GEN_BETA_CONVPairedLambda.GEN_BETA_CONV : convBeta-reduces single or paired beta-redexes, creating a paired argument if needed.
The conversion GEN_BETA_CONV will perform beta-reduction
of simple beta-redexes in the manner of BETA_CONV, or of
tupled beta-redexes in the manner of PAIRED_BETA_CONV.
Unlike the latter, it will force through a beta-reduction by introducing
arbitrarily nested pair destructors if necessary. The following shows
the action for one level of pairing; others are similar.
GEN_BETA_CONV "(\(x,y). t) p" = t[(FST p)/x, (SND p)/y]GEN_BETA_CONV tm fails if tm is neither a
simple nor a tupled beta-redex.
The following examples show the action of GEN_BETA_CONV
on tupled redexes. In the following, it acts in the same way as
PAIRED_BETA_CONV:
- pairLib.GEN_BETA_CONV (Term `(\(x,y). x + y) (1,2)`);
val it = |- (\(x,y). x + y)(1,2) = 1 + 2 : thmwhereas in the following, the operand of the beta-redex is not a
pair, so FST and SND are introduced:
- pairLib.GEN_BETA_CONV (Term `(\(x,y). x + y) numpair`);
> val it = |- (\(x,y). x + y) numpair = FST numpair + SND numpair : thmThe introduction of FST and SND will be
done more than once as necessary:
- pairLib.GEN_BETA_CONV (Term `(\(w,x,y,z). w + x + y + z) (1,triple)`);
> val it =
|- (\(w,x,y,z). w + x + y + z) (1,triple) =
1 + FST triple + FST (SND triple) + SND (SND triple) : thm