diff -r 3a8d722fd3ff -r 16c4ea954511 Subst/Unifier.ML --- a/Subst/Unifier.ML Fri Nov 11 10:35:03 1994 +0100 +++ b/Subst/Unifier.ML Mon Nov 21 17:50:34 1994 +0100 @@ -16,29 +16,29 @@ goalw Unifier.thy [Unifier_def] "Unifier(s,t,u) = (t <| s = u <| s)"; by (rtac refl 1); -val Unifier_iff = result(); +qed "Unifier_iff"; goal Unifier.thy "Unifier(s,Comb(t,u),Comb(v,w)) --> Unifier(s,t,v) & Unifier(s,u,w)"; by (simp_tac (subst_ss addsimps [Unifier_iff]) 1); -val Unifier_Comb = result() RS mp RS conjE; +val Unifier_Comb = store_thm("Unifier_Comb", result() RS mp RS conjE); goal Unifier.thy "~v : vars_of(t) --> ~v : vars_of(u) -->Unifier(s,t,u) --> \ \ Unifier(#s,t,u)"; by (simp_tac (subst_ss addsimps [Unifier_iff,repl_invariance]) 1); -val Cons_Unifier = result() RS mp RS mp RS mp; +val Cons_Unifier = store_thm("Cons_Unifier", result() RS mp RS mp RS mp); (**** Most General Unifiers ****) goalw Unifier.thy [MoreGeneral_def] "r >> s = (EX q. s =s= r <> q)"; by (rtac refl 1); -val MoreGen_iff = result(); +qed "MoreGen_iff"; goal Unifier.thy "Nil >> s"; by (simp_tac (subst_ss addsimps [MoreGen_iff]) 1); by (fast_tac (set_cs addIs [refl RS subst_refl]) 1); -val MoreGen_Nil = result(); +qed "MoreGen_Nil"; goalw Unifier.thy unify_defs "MGUnifier(s,t,u) = (ALL r.Unifier(r,t,u) = s >> r)"; @@ -46,7 +46,7 @@ eresolve_tac [conjE,allE,mp,exE,ssubst_subst2] 1)); by (asm_simp_tac (subst_ss addsimps [subst_comp]) 1); by (fast_tac (set_cs addIs [comp_Nil RS sym RS subst_refl]) 1); -val MGU_iff = result(); +qed "MGU_iff"; val [prem] = goal Unifier.thy "~ Var(v) <: t ==> MGUnifier(#Nil,Var(v),t)"; @@ -56,52 +56,52 @@ by (etac ssubst_subst2 2); by (rtac (Cons_trivial RS subst_sym) 1); by (simp_tac (subst_ss addsimps [prem RS Var_not_occs,Var_subst]) 1); -val MGUnifier_Var = result(); +qed "MGUnifier_Var"; (**** Most General Idempotent Unifiers ****) goal Unifier.thy "r <> r =s= r --> s =s= r <> q --> r <> s =s= s"; by (simp_tac (subst_ss addsimps [subst_eq_iff,subst_comp]) 1); -val MGIU_iff_lemma = result() RS mp RS mp; +val MGIU_iff_lemma = store_thm("MGIU_iff_lemma", result() RS mp RS mp); goalw Unifier.thy unify_defs "MGIUnifier(s,t,u) = \ \ (Idem(s) & Unifier(s,t,u) & (ALL r.Unifier(r,t,u) --> s<>r=s=r))"; by (fast_tac (set_cs addEs [subst_sym,MGIU_iff_lemma]) 1); -val MGIU_iff = result(); +qed "MGIU_iff"; (**** Idempotence ****) goalw Unifier.thy unify_defs "Idem(s) = (s <> s =s= s)"; by (rtac refl 1); -val raw_Idem_iff = result(); +qed "raw_Idem_iff"; goal Unifier.thy "Idem(s) = (sdom(s) Int srange(s) = {})"; by (simp_tac (subst_ss addsimps [raw_Idem_iff,subst_eq_iff,subst_comp, invariance,dom_range_disjoint])1); -val Idem_iff = result(); +qed "Idem_iff"; goal Unifier.thy "Idem(Nil)"; by (simp_tac (subst_ss addsimps [raw_Idem_iff,refl RS subst_refl]) 1); -val Idem_Nil = result(); +qed "Idem_Nil"; goal Unifier.thy "~ (Var(v) <: t) --> Idem(#Nil)"; by (simp_tac (subst_ss addsimps [Var_subst,vars_iff_occseq,Idem_iff,srange_iff] setloop (split_tac [expand_if])) 1); by (fast_tac set_cs 1); -val Var_Idem = result() RS mp; +val Var_Idem = store_thm("Var_Idem", result() RS mp); val [prem] = goalw Unifier.thy [Idem_def] "Idem(r) ==> Unifier(s,t <| r,u <| r) --> Unifier(r <> s,t <| r,u <| r)"; by (simp_tac (subst_ss addsimps [Unifier_iff,subst_comp,prem RS comp_subst_subst]) 1); -val Unifier_Idem_subst = result() RS mp; +val Unifier_Idem_subst = store_thm("Unifier_Idem_subst", result() RS mp); val [prem] = goal Unifier.thy "r <> s =s= s ==> Unifier(s,t,u) --> Unifier(s,t <| r,u <| r)"; by (simp_tac (subst_ss addsimps [Unifier_iff,subst_comp,prem RS comp_subst_subst]) 1); -val Unifier_comp_subst = result() RS mp; +val Unifier_comp_subst = store_thm("Unifier_comp_subst", result() RS mp); (*** The domain of a MGIU is a subset of the variables in the terms ***) (*** NB this and one for range are only needed for termination ***) @@ -110,7 +110,7 @@ "~ vars_of(Var(x) <| r) = vars_of(Var(x) <| s) ==> ~r =s= s"; by (rtac (prem RS contrapos) 1); by (fast_tac (set_cs addEs [subst_subst2]) 1); -val lemma_lemma = result(); +qed "lemma_lemma"; val prems = goal Unifier.thy "x : sdom(s) --> ~x : srange(s) --> \ @@ -122,7 +122,7 @@ br conjI 1; by (asm_simp_tac (subst_ss addsimps [Var_elim,subst_comp,repl_invariance]) 1); by (asm_simp_tac (subst_ss addsimps [Var_subst]) 1); -val MGIU_sdom_lemma = result() RS mp RS mp RS lemma_lemma RS notE;; +val MGIU_sdom_lemma = store_thm("MGIU_sdom_lemma", result() RS mp RS mp RS lemma_lemma RS notE); goal Unifier.thy "MGIUnifier(s,t,u) --> sdom(s) <= vars_of(t) Un vars_of(u)"; by (subgoal_tac "! P Q.(P | Q) = (~( ~P & ~Q))" 1); @@ -131,13 +131,13 @@ by (eresolve_tac ([spec] RL [impE]) 1); by (rtac Cons_Unifier 1); by (ALLGOALS (fast_tac (set_cs addIs [Cons_Unifier,MGIU_sdom_lemma]))); -val MGIU_sdom = result() RS mp; +val MGIU_sdom = store_thm("MGIU_sdom", result() RS mp); (*** The range of a MGIU is a subset of the variables in the terms ***) val prems = goal HOL.thy "P = Q ==> (~P) = (~Q)"; by (simp_tac (set_ss addsimps prems) 1); -val not_cong = result(); +qed "not_cong"; val prems = goal Unifier.thy "~w=x --> x : vars_of(Var(w) <| s) --> w : sdom(s) --> ~w : srange(s) --> \ @@ -149,7 +149,7 @@ by (ALLGOALS (asm_simp_tac (subst_ss addsimps [Var_elim,subst_comp, vars_var_iff RS not_cong RS iffD2 RS repl_invariance]) )); by (fast_tac (set_cs addIs [Var_in_subst]) 1); -val MGIU_srange_lemma =result() RS mp RS mp RS mp RS mp RS lemma_lemma RS notE; +val MGIU_srange_lemma = store_thm("MGIU_srange_lemma", result() RS mp RS mp RS mp RS mp RS lemma_lemma RS notE); goal Unifier.thy "MGIUnifier(s,t,u) --> srange(s) <= vars_of(t) Un vars_of(u)"; by (subgoal_tac "! P Q.(P | Q) = (~( ~P & ~Q))" 1); @@ -161,7 +161,7 @@ by (imp_excluded_middle_tac "w=ta" 4); by (fast_tac (set_cs addEs [MGIU_srange_lemma]) 5); by (ALLGOALS (fast_tac (set_cs addIs [Var_elim2]))); -val MGIU_srange = result() RS mp; +val MGIU_srange = store_thm("MGIU_srange", result() RS mp); (*************** Correctness of a simple unification algorithm ***************) (* *) @@ -179,41 +179,41 @@ goalw Unifier.thy unify_defs "MGIUnifier(s,t,u) = MGIUnifier(s,u,t)"; by (safe_tac (HOL_cs addSEs ([sym]@([spec] RL [mp])))); -val Unify_comm = result(); +qed "Unify_comm"; goal Unifier.thy "MGIUnifier(Nil,Const(n),Const(n))"; by (simp_tac (subst_ss addsimps [MGIU_iff,MGU_iff,Unifier_iff,subst_eq_iff,Idem_Nil]) 1); -val Unify1 = result(); +qed "Unify1"; goal Unifier.thy "~m=n --> (ALL l.~Unifier(l,Const(m),Const(n)))"; by (simp_tac (subst_ss addsimps[Unifier_iff]) 1); -val Unify2 = result() RS mp; +val Unify2 = store_thm("Unify2", result() RS mp); val [prem] = goalw Unifier.thy [MGIUnifier_def] "~Var(v) <: t ==> MGIUnifier(#Nil,Var(v),t)"; by (fast_tac (HOL_cs addSIs [prem RS MGUnifier_Var,prem RS Var_Idem]) 1); -val Unify3 = result(); +qed "Unify3"; val [prem] = goal Unifier.thy "Var(v) <: t ==> (ALL l.~Unifier(l,Var(v),t))"; by (simp_tac (subst_ss addsimps [Unifier_iff,prem RS subst_mono RS occs_irrefl2]) 1); -val Unify4 = result(); +qed "Unify4"; goal Unifier.thy "ALL l.~Unifier(l,Const(m),Comb(t,u))"; by (simp_tac (subst_ss addsimps [Unifier_iff]) 1); -val Unify5 = result(); +qed "Unify5"; goal Unifier.thy "(ALL l.~Unifier(l,t,v)) --> (ALL l.~Unifier(l,Comb(t,u),Comb(v,w)))"; by (simp_tac (subst_ss addsimps [Unifier_iff]) 1); -val Unify6 = result() RS mp; +val Unify6 = store_thm("Unify6", result() RS mp); goal Unifier.thy "MGIUnifier(s,t,v) --> (ALL l.~Unifier(l,u <| s,w <| s)) --> \ \ (ALL l.~Unifier(l,Comb(t,u),Comb(v,w)))"; by (simp_tac (subst_ss addsimps [MGIU_iff]) 1); by (fast_tac (set_cs addIs [Unifier_comp_subst] addSEs [Unifier_Comb]) 1); -val Unify7 = result() RS mp RS mp; +val Unify7 = store_thm("Unify7", result() RS mp RS mp); val [p1,p2,p3] = goal Unifier.thy "[| Idem(r); Unifier(s,t <| r,u <| r); \ @@ -223,7 +223,7 @@ p2 RS (p1 RS Unifier_Idem_subst RS (p3 RS spec RS mp))] 1); by (REPEAT_SOME (etac rev_mp)); by (simp_tac (subst_ss addsimps [raw_Idem_iff,subst_eq_iff,subst_comp]) 1); -val Unify8_lemma1 = result(); +qed "Unify8_lemma1"; val [p1,p2,p3,p4] = goal Unifier.thy "[| Unifier(q,t,v); Unifier(q,u,w); (! q.Unifier(q,t,v) --> r <> q =s= q); \ @@ -234,7 +234,7 @@ p2 RS (pp RS Unifier_comp_subst) RS (p4 RS spec RS mp)] 1); by (REPEAT_SOME (etac rev_mp)); by (simp_tac (subst_ss addsimps [subst_eq_iff,subst_comp]) 1); -val Unify8_lemma2 = result(); +qed "Unify8_lemma2"; goal Unifier.thy "MGIUnifier(r,t,v) --> MGIUnifier(s,u <| r,w <| r) --> \ \ MGIUnifier(r <> s,Comb(t,u),Comb(v,w))"; @@ -245,7 +245,7 @@ [Unifier_iff,MGIU_iff,subst_comp,comp_assoc]) 2); by (ALLGOALS (fast_tac (set_cs addEs [Unifier_Comb,Unify8_lemma1,Unify8_lemma2]))); -val Unify8 = result(); +qed "Unify8"; (********************** Termination of the algorithm *************************) @@ -257,7 +257,7 @@ goalw Unifier.thy [UWFD_def] "UWFD(t,t',Comb(t,u),Comb(t',u'))"; by (simp_tac subst_ss 1); by (fast_tac set_cs 1); -val UnifyWFD1 = result(); +qed "UnifyWFD1"; val [prem] = goal Unifier.thy "MGIUnifier(s,t,t') ==> vars_of(u <| s) Un vars_of(u' <| s) <= \ @@ -268,7 +268,7 @@ by (ALLGOALS (simp_tac (subst_ss addsimps [Var_intro,subset_iff]))); by (ALLGOALS (fast_tac (set_cs addDs [Var_intro,prem RS MGIU_srange RS subsetD]))); -val UWFD2_lemma1 = result(); +qed "UWFD2_lemma1"; val [major,minor] = goal Unifier.thy "[| MGIUnifier(s,t,t'); ~ u <| s = u |] ==> \ @@ -282,7 +282,7 @@ by (REPEAT (etac rev_mp 1)); by (asm_simp_tac subst_ss 1); by (fast_tac (set_cs addIs [Var_elim2]) 1); -val UWFD2_lemma2 = result(); +qed "UWFD2_lemma2"; val [prem] = goalw Unifier.thy [UWFD_def] "MGIUnifier(s,t,t') ==> UWFD(u <| s,u' <| s,Comb(t,u),Comb(t',u'))"; @@ -296,4 +296,4 @@ by (asm_simp_tac (set_ss addsimps [subseteq_iff_subset_eq]) 1); by (asm_simp_tac subst_ss 1); by (fast_tac (set_cs addDs [prem RS UWFD2_lemma2]) 1); -val UnifyWFD2 = result(); +qed "UnifyWFD2";