FOLDR_CONV
listLib.FOLDR_CONV : conv -> conv
Computes by inference the result of applying a function to the elements of a list.
FOLDR_CONV takes a conversion conv and a term tm in the following
form:
FOLDR f e [x0;...xn]
It returns the theorem
|- FOLDR f e [x0;...xn] = tm'
where tm' is the result of applying the function f iteratively to
the successive elements of the list and the result of the previous
application starting from the tail end of the list. During each
iteration, an expression f xi ei is evaluated. The user supplied
conversion conv is used to derive a theorem
|- f xi ei = e(i+1)
which is used in the next iteration.
Failure
FOLDR_CONV conv tm fails if tm is not of the form described above.
Example
To sum the elements of a list, one can use FOLDR_CONV with
REDUCE_CONV from the library numLib.
- FOLDR_CONV numLib.REDUCE_CONV ``FOLDR $+ 0 [0;1;2;3]``;
val it = |- FOLDR $+ 0[0;1;2;3] = 6 : thm
In general, if the function f is an explicit lambda abstraction
(\x x'. t[x,x']), the conversion should be in the form
((RATOR_CONV BETA_CONV) THENC BETA_CONV THENC conv'))
where conv' applied to t[x,x'] returns the theorem
|-t[x,x'] = e''.