) = f0 x) /\
        (!b1 b2. fn(NODE b1 b2) = f1(fn b1)(fn b2)b1 b2)

prove_rec_fn_exists can be used to prove the existence of primitive recursive functions over binary trees. Suppose the value of th is this theorem. Then the existence of a recursive function Leaves, which computes the number of leaves in a binary tree, can be proved as shown below:

   #prove_rec_fn_exists th
   #  "(Leaves (LEAF (x:*)) = 1) /\
   #   (Leaves (NODE t1 t2) = (Leaves t1) + (Leaves t2))";;
   |- ?Leaves. (!x. Leaves(LEAF x) = 1) /\
               (!t1 t2. Leaves(NODE t1 t2) = (Leaves t1) + (Leaves t2))

The result should be compared with the example given under new_recursive_definition.

SEEALSO  define_type,   new_recursive_definition