-- generic set 
mod! SET(X :: TRIV) {
[Elt.X < Set]
-- empty set
op empty : -> Set {constr} .
-- assicative and commutative set constructor with identity empty
op (_ _) : Set Set -> Set {constr assoc comm id: empty} .
-- (_ _) is idempotent with respect to the sort Elt
eq E:Elt E = E .
}

-- :m-and :m-or examples
mod NAT-SET-PRED {pr(SET(NAT)*{sort Set -> NatSet})
pred p1 : Nat .
pred p2 : Nat NatSet .
pred p3 : Nat Nat NatSet .
ops q1 q2 q3 : NatSet -> Bool .
eq [:m-and]: q1(N1:Nat NS:NatSet) = p1(N1) .
eq [:m-and]: q2(N1:Nat NS:NatSet) = p2(N1,NS) .
eq [:m-and]: q3(N1:Nat N2:Nat NS:NatSet) = p3(N1,N2,NS) .

ops r1 r2 : NatSet -> Bool .
eq [:m-or]: r1(N1:Nat NS:NatSet) = p1(N1) .
eq [:m-or]: r2(N1:Nat N2:Nat NS:NatSet) = p2(N1,N2) .
}

open NAT-SET-PRED .
set debug meta on

red q1(1 2 3) .
red q2(1 2 3) .
red q3(1 2 3) .


red q1(1 2 3 4) .
red q2(1 2 3 4) .
red q3(1 2 3 4) .

--
red r1(1 2 3) .
red r2(1 2 3) .

red r1(1 2 3 4) .
-- red r2(1 2 3 4) .

set debug meta off
close