pred_setLib.DELETE

STRUCTURE

SYNOPSIS

Reduce {t1;...;tn} DELETE t by deleting t from {t1;...;tn}.

LIBRARY

pred_set

DESCRIPTION

The function DELETE_CONV is a parameterized conversion for reducing finite sets of the form {t1;...;tn} DELETE t, where the term t and the elements of {t1;...;tn} are of some base type ty. The first argument to DELETE_CONV is expected to be a conversion that decides equality between values of the base type ty. Given an equation e1 = e2, where e1 and e2 are terms of type ty, this conversion should return the theorem |- (e1 = e2) = T or the theorem |- (e1 = e2) = F, as appropriate.

Given such a conversion conv, the function DELETE_CONV returns a conversion that maps a term of the form {t1;...;tn} DELETE t to the theorem

   |- {t1;...;tn} DELETE t = {ti;...;tj}

where {ti;...;tj} is the subset of {t1;...;tn} for which the supplied equality conversion conv proves

   |- (ti = t) = F, ..., |- (tj = t) = F

and for all the elements tk in {t1;...;tn} but not in {ti;...;tj}, either conv proves |- (tk = t) = T or tk is alpha-equivalent to t. That is, the reduced set {ti;...;tj} comprises all those elements of the original set that are provably not equal to the deleted element t.

EXAMPLE

In the following example, the conversion REDUCE_CONV is supplied as a parameter and used to test equality of the deleted value 2 with the elements of the set.

   - DELETE_CONV REDUCE_CONV ``{2; 1; SUC 1; 3} DELETE 2``;
   > val it = |- {2; 1; SUC 1; 3} DELETE 2 = {1; 3} : thm

‘

FAILURE

DELETE_CONV conv fails if applied to a term not of the form {t1;...;tn} DELETE t. A call DELETE_CONV conv ``{t1;...;tn} DELETE t`` fails unless for each element ti of the set {t1;...;tn}, the term t is either alpha-equivalent to ti or conv ``ti = t`` returns |- (ti = t) = T or |- (ti = t) = F.

SEEALSO

INSERT_CONV, REDUCE_CONV