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\DOC GEN_BETA_CONV
\TYPE {GEN_BETA_CONV : term -> thm}
\SYNOPSIS
Beta-reduces general beta-redexes (e.g. paired ones).
\KEYWORDS
conversion.
\DESCRIBE
The conversion {GEN_BETA_CONV} will perform beta-reduction of simple
beta-redexes in the manner of {BETA_CONV}, or of generalized beta-redexes such
as paired redexes.
\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 and
others:
{
# GEN_BETA_CONV `(\x. x + 1) 2`;;
val it : thm = |- (\x. x + 1) 2 = 2 + 1
# GEN_BETA_CONV `(\(x,y,z). x + y + z) (1,2,3)`;;
val it : thm = |- (\(x,y,z). x + y + z) (1,2,3) = 1 + 2 + 3
# GEN_BETA_CONV `(\[a;b;c]. b) [1;2;3]`;;
val it : thm = |- (\[a; b; c]. b) [1; 2; 3] = 2
}
However, it will fail if there is a mismatch between the varstruct and the
argument, or if it is unable to make sense of the generalized abstraction:
{
# GEN_BETA_CONV `(\(SUC n). n) 3`;;
Exception: Failure "term_pmatch".
# GEN_BETA_CONV `(\(x,y,z). x + y + z) (1,x)`;;
Exception: Failure "dest_comb: not a combination".
}
\SEEALSO
BETA_CONV, MATCH_CONV.
\ENDDOC
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