--- a/src/CCL/ex/Nat.ML Mon Jul 17 18:42:38 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,68 +0,0 @@
-(* Title: CCL/ex/Nat.ML
- ID: $Id$
- Author: Martin Coen, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-*)
-
-val nat_defs = [not_def,add_def,mult_def,sub_def,le_def,lt_def,ack_def,napply_def];
-
-val natBs = map (fn s=>prove_goalw (the_context ()) nat_defs s (fn _ => [simp_tac term_ss 1]))
- ["not(true) = false",
- "not(false) = true",
- "zero #+ n = n",
- "succ(n) #+ m = succ(n #+ m)",
- "zero #* n = zero",
- "succ(n) #* m = m #+ (n #* m)",
- "f^zero`a = a",
- "f^succ(n)`a = f(f^n`a)"];
-
-val nat_ss = term_ss addsimps natBs;
-
-(*** Lemma for napply ***)
-
-val [prem] = goal (the_context ()) "n:Nat ==> f^n`f(a) = f^succ(n)`a";
-by (rtac (prem RS Nat_ind) 1);
-by (ALLGOALS (asm_simp_tac nat_ss));
-qed "napply_f";
-
-(****)
-
-val prems = goalw (the_context ()) [add_def] "[| a:Nat; b:Nat |] ==> a #+ b : Nat";
-by (typechk_tac prems 1);
-qed "addT";
-
-val prems = goalw (the_context ()) [mult_def] "[| a:Nat; b:Nat |] ==> a #* b : Nat";
-by (typechk_tac (addT::prems) 1);
-qed "multT";
-
-(* Defined to return zero if a<b *)
-val prems = goalw (the_context ()) [sub_def] "[| a:Nat; b:Nat |] ==> a #- b : Nat";
-by (typechk_tac (prems) 1);
-by clean_ccs_tac;
-by (etac (NatPRI RS wfstI RS (NatPR_wf RS wmap_wf RS wfI)) 1);
-qed "subT";
-
-val prems = goalw (the_context ()) [le_def] "[| a:Nat; b:Nat |] ==> a #<= b : Bool";
-by (typechk_tac (prems) 1);
-by clean_ccs_tac;
-by (etac (NatPRI RS wfstI RS (NatPR_wf RS wmap_wf RS wfI)) 1);
-qed "leT";
-
-val prems = goalw (the_context ()) [not_def,lt_def] "[| a:Nat; b:Nat |] ==> a #< b : Bool";
-by (typechk_tac (prems@[leT]) 1);
-qed "ltT";
-
-(* Correctness conditions for subtractive division **)
-
-val prems = goalw (the_context ()) [div_def]
- "[| a:Nat; b:{x:Nat.~x=zero} |] ==> a ## b : {x:Nat. DIV(a,b,x)}";
-by (gen_ccs_tac (prems@[ltT,subT]) 1);
-
-(* Termination Conditions for Ackermann's Function *)
-
-val prems = goalw (the_context ()) [ack_def]
- "[| a:Nat; b:Nat |] ==> ackermann(a,b) : Nat";
-by (gen_ccs_tac prems 1);
-val relI = NatPR_wf RS (NatPR_wf RS lex_wf RS wfI);
-by (REPEAT (eresolve_tac [NatPRI RS (lexI1 RS relI),NatPRI RS (lexI2 RS relI)] 1));
-result();