--- a/src/HOL/While.ML Wed Oct 18 23:31:16 2000 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,92 +0,0 @@
-(* Title: HOL/While
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 2000 TU Muenchen
-*)
-
-goalw_cterm [] (cterm_of (sign_of thy)
- (HOLogic.mk_Trueprop (hd while_aux.tcs)));
-br wf_same_fstI 1;
-br wf_same_fstI 1;
-by (asm_full_simp_tac (simpset() addsimps [wf_iff_no_infinite_down_chain]) 1);
-by(Blast_tac 1);
-val while_aux_tc = result();
-
-Goal
- "while_aux(b,c,s) = (if ? f. f 0 = s & (!i. b(f i) & c(f i) = f(i+1)) \
-\ then arbitrary \
-\ else (if b s then while_aux(b,c,c s) else s))";
-by(rtac (while_aux_tc RS (hd while_aux.simps) RS trans) 1);
- by(simp_tac (simpset() addsimps [same_fst_def]) 1);
-br refl 1;
-qed "while_aux_unfold";
-
-(*** The recursion equation for while: directly executable! ***)
-
-Goalw [while_def] "while b c s = (if b s then while b c (c s) else s)";
-by(rtac (while_aux_unfold RS trans) 1);
-by (Auto_tac);
-by(stac while_aux_unfold 1);
-by(Asm_full_simp_tac 1);
-by(Clarify_tac 1);
-by(eres_inst_tac [("x","%i. f(Suc i)")] allE 1);
-by(Blast_tac 1);
-qed "while_unfold";
-
-(*** The proof rule for while; P is the invariant ***)
-
-val [prem1,prem2,prem3] = Goal
-"[| !!s. [| P s; b s |] ==> P(c s); \
-\ !!s. [| P s; ~b s |] ==> Q s; \
-\ wf{(t,s). P s & b s & t = c s} |] \
-\ ==> P s --> Q(while b c s)";
-by(induct_thm_tac (prem3 RS wf_induct) "s" 1);
-by(Asm_full_simp_tac 1);
-by(Clarify_tac 1);
-by(stac while_unfold 1);
-by(asm_full_simp_tac (simpset() addsimps [prem1,prem2]) 1);
-qed_spec_mp "while_rule";
-
-(*** An application: computation of the lfp on finite sets via iteration ***)
-
-Goal
- "[| mono f; finite U; f U = U |] \
-\ ==> lfp f = fst(while (%(A,fA). A~=fA) (%(A,fA). (fA, f fA)) ({},f{}))";
-by(res_inst_tac [("P","%(A,B).(A <= U & B = f A & A <= B & B <= lfp f)")]
- while_rule 1);
- by(stac lfp_unfold 1);
- ba 1;
- by(Clarsimp_tac 1);
- by(blast_tac (claset() addDs [monoD]) 1);
- by(fast_tac (claset() addSIs [lfp_lowerbound] addss simpset()) 1);
- by(res_inst_tac [("r","((Pow U <*> UNIV) <*> (Pow U <*> UNIV)) Int \
- \ inv_image finite_psubset (op - U o fst)")]
- wf_subset 1);
- by(blast_tac (claset() addIs
- [wf_finite_psubset,Int_lower2 RSN (2,wf_subset)]) 1);
- by(clarsimp_tac (claset(),simpset() addsimps
- [inv_image_def,finite_psubset_def,order_less_le]) 1);
- by(blast_tac (claset() addSIs [finite_Diff] addDs [monoD]) 1);
-by(stac lfp_unfold 1);
- ba 1;
-by(asm_simp_tac (simpset() addsimps [monoD]) 1);
-qed "lfp_conv_while";
-
-(*** An example; requires integers
-
-Goal "{f n|n. A n | B n} = {f n|n. A n} Un {f n|n. B n}";
-by(Blast_tac 1);
-qed "lemma";
-
-Goal "P(lfp (%N::int set. {#0} Un {(n + #2) mod #6 |n. n:N})) = P{#0,#4,#2}";
-by(stac (read_instantiate [("U","{#0,#1,#2,#3,#4,#5}")] lfp_conv_while) 1);
- br monoI 1;
- by(Blast_tac 1);
- by(Simp_tac 1);
- by(simp_tac (simpset() addsimps [lemma,set_eq_subset]) 1);
-(* The fixpoint computation is performed purely by rewriting: *)
-by(simp_tac (simpset() addsimps [while_unfold,lemma,set_eq_subset]
- delsimps [subset_empty]) 1);
-result();
-
-***)
--- a/src/HOL/While.thy Wed Oct 18 23:31:16 2000 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,28 +0,0 @@
-(* Title: HOL/While
- ID: $Id$
- Author: Tobias Nipkow
- Copyright 2000 TU Muenchen
-
-Defines a while-combinator "while" and proves
-a) an unrestricted unfolding law (even if while diverges!)
- (I got this idea from Wolfgang Goerigk)
-b) the invariant rule for reasoning about while
-*)
-
-While = Recdef +
-
-consts while_aux :: "('a => bool) * ('a => 'a) * 'a => 'a"
-recdef while_aux
- "same_fst (%b. True) (%b. same_fst (%c. True) (%c.
- {(t,s). b s & c s = t &
- ~(? f. f 0 = s & (!i. b(f i) & c(f i) = f(i+1)))}))"
-"while_aux(b,c,s) =
- (if (? f. f 0 = s & (!i. b(f i) & c(f i) = f(i+1)))
- then arbitrary
- else if b s then while_aux(b,c,c s) else s)"
-
-constdefs
- while :: "('a => bool) => ('a => 'a) => 'a => 'a"
-"while b c s == while_aux(b,c,s)"
-
-end