;; _fn <- "sets.cam";

flat(l) = CONC(< if (is-STR(x) || is-INT(x) || is-SYM(x)) then < x >
               else flat(x) | x <- l >);

;; i1(x)=<1,x>;

;; i2(x)=<2,x>;

;; j606o(y) = let (a=p1(y),b=p2(y),k=p1(b),x=p2(b)) in < k,<a,x> >;

;; nilit(x)=<x,nil>;

;; swap(x)=<p2(x),p1(x)>;

;; PLUS(s) = plus-orio([],s);

;; prod(f,g)= lambda(t).<f(p1(t)),g(p2(t))>;

;; const(f,g)= lambda(x).<f(x),g(x)>;

;; comp(f,g)= lambda(x).f(g(x));

;; Kons(c)= lambda(x).c;

;; id(x)=x;

;; FUNC curry(f:AxB->C):A->(B->C)
;; RETURN let (X=dom(f),
;;             Y=p1-set(X))
;;         in [ a -> [ p2(p) -> f[p] | p <- X : p1(p)==a ] | a <- Y ];

;; FUNC uncurry(f:A->(B->C)):AxB->C 
;; RETURN
;;      PLUS({ let (g=f[a]) in [ < a, b>  -> g[b] | b <- dom(g) ] | a <- dom(f) });

;; ffAset(s) = [ a -> nil  | a <- s ];

;; join(f1,f2) = [ a -> < f1[a],f2[a]> | a <- dom(f1) * dom(f2) ];

;; joinInv <- const((*->p1),(*->p2));

;; uplus(p) = p1(p) + p2(p);

;; ujoin(p) = join(p1(p),p2(p));

;; nJoin <- comp(ujoin,const(p1,comp(uplus,prod((*->Kons(nil)),curry))));

;; nJoinInv <- const((*->p1),comp(uncurry,(*->p2)));

;; pJoinInv(f) = let (a=[ p2(x) -> f[x] | x <- dom(f): p1(x) == 1 ],
;;                    b=[ p2(x) -> f[x] | x <- dom(f): p1(x) == 2 ])
;;               in < a , b >;

;; discollect(f) = UNION({ { <a,b> | b <- f[a] } | a <- dom(f) });

;; collect(r) = [ a -> { p2(q) | q <- r: a==p1(q) }
;;                             | a <- { p1(p) | p <- r } ];

;; pair2ff(p)= [ "Att1"-> p1(p), "Att2"-> p2(p) ];

;; ;seq2ff(t)= let (f=lambda(i)."Att"++itoa(i)) in (f->*)(seq2ff(t));

;; ff2pair(f)= ff2seq(f,"");

;; mkr(f) = { <a,f[a]> | a <- dom(f) };

;; mkf(r) = [ p1(t) -> p2(t) | t <- r ];

;; rinv(r) = { <p2(p),p1(p)> | p <- r };

;; FUNC f822(p:AxB):BxA
;; RETURN <p2(p),p1(p)>;

;; f870 <- uncurry;
;; f87x <- curry;

;; flatten(r) = UNION({ { <p1(p),b> | b <- p2(p) } | p <- r });

;; rcircle(r,s) = { <p1(p),p2(q)> | p <- r, q <- s: p2(p)==p1(q) };