formal/hol/Help/ASSOC_CONV.doc

\DOC ASSOC_CONV

\TYPE {ASSOC_CONV : thm -> term -> thm}

\SYNOPSIS
Right-associates a term with respect to an associative binary operator.

\DESCRIBE
The conversion {ASSOC_CONV} expects a theorem asserting that a certain binary
operator is associative, in the standard form (with optional universal
quantifiers):
{
  x op (y op z) = (x op y) op z
}
It is then applied to a term, and will right-associate any toplevel
combinations built up from the operator {op}. Note that if {op} is polymorphic,
the type instance of the theorem needs to be the same as in the term to which
it is applied.

\FAILURE
May fail if the theorem is malformed. On application to the term, it never
fails, but returns a reflexive theorem when itis inapplicable.

\EXAMPLE
{
  # ASSOC_CONV ADD_ASSOC `((1 + 2) + 3) + (4 + 5) + (6 + 7)`;;
  val it : thm = |- ((1 + 2) + 3) + (4 + 5) + 6 + 7 = 1 + 2 + 3 + 4 + 5 + 6 + 7

  # ASSOC_CONV CONJ_ASSOC `((p /\ q) /\ (r /\ s)) /\ t`;;
  val it : thm = |- ((p /\ q) /\ r /\ s) /\ t <=> p /\ q /\ r /\ s /\ t
}

\SEEALSO
AC, CNF_CONV, CONJ_ACI_RULE, DISJ_ACI_RULE, DNF_CONV.

\ENDDOC