PairedLambda.GEN_BETA

STRUCTURE

SYNOPSIS

Beta-reduces single or paired beta-redexes, creating a paired argument if needed.

DESCRIPTION

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]

FAILURE

GEN_BETA_CONV tm fails if tm is neither a simple nor a tupled beta-redex.

EXAMPLE

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 : thm

whereas 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 : thm

The 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

SEEALSO

BETA_CONV, PAIRED_BETA_CONV