A:Realizer, ds:x:Id fp Type, i, x:Id, T, T':Type, k:Knd,
f:((State(x : T  ds)T'T) + (State(x : T  ds)T'T)).
R-Feasible(A)
 ((x  dom(R-state(A;i))))
 ds || R-state(A;i)
 ((isrcv(k))  (R-da(A;source(lnk(k)))(k)?Void r T'))
 ((k  dom(R-da(A;i)))  (T' = Valtype(R-da(A;i);k)))
 ((write-restricted(A;i;k)))
 (y:Id. (y  dom(x : T  ds))  ((read-restricted(A; i; y))))
 Reffect(i;x : T  ds;k;T';x;f) || A 

latex

Definitions

read-restricted(R; i; y), write-restricted(R;i;k), T, f(x)?z, Valtype(da;k), P  Q, A, Rinit-v(x1), Reffect-f(x1), Rinit-discrete(A), Rinit-x(x1), Rinit?(x1), Reffect-discrete(A), SQType(T), P  Q, P  Q, Rsends-T(x1), Reffect-T(x1), Rsends-dt(x1), let x = a in b(x), Rpre-a(x1), Rpre-ds(x1), Rpre?(x1), Rsends-ds(x1), Rbframe-L(x1), Rbframe-k(x1), Rbframe?(x1), Rsframe-L(x1), Rsends-knd(x1), Rsends-g(x1), Rsframe-tag(x1), Rsends-l(x1), Rsframe-lnk(x1), Rsframe?(x1), Rsends?(x1), Rrframe-L(x1), Reffect-ds(x1), Rrframe-x(x1), Rrframe?(x1), Raframe-L(x1), Raframe-k(x1), Raframe?(x1), Rframe-L(x1), Reffect-knd(x1), Reffect-x(x1), Rframe-x(x1), Rframe?(x1), Reffect?(x1), tt, t.2, (i = j), p  q, R-interface-compat(A;B), R-discrete_compat(A;B), R-frame-compat(A;B), R-base-domain(R), p = q, Rda(R), Rds(R), R-loc(R), Rnone?(x1), Rplus-right(x1), Rplus-left(x1), P & Q, Rplus?(x1), True, Y, ff, p q, t.1, if b then t else f fi , suptype(S; T), S  T, Top, t  T, x. t(x), {T}, DeclaredType(ds;x), , A || B, P  Q, x:A. B(x), f || g, R-Feasible(R), Unit, False, reduce(f;k;as), deq-member(eq;x;L), , , x(s), R-da(R;i), R-state(R;i), x  dom(f), b,

Lemmas

and functionality wrt iff, assert of band, band wf, lnk-decl-cap, lnk-decl-dom, isrcv-implies, or functionality wrt iff, bool cases, bool sq, deq wf, true wf, squash wf, R-Feasible-effect, Knd sq, R-compat-da, fpf-sub-join-right, fpf-sub-join-left, subtype-fpf-cap-void, subtype rel transitivity, fpf-join-dom, fpf-compatible-join-iff, R-compat-state, assert of bor, bor wf, all functionality wrt iff, R-compat-Rplus2, fpf-cap-single1, fpf-join-cap-sq, Rrframe wf, Rbframe wf, Raframe wf, finite-prob-space wf, Rpre wf, p-outcome wf, locl wf, Rsends wf, IdLnk sq, eq lnk wf, tagof wf, assert-eq-lnk, lnk-decl-compatible-single, fpf-compatible-symmetry, lnk-decl wf, fpf-compatible-join, assert-eq-knd, eq knd wf, fpf-compatible-single2, implies functionality wrt iff, IdLnk wf, Rsframe wf, Rframe wf, Rinit wf, assert of bnot, eqff to assert, bnot wf, fpf-empty-compatible-right, fpf-compatible-singles, fpf-compatible-join2, fpf-single-dom, not functionality wrt iff, eq id self, Id sq, assert-eq-id, eqtt to assert, iff transitivity, bool wf, eq id wf, Rnone wf, es realizer wf, decl-type wf, fpf-cap-single-join, Reffect wf, R-compat wf, read-restricted wf, fpf-single wf, write-restricted wf, ma-valtype wf, Kind-deq wf, lnk wf, lsrc wf, R-da wf, fpf-cap wf, subtype rel wf, isrcv wf, fpf-compatible wf, top wf, fpf-trivial-subtype-top, R-state wf, fpf-dom wf, assert wf, not wf, R-Feasible wf, rationals wf, id-deq wf, fpf-single wf3, fpf-join wf, decl-state wf, Knd wf, Id wf, fpf wf, es realizer-induction