`PSUB_CONV : (conv -> conv)`
STRUCTURE
LIBRARY
pair
SYNOPSIS
Applies a conversion to the top-level subterms of a term.
DESCRIPTION
For any conversion c, the function returned by PSUB_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 a paired abstraction "\p.t" to the theorem:
```   |- (\p.t) = (\p.t')
```
That is, PSUB_CONV c "\p.t" applies c to the body of the paired abstraction "\p.t". If c is a conversion that maps "t1" to the theorem |- t1 = t1' and "t2" to the theorem |- t2 = t2', then the conversion PSUB_CONV c maps an application "t1 t2" to the theorem:
```   |- (t1 t2) = (t1' t2')
```
That is, PSUB_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 PSUB_CONV c acts as the identity conversion on variables and constants. That is, if "t" is a variable or constant, then PSUB_CONV c "t" returns |- t = t.
FAILURE
PSUB_CONV c tm fails if tm is a paired abstraction "\p.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 PSUB_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
HOL  Kananaskis-14