SUB_CONV : (conv -> conv)

SYNOPSIS
Applies a conversion to the top-level subterms of a term.

DESCRIBE
For any conversion c, the function returned by SUB_CONV c is a conversion that applies c to all the top-level subterms of a term. If the conversion c maps t to |- t = t', then SUB_CONV c maps an abstraction "\x.t" to the theorem:
   |- (\x.t) = (\x.t')
That is, SUB_CONV c "\x.t" applies c to the body of the abstraction "\x.t". If c is a conversion that maps "t1" to the theorem |- t1 = t1' and "t2" to the theorem |- t2 = t2', then the conversion SUB_CONV c maps an application "t1 t2" to the theorem:
   |- (t1 t2) = (t1' t2')
That is, SUB_CONV c "t1 t2" applies c to the both the operator t1 and the operand t2 of the application "t1 t2". Finally, for any conversion c, the function returned by SUB_CONV c acts as the identity conversion on variables and constants. That is, if "t" is a variable or constant, then SUB_CONV c "t" returns |- t = t.

FAILURE
SUB_CONV c tm fails if tm is an abstraction "\x.t" and the conversion c fails when applied to t, or if tm is an application "t1 t2" and the conversion c fails when applied to either t1 or t2. The function returned by SUB_CONV c may also fail if the ML function c:term->thm is not, in fact, a conversion (i.e. a function that maps a term t to a theorem |- t = t').

SEEALSO  ABS_CONV,   RAND_CONV,   RATOR_CONV

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