src/ZF/ex/contract0.ML

--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/ZF/ex/contract0.ML	Thu Sep 16 12:20:38 1993 +0200
@@ -0,0 +1,117 @@
+(*  Title: 	ZF/ex/contract.ML
+    ID:         $Id$
+    Author: 	Tobias Nipkow & Lawrence C Paulson
+    Copyright   1992  University of Cambridge
+
+For ex/contract.thy.
+*)
+
+open Contract0;
+
+structure Contract = Inductive_Fun
+ (val thy = Contract0.thy;
+  val rec_doms = [("contract","comb*comb")];
+  val sintrs = 
+      ["[| p:comb;  q:comb |] ==> K#p#q -1-> p",
+       "[| p:comb;  q:comb;  r:comb |] ==> S#p#q#r -1-> (p#r)#(q#r)",
+       "[| p-1->q;  r:comb |] ==> p#r -1-> q#r",
+       "[| p-1->q;  r:comb |] ==> r#p -1-> r#q"];
+  val monos = [];
+  val con_defs = [];
+  val type_intrs = Comb.intrs@[SigmaI];
+  val type_elims = [SigmaE2]);
+
+val [K_contract,S_contract,Ap_contract1,Ap_contract2] = Contract.intrs;
+
+val contract_induct = standard
+    (Contract.mutual_induct RS spec RS spec RSN (2,rev_mp));
+
+(*For type checking: replaces a-1->b by a,b:comb *)
+val contract_combE2 = Contract.dom_subset RS subsetD RS SigmaE2;
+val contract_combD1 = Contract.dom_subset RS subsetD RS SigmaD1;
+val contract_combD2 = Contract.dom_subset RS subsetD RS SigmaD2;
+
+goal Contract.thy "field(contract) = comb";
+by (fast_tac (ZF_cs addIs [equalityI,K_contract] addSEs [contract_combE2]) 1);
+val field_contract_eq = result();
+
+val reduction_refl = standard
+    (field_contract_eq RS equalityD2 RS subsetD RS rtrancl_refl);
+
+val rtrancl_into_rtrancl2 = standard
+    (r_into_rtrancl RS (trans_rtrancl RS transD));
+
+val reduction_rls = [reduction_refl, K_contract, S_contract, 
+		     K_contract RS rtrancl_into_rtrancl2,
+		     S_contract RS rtrancl_into_rtrancl2,
+		     Ap_contract1 RS rtrancl_into_rtrancl2,
+		     Ap_contract2 RS rtrancl_into_rtrancl2];
+
+goalw Contract.thy [I_def] "!!p. p:comb ==> I#p ---> p";
+by (REPEAT (ares_tac (Comb.intrs @ reduction_rls) 1));
+val I_reduce = result();
+
+goalw Contract.thy [I_def] "I: comb";
+by (REPEAT (ares_tac Comb.intrs 1));
+val I_comb = result();
+
+(** Non-contraction results **)
+
+(*Derive a case for each combinator constructor*)
+val K_contract_case = Contract.mk_cases Comb.con_defs "K -1-> r";
+val S_contract_case = Contract.mk_cases Comb.con_defs "S -1-> r";
+val Ap_contract_case = Contract.mk_cases Comb.con_defs "p#q -1-> r";
+
+val contract_cs =
+    ZF_cs addSIs Comb.intrs
+	  addIs  Contract.intrs
+	  addSEs [contract_combD1,contract_combD2]     (*type checking*)
+	  addSEs [K_contract_case, S_contract_case, Ap_contract_case]
+	  addSEs Comb.free_SEs;
+
+goalw Contract.thy [I_def] "!!r. I -1-> r ==> P";
+by (fast_tac contract_cs 1);
+val I_contract_case = result();
+
+goal Contract.thy "!!p r. K#p -1-> r ==> (EX q. r = K#q & p -1-> q)";
+by (fast_tac contract_cs 1);
+val K1_contractD = result();
+
+goal Contract.thy "!!p r. [| p ---> q;  r: comb |] ==> p#r ---> q#r";
+by (forward_tac [rtrancl_type RS subsetD RS SigmaD1] 1);
+by (dtac (field_contract_eq RS equalityD1 RS subsetD) 1);
+by (etac rtrancl_induct 1);
+by (fast_tac (contract_cs addIs reduction_rls) 1);
+by (etac (trans_rtrancl RS transD) 1);
+by (fast_tac (contract_cs addIs reduction_rls) 1);
+val Ap_reduce1 = result();
+
+goal Contract.thy "!!p r. [| p ---> q;  r: comb |] ==> r#p ---> r#q";
+by (forward_tac [rtrancl_type RS subsetD RS SigmaD1] 1);
+by (dtac (field_contract_eq RS equalityD1 RS subsetD) 1);
+by (etac rtrancl_induct 1);
+by (fast_tac (contract_cs addIs reduction_rls) 1);
+by (etac (trans_rtrancl RS transD) 1);
+by (fast_tac (contract_cs addIs reduction_rls) 1);
+val Ap_reduce2 = result();
+
+(** Counterexample to the diamond property for -1-> **)
+
+goal Contract.thy "K#I#(I#I) -1-> I";
+by (REPEAT (ares_tac [K_contract, I_comb, Ap_comb] 1));
+val KIII_contract1 = result();
+
+goalw Contract.thy [I_def] "K#I#(I#I) -1-> K#I#((K#I)#(K#I))";
+by (DEPTH_SOLVE (resolve_tac (Comb.intrs @ Contract.intrs) 1));
+val KIII_contract2 = result();
+
+goal Contract.thy "K#I#((K#I)#(K#I)) -1-> I";
+by (REPEAT (ares_tac (Comb.intrs @ [K_contract, I_comb]) 1));
+val KIII_contract3 = result();
+
+goalw Contract.thy [diamond_def] "~ diamond(contract)";
+by (fast_tac (ZF_cs addIs [KIII_contract1,KIII_contract2,KIII_contract3]
+                    addSEs [I_contract_case]) 1);
+val not_diamond_contract = result();
+
+writeln"Reached end of file.";