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1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 | )abbrev package ORDCOMP2 OrderedCompletionFunctions2
++ Author: Manuel Bronstein
++ Date Created: 4 Oct 1989
++ Date Last Updated: 4 Oct 1989
++ Description:
++ Lifting of maps to ordered completions.
OrderedCompletionFunctions2(R, S) : SIG == CODE where
R : SetCategory
S : SetCategory
ORR ==> OrderedCompletion R
ORS ==> OrderedCompletion S
SIG ==> with
map : (R -> S, ORR) -> ORS
++ map(f, r) lifts f and applies it to r, assuming that
++ f(plusInfinity) = plusInfinity and that
++ f(minusInfinity) = minusInfinity.
map : (R -> S, ORR, ORS, ORS) -> ORS
++ map(f, r, p, m) lifts f and applies it to r, assuming that
++ f(plusInfinity) = p and that f(minusInfinity) = m.
CODE ==> add
map(f, r) == map(f, r, plusInfinity(), minusInfinity())
map(f, r, p, m) ==
zero?(n := whatInfinity r) => (f retract r)::ORS
(n = 1) => p
m
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