--- a/src/CCL/genrec.ML Mon Jul 17 18:42:38 2006 +0200
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,165 +0,0 @@
-(* Title: CCL/genrec.ML
- ID: $Id$
- Author: Martin Coen, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-*)
-
-(*** General Recursive Functions ***)
-
-val major::prems = goal (the_context ())
- "[| a : A; \
-\ !!p g.[| p:A; ALL x:{x: A. <x,p>:wf(R)}. g(x) : D(x) |] ==>\
-\ h(p,g) : D(p) |] ==> \
-\ letrec g x be h(x,g) in g(a) : D(a)";
-by (rtac (major RS rev_mp) 1);
-by (rtac (wf_wf RS wfd_induct) 1);
-by (stac letrecB 1);
-by (rtac impI 1);
-by (eresolve_tac prems 1);
-by (rtac ballI 1);
-by (etac (spec RS mp RS mp) 1);
-by (REPEAT (eresolve_tac [SubtypeD1,SubtypeD2] 1));
-qed "letrecT";
-
-goalw (the_context ()) [SPLIT_def] "SPLIT(<a,b>,B) = B(a,b)";
-by (rtac set_ext 1);
-by (fast_tac ccl_cs 1);
-qed "SPLITB";
-
-val prems = goalw (the_context ()) [letrec2_def]
- "[| a : A; b : B; \
-\ !!p q g.[| p:A; q:B; \
-\ ALL x:A. ALL y:{y: B. <<x,y>,<p,q>>:wf(R)}. g(x,y) : D(x,y) |] ==>\
-\ h(p,q,g) : D(p,q) |] ==> \
-\ letrec g x y be h(x,y,g) in g(a,b) : D(a,b)";
-by (rtac (SPLITB RS subst) 1);
-by (REPEAT (ares_tac ([letrecT,pairT,splitT]@prems) 1));
-by (stac SPLITB 1);
-by (REPEAT (ares_tac ([ballI,SubtypeI]@prems) 1));
-by (rtac (SPLITB RS subst) 1);
-by (REPEAT (ares_tac ([letrecT,SubtypeI,pairT,splitT]@prems) 1 ORELSE
- eresolve_tac [bspec,SubtypeE,sym RS subst] 1));
-qed "letrec2T";
-
-goal (the_context ()) "SPLIT(<a,<b,c>>,%x xs. SPLIT(xs,%y z. B(x,y,z))) = B(a,b,c)";
-by (simp_tac (ccl_ss addsimps [SPLITB]) 1);
-qed "lemma";
-
-val prems = goalw (the_context ()) [letrec3_def]
- "[| a : A; b : B; c : C; \
-\ !!p q r g.[| p:A; q:B; r:C; \
-\ ALL x:A. ALL y:B. ALL z:{z:C. <<x,<y,z>>,<p,<q,r>>> : wf(R)}. \
-\ g(x,y,z) : D(x,y,z) |] ==>\
-\ h(p,q,r,g) : D(p,q,r) |] ==> \
-\ letrec g x y z be h(x,y,z,g) in g(a,b,c) : D(a,b,c)";
-by (rtac (lemma RS subst) 1);
-by (REPEAT (ares_tac ([letrecT,pairT,splitT]@prems) 1));
-by (simp_tac (ccl_ss addsimps [SPLITB]) 1);
-by (REPEAT (ares_tac ([ballI,SubtypeI]@prems) 1));
-by (rtac (lemma RS subst) 1);
-by (REPEAT (ares_tac ([letrecT,SubtypeI,pairT,splitT]@prems) 1 ORELSE
- eresolve_tac [bspec,SubtypeE,sym RS subst] 1));
-qed "letrec3T";
-
-val letrecTs = [letrecT,letrec2T,letrec3T];
-
-
-(*** Type Checking for Recursive Calls ***)
-
-val major::prems = goal (the_context ())
- "[| ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x); \
-\ g(a) : D(a) ==> g(a) : E; a:A; <a,p>:wf(R) |] ==> \
-\ g(a) : E";
-by (REPEAT (ares_tac ([SubtypeI,major RS bspec,major]@prems) 1));
-qed "rcallT";
-
-val major::prems = goal (the_context ())
- "[| ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); \
-\ g(a,b) : D(a,b) ==> g(a,b) : E; a:A; b:B; <<a,b>,<p,q>>:wf(R) |] ==> \
-\ g(a,b) : E";
-by (REPEAT (ares_tac ([SubtypeI,major RS bspec RS bspec,major]@prems) 1));
-qed "rcall2T";
-
-val major::prems = goal (the_context ())
- "[| ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}. g(x,y,z):D(x,y,z); \
-\ g(a,b,c) : D(a,b,c) ==> g(a,b,c) : E; \
-\ a:A; b:B; c:C; <<a,<b,c>>,<p,<q,r>>> : wf(R) |] ==> \
-\ g(a,b,c) : E";
-by (REPEAT (ares_tac ([SubtypeI,major RS bspec RS bspec RS bspec,major]@prems) 1));
-qed "rcall3T";
-
-val rcallTs = [rcallT,rcall2T,rcall3T];
-
-(*** Instantiating an induction hypothesis with an equality assumption ***)
-
-val prems = goal (the_context ())
- "[| g(a) = b; ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x); \
-\ [| ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x); b=g(a); g(a) : D(a) |] ==> P; \
-\ ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) ==> a:A; \
-\ ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x) ==> <a,p>:wf(R) |] ==> \
-\ P";
-by (resolve_tac (prems RL prems) 1);
-by (resolve_tac (prems RL [sym]) 1);
-by (rtac rcallT 1);
-by (REPEAT (ares_tac prems 1));
-val hyprcallT = result();
-
-val prems = goal (the_context ())
- "[| g(a) = b; ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x);\
-\ [| b=g(a); g(a) : D(a) |] ==> P; a:A; <a,p>:wf(R) |] ==> \
-\ P";
-by (resolve_tac (prems) 1);
-by (resolve_tac (prems RL [sym]) 1);
-by (rtac rcallT 1);
-by (REPEAT (ares_tac prems 1));
-qed "hyprcallT";
-
-val prems = goal (the_context ())
- "[| g(a,b) = c; ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); \
-\ [| c=g(a,b); g(a,b) : D(a,b) |] ==> P; \
-\ a:A; b:B; <<a,b>,<p,q>>:wf(R) |] ==> \
-\ P";
-by (resolve_tac (prems) 1);
-by (resolve_tac (prems RL [sym]) 1);
-by (rtac rcall2T 1);
-by (REPEAT (ares_tac prems 1));
-qed "hyprcall2T";
-
-val prems = goal (the_context ())
- "[| g(a,b,c) = d; \
-\ ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); \
-\ [| d=g(a,b,c); g(a,b,c) : D(a,b,c) |] ==> P; \
-\ a:A; b:B; c:C; <<a,<b,c>>,<p,<q,r>>> : wf(R) |] ==> \
-\ P";
-by (resolve_tac (prems) 1);
-by (resolve_tac (prems RL [sym]) 1);
-by (rtac rcall3T 1);
-by (REPEAT (ares_tac prems 1));
-qed "hyprcall3T";
-
-val hyprcallTs = [hyprcallT,hyprcall2T,hyprcall3T];
-
-(*** Rules to Remove Induction Hypotheses after Type Checking ***)
-
-val prems = goal (the_context ())
- "[| ALL x:{x:A.<x,p>:wf(R)}.g(x):D(x); P |] ==> \
-\ P";
-by (REPEAT (ares_tac prems 1));
-qed "rmIH1";
-
-val prems = goal (the_context ())
- "[| ALL x:A. ALL y:{y:B.<<x,y>,<p,q>>:wf(R)}.g(x,y):D(x,y); P |] ==> \
-\ P";
-by (REPEAT (ares_tac prems 1));
-qed "rmIH2";
-
-val prems = goal (the_context ())
- "[| ALL x:A. ALL y:B. ALL z:{z:C.<<x,<y,z>>,<p,<q,r>>>:wf(R)}.g(x,y,z):D(x,y,z); \
-\ P |] ==> \
-\ P";
-by (REPEAT (ares_tac prems 1));
-qed "rmIH3";
-
-val rmIHs = [rmIH1,rmIH2,rmIH3];
-