FILTER_CONV

`FILTER_CONV`

listLib.FILTER_CONV : conv -> conv

Computes by inference the result of applying a predicate to the elements of a list.

FILTER_CONV takes a conversion conv and a term tm in the following form:

   FILTER P [x0;...xn]

It returns the theorem

   |- FILTER P [x0;...xn] = [...xi...]

where for every xi occurring in the right-hand side of the resulting theorem, conv “P xi” returns a theorem |- P xi = T.

FILTER_CONV conv tm fails if tm is not of the form described above.

Evaluating

   FILTER_CONV bool_EQ_CONV “FILTER ($= T) [T;F;T]”;

returns the following theorem:

   |- FILTER($= T)[T;F;T] = [T;T]

In general, if the predicate P is an explicit lambda abstraction (\x. P x), the conversion should be in the form

   (BETA_CONV THENC conv')