replaced ex.ML by ex/ROOT.ML, ex/ex.ML;

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Cube/ex/ROOT.ML	Thu Mar 20 10:47:29 1997 +0100
@@ -0,0 +1,10 @@
+
+writeln"Root file for Cube examples";
+Cube_build_completed;    (*Cause examples to fail if Cube did*)
+
+proof_timing := true;
+
+use"ex.ML";
+
+cd "..";
+maketest"END: file for Lambda-Cube examples";

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/Cube/ex/ex.ML	Thu Mar 20 10:47:29 1997 +0100
@@ -0,0 +1,234 @@
+(* Examples taken from
+        H. Barendregt. Introduction to Generalised Type Systems.
+        J. Functional Programming.
+*)
+
+fun strip_asms_tac thms  i =
+    REPEAT(resolve_tac[strip_b,strip_s]i THEN DEPTH_SOLVE_1(ares_tac thms i));
+
+val imp_elim = prove_goal thy "[| f:A->B; a:A; f^a:B ==> PROP P |] ==> PROP P"
+        (fn asms => [REPEAT(resolve_tac (app::asms) 1)]);
+
+val pi_elim = prove_goal thy
+        "[| F:Prod(A,B); a:A; F^a:B(a) ==> PROP P |] ==> PROP P"
+        (fn asms => [REPEAT(resolve_tac (app::asms) 1)]);
+
+(* SIMPLE TYPES *)
+
+goal thy "A:* |- A->A : ?T";
+by (DEPTH_SOLVE (ares_tac simple 1));
+uresult();
+
+goal thy "A:* |- Lam a:A.a : ?T";
+by (DEPTH_SOLVE (ares_tac simple 1));
+uresult();
+
+goal thy "A:* B:* b:B |- Lam x:A.b : ?T";
+by (DEPTH_SOLVE (ares_tac simple 1));
+uresult();
+
+goal thy "A:* b:A |- (Lam a:A.a)^b: ?T";
+by (DEPTH_SOLVE (ares_tac simple 1));
+uresult();
+
+goal thy "A:* B:* c:A b:B |- (Lam x:A.b)^ c: ?T";
+by (DEPTH_SOLVE (ares_tac simple 1));
+uresult();
+
+goal thy "A:* B:* |- Lam a:A.Lam b:B.a : ?T";
+by (DEPTH_SOLVE (ares_tac simple 1));
+uresult();
+
+(* SECOND-ORDER TYPES *)
+
+goal L2_thy "|- Lam A:*. Lam a:A.a : ?T";
+by (DEPTH_SOLVE (ares_tac L2 1));
+uresult();
+
+goal L2_thy "A:* |- (Lam B:*.Lam b:B.b)^A : ?T";
+by (DEPTH_SOLVE (ares_tac L2 1));
+uresult();
+
+goal L2_thy "A:* b:A |- (Lam B:*.Lam b:B.b) ^ A ^ b: ?T";
+by (DEPTH_SOLVE (ares_tac L2 1));
+uresult();
+
+goal L2_thy "|- Lam B:*.Lam a:(Pi A:*.A).a ^ ((Pi A:*.A)->B) ^ a: ?T";
+by (DEPTH_SOLVE (ares_tac L2 1));
+uresult();
+
+(* Weakly higher-order proposiional logic *)
+
+goal Lomega_thy "|- Lam A:*.A->A : ?T";
+by (DEPTH_SOLVE (ares_tac Lomega 1));
+uresult();
+
+goal Lomega_thy "B:* |- (Lam A:*.A->A) ^ B : ?T";
+by (DEPTH_SOLVE (ares_tac Lomega 1));
+uresult();
+
+goal Lomega_thy "B:* b:B |- (Lam y:B.b): ?T";
+by (DEPTH_SOLVE (ares_tac Lomega 1));
+uresult();
+
+goal Lomega_thy "A:* F:*->* |- F^(F^A): ?T";
+by (DEPTH_SOLVE (ares_tac Lomega 1));
+uresult();
+
+goal Lomega_thy "A:* |- Lam F:*->*.F^(F^A): ?T";
+by (DEPTH_SOLVE (ares_tac Lomega 1));
+uresult();
+
+(* LF *)
+
+goal LP_thy "A:* |- A -> * : ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->* a:A |- P^a: ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->A->* a:A |- Pi a:A.P^a^a: ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->* Q:A->* |- Pi a:A.P^a -> Q^a: ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->* |- Pi a:A.P^a -> P^a: ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->* |- Lam a:A.Lam x:P^a.x: ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->* Q:* |- (Pi a:A.P^a->Q) -> (Pi a:A.P^a) -> Q : ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+goal LP_thy "A:* P:A->* Q:* a0:A |- \
+\       Lam x:Pi a:A.P^a->Q. Lam y:Pi a:A.P^a. x^a0^(y^a0): ?T";
+by (DEPTH_SOLVE (ares_tac LP 1));
+uresult();
+
+(* OMEGA-ORDER TYPES *)
+
+goal L2_thy "A:* B:* |- Pi C:*.(A->B->C)->C : ?T";
+by (DEPTH_SOLVE (ares_tac L2 1));
+uresult();
+
+goal LOmega_thy "|- Lam A:*.Lam B:*.Pi C:*.(A->B->C)->C : ?T";
+by (DEPTH_SOLVE (ares_tac LOmega 1));
+uresult();
+
+goal LOmega_thy "|- Lam A:*.Lam B:*.Lam x:A.Lam y:B.x : ?T";
+by (DEPTH_SOLVE (ares_tac LOmega 1));
+uresult();
+
+goal LOmega_thy "A:* B:* |- ?p : (A->B) -> ((B->Pi P:*.P)->(A->Pi P:*.P))";
+by (strip_asms_tac LOmega 1);
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac LOmega 1));
+by (DEPTH_SOLVE_1(ares_tac LOmega 2));
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac LOmega 1));
+by (DEPTH_SOLVE_1(ares_tac LOmega 2));
+by (rtac lam_ss 1);
+by (assume_tac 1);
+by (DEPTH_SOLVE_1(ares_tac LOmega 2));
+by (etac pi_elim 1);
+by (assume_tac 1);
+by (etac pi_elim 1);
+by (assume_tac 1);
+by (assume_tac 1);
+uresult();
+
+(* Second-order Predicate Logic *)
+
+goal LP2_thy "A:* P:A->* |- Lam a:A.P^a->(Pi A:*.A) : ?T";
+by (DEPTH_SOLVE (ares_tac LP2 1));
+uresult();
+
+goal LP2_thy "A:* P:A->A->* |- \
+\       (Pi a:A.Pi b:A.P^a^b->P^b^a->Pi P:*.P) -> Pi a:A.P^a^a->Pi P:*.P : ?T";
+by (DEPTH_SOLVE (ares_tac LP2 1));
+uresult();
+
+(* Antisymmetry implies irreflexivity: *)
+goal LP2_thy "A:* P:A->A->* |- \
+\       ?p: (Pi a:A.Pi b:A.P^a^b->P^b^a->Pi P:*.P) -> Pi a:A.P^a^a->Pi P:*.P";
+by (strip_asms_tac LP2 1);
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 1));
+by (DEPTH_SOLVE_1(ares_tac LP2 2));
+by (rtac lam_ss 1);
+by (assume_tac 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 2));
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 1));
+by (DEPTH_SOLVE_1(ares_tac LP2 2));
+by (REPEAT(EVERY[etac pi_elim 1, assume_tac 1, TRY(assume_tac 1)]));
+uresult();
+
+(* LPomega *)
+
+goal LPomega_thy "A:* |- Lam P:A->A->*.Lam a:A.P^a^a : ?T";
+by (DEPTH_SOLVE (ares_tac LPomega 1));
+uresult();
+
+goal LPomega_thy "|- Lam A:*.Lam P:A->A->*.Lam a:A.P^a^a : ?T";
+by (DEPTH_SOLVE (ares_tac LPomega 1));
+uresult();
+
+(* CONSTRUCTIONS *)
+
+goal CC_thy "|- Lam A:*.Lam P:A->*.Lam a:A.P^a->Pi P:*.P: ?T";
+by (DEPTH_SOLVE (ares_tac CC 1));
+uresult();
+
+goal CC_thy "|- Lam A:*.Lam P:A->*.Pi a:A.P^a: ?T";
+by (DEPTH_SOLVE (ares_tac CC 1));
+uresult();
+
+goal CC_thy "A:* P:A->* a:A |- ?p : (Pi a:A.P^a)->P^a";
+by (strip_asms_tac CC 1);
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac CC 1));
+by (DEPTH_SOLVE_1(ares_tac CC 2));
+by (EVERY[etac pi_elim 1, assume_tac 1, assume_tac 1]);
+uresult();
+
+(* Some random examples *)
+
+goal LP2_thy "A:* c:A f:A->A |- \
+\       Lam a:A. Pi P:A->*.P^c -> (Pi x:A. P^x->P^(f^x)) -> P^a : ?T";
+by (DEPTH_SOLVE(ares_tac LP2 1));
+uresult();
+
+goal CC_thy "Lam A:*.Lam c:A.Lam f:A->A. \
+\       Lam a:A. Pi P:A->*.P^c -> (Pi x:A. P^x->P^(f^x)) -> P^a : ?T";
+by (DEPTH_SOLVE(ares_tac CC 1));
+uresult();
+
+(* Symmetry of Leibnitz equality *)
+goal LP2_thy "A:* a:A b:A |- ?p: (Pi P:A->*.P^a->P^b) -> (Pi P:A->*.P^b->P^a)";
+by (strip_asms_tac LP2 1);
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 1));
+by (DEPTH_SOLVE_1(ares_tac LP2 2));
+by (eres_inst_tac [("a","Lam x:A.Pi Q:A->*.Q^x->Q^a")] pi_elim 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 1));
+by (rewtac beta);
+by (etac imp_elim 1);
+by (rtac lam_bs 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 1));
+by (DEPTH_SOLVE_1(ares_tac LP2 2));
+by (rtac lam_ss 1);
+by (DEPTH_SOLVE_1(ares_tac LP2 1));
+by (DEPTH_SOLVE_1(ares_tac LP2 2));
+by (assume_tac 1);
+by (assume_tac 1);
+uresult();