--- a/Subst/UTerm.ML Tue Oct 24 14:59:17 1995 +0100
+++ /dev/null Thu Jan 01 00:00:00 1970 +0000
@@ -1,270 +0,0 @@
-(* Title: Substitutions/uterm.ML
- Author: Martin Coen, Cambridge University Computer Laboratory
- Copyright 1993 University of Cambridge
-
-Simple term structure for unifiation.
-Binary trees with leaves that are constants or variables.
-*)
-
-open UTerm;
-
-val uterm_con_defs = [VAR_def, CONST_def, COMB_def];
-
-goal UTerm.thy "uterm(A) = A <+> A <+> (uterm(A) <*> uterm(A))";
-let val rew = rewrite_rule uterm_con_defs in
-by (fast_tac (univ_cs addSIs (equalityI :: map rew uterm.intrs)
- addEs [rew uterm.elim]) 1)
-end;
-qed "uterm_unfold";
-
-(** the uterm functional **)
-
-(*This justifies using uterm in other recursive type definitions*)
-goalw UTerm.thy uterm.defs "!!A B. A<=B ==> uterm(A) <= uterm(B)";
-by (REPEAT (ares_tac (lfp_mono::basic_monos) 1));
-qed "uterm_mono";
-
-(** Type checking rules -- uterm creates well-founded sets **)
-
-goalw UTerm.thy (uterm_con_defs @ uterm.defs) "uterm(sexp) <= sexp";
-by (rtac lfp_lowerbound 1);
-by (fast_tac (univ_cs addIs sexp.intrs@[sexp_In0I,sexp_In1I]) 1);
-qed "uterm_sexp";
-
-(* A <= sexp ==> uterm(A) <= sexp *)
-bind_thm ("uterm_subset_sexp", ([uterm_mono, uterm_sexp] MRS subset_trans));
-
-(** Induction **)
-
-(*Induction for the type 'a uterm *)
-val prems = goalw UTerm.thy [Var_def,Const_def,Comb_def]
- "[| !!x.P(Var(x)); !!x.P(Const(x)); \
-\ !!u v. [| P(u); P(v) |] ==> P(Comb(u,v)) |] ==> P(t)";
-by (rtac (Rep_uterm_inverse RS subst) 1); (*types force good instantiation*)
-by (rtac (Rep_uterm RS uterm.induct) 1);
-by (REPEAT (ares_tac prems 1
- ORELSE eresolve_tac [rangeE, ssubst, Abs_uterm_inverse RS subst] 1));
-qed "uterm_induct";
-
-(*Perform induction on xs. *)
-fun uterm_ind_tac a M =
- EVERY [res_inst_tac [("t",a)] uterm_induct M,
- rename_last_tac a ["1"] (M+1)];
-
-
-(*** Isomorphisms ***)
-
-goal UTerm.thy "inj(Rep_uterm)";
-by (rtac inj_inverseI 1);
-by (rtac Rep_uterm_inverse 1);
-qed "inj_Rep_uterm";
-
-goal UTerm.thy "inj_onto(Abs_uterm,uterm(range(Leaf)))";
-by (rtac inj_onto_inverseI 1);
-by (etac Abs_uterm_inverse 1);
-qed "inj_onto_Abs_uterm";
-
-(** Distinctness of constructors **)
-
-goalw UTerm.thy uterm_con_defs "~ CONST(c) = COMB(u,v)";
-by (rtac notI 1);
-by (etac (In1_inject RS (In0_not_In1 RS notE)) 1);
-qed "CONST_not_COMB";
-bind_thm ("COMB_not_CONST", (CONST_not_COMB RS not_sym));
-bind_thm ("CONST_neq_COMB", (CONST_not_COMB RS notE));
-val COMB_neq_CONST = sym RS CONST_neq_COMB;
-
-goalw UTerm.thy uterm_con_defs "~ COMB(u,v) = VAR(x)";
-by (rtac In1_not_In0 1);
-qed "COMB_not_VAR";
-bind_thm ("VAR_not_COMB", (COMB_not_VAR RS not_sym));
-bind_thm ("COMB_neq_VAR", (COMB_not_VAR RS notE));
-val VAR_neq_COMB = sym RS COMB_neq_VAR;
-
-goalw UTerm.thy uterm_con_defs "~ VAR(x) = CONST(c)";
-by (rtac In0_not_In1 1);
-qed "VAR_not_CONST";
-bind_thm ("CONST_not_VAR", (VAR_not_CONST RS not_sym));
-bind_thm ("VAR_neq_CONST", (VAR_not_CONST RS notE));
-val CONST_neq_VAR = sym RS VAR_neq_CONST;
-
-
-goalw UTerm.thy [Const_def,Comb_def] "~ Const(c) = Comb(u,v)";
-by (rtac (CONST_not_COMB RS (inj_onto_Abs_uterm RS inj_onto_contraD)) 1);
-by (REPEAT (resolve_tac (uterm.intrs @ [rangeI, Rep_uterm]) 1));
-qed "Const_not_Comb";
-bind_thm ("Comb_not_Const", (Const_not_Comb RS not_sym));
-bind_thm ("Const_neq_Comb", (Const_not_Comb RS notE));
-val Comb_neq_Const = sym RS Const_neq_Comb;
-
-goalw UTerm.thy [Comb_def,Var_def] "~ Comb(u,v) = Var(x)";
-by (rtac (COMB_not_VAR RS (inj_onto_Abs_uterm RS inj_onto_contraD)) 1);
-by (REPEAT (resolve_tac (uterm.intrs @ [rangeI, Rep_uterm]) 1));
-qed "Comb_not_Var";
-bind_thm ("Var_not_Comb", (Comb_not_Var RS not_sym));
-bind_thm ("Comb_neq_Var", (Comb_not_Var RS notE));
-val Var_neq_Comb = sym RS Comb_neq_Var;
-
-goalw UTerm.thy [Var_def,Const_def] "~ Var(x) = Const(c)";
-by (rtac (VAR_not_CONST RS (inj_onto_Abs_uterm RS inj_onto_contraD)) 1);
-by (REPEAT (resolve_tac (uterm.intrs @ [rangeI, Rep_uterm]) 1));
-qed "Var_not_Const";
-bind_thm ("Const_not_Var", (Var_not_Const RS not_sym));
-bind_thm ("Var_neq_Const", (Var_not_Const RS notE));
-val Const_neq_Var = sym RS Var_neq_Const;
-
-
-(** Injectiveness of CONST and Const **)
-
-val inject_cs = HOL_cs addSEs [Scons_inject]
- addSDs [In0_inject,In1_inject];
-
-goalw UTerm.thy [VAR_def] "(VAR(M)=VAR(N)) = (M=N)";
-by (fast_tac inject_cs 1);
-qed "VAR_VAR_eq";
-
-goalw UTerm.thy [CONST_def] "(CONST(M)=CONST(N)) = (M=N)";
-by (fast_tac inject_cs 1);
-qed "CONST_CONST_eq";
-
-goalw UTerm.thy [COMB_def] "(COMB(K,L)=COMB(M,N)) = (K=M & L=N)";
-by (fast_tac inject_cs 1);
-qed "COMB_COMB_eq";
-
-bind_thm ("VAR_inject", (VAR_VAR_eq RS iffD1));
-bind_thm ("CONST_inject", (CONST_CONST_eq RS iffD1));
-bind_thm ("COMB_inject", (COMB_COMB_eq RS iffD1 RS conjE));
-
-
-(*For reasoning about abstract uterm constructors*)
-val uterm_cs = set_cs addIs uterm.intrs @ [Rep_uterm]
- addSEs [CONST_neq_COMB,COMB_neq_VAR,VAR_neq_CONST,
- COMB_neq_CONST,VAR_neq_COMB,CONST_neq_VAR,
- COMB_inject]
- addSDs [VAR_inject,CONST_inject,
- inj_onto_Abs_uterm RS inj_ontoD,
- inj_Rep_uterm RS injD, Leaf_inject];
-
-goalw UTerm.thy [Var_def] "(Var(x)=Var(y)) = (x=y)";
-by (fast_tac uterm_cs 1);
-qed "Var_Var_eq";
-bind_thm ("Var_inject", (Var_Var_eq RS iffD1));
-
-goalw UTerm.thy [Const_def] "(Const(x)=Const(y)) = (x=y)";
-by (fast_tac uterm_cs 1);
-qed "Const_Const_eq";
-bind_thm ("Const_inject", (Const_Const_eq RS iffD1));
-
-goalw UTerm.thy [Comb_def] "(Comb(u,v)=Comb(x,y)) = (u=x & v=y)";
-by (fast_tac uterm_cs 1);
-qed "Comb_Comb_eq";
-bind_thm ("Comb_inject", (Comb_Comb_eq RS iffD1 RS conjE));
-
-val [major] = goal UTerm.thy "VAR(M): uterm(A) ==> M : A";
-by (rtac (major RS setup_induction) 1);
-by (etac uterm.induct 1);
-by (ALLGOALS (fast_tac uterm_cs));
-qed "VAR_D";
-
-val [major] = goal UTerm.thy "CONST(M): uterm(A) ==> M : A";
-by (rtac (major RS setup_induction) 1);
-by (etac uterm.induct 1);
-by (ALLGOALS (fast_tac uterm_cs));
-qed "CONST_D";
-
-val [major] = goal UTerm.thy
- "COMB(M,N): uterm(A) ==> M: uterm(A) & N: uterm(A)";
-by (rtac (major RS setup_induction) 1);
-by (etac uterm.induct 1);
-by (ALLGOALS (fast_tac uterm_cs));
-qed "COMB_D";
-
-(*Basic ss with constructors and their freeness*)
-val uterm_free_simps = uterm.intrs @
- [Const_not_Comb,Comb_not_Var,Var_not_Const,
- Comb_not_Const,Var_not_Comb,Const_not_Var,
- Var_Var_eq,Const_Const_eq,Comb_Comb_eq,
- CONST_not_COMB,COMB_not_VAR,VAR_not_CONST,
- COMB_not_CONST,VAR_not_COMB,CONST_not_VAR,
- VAR_VAR_eq,CONST_CONST_eq,COMB_COMB_eq];
-val uterm_free_ss = HOL_ss addsimps uterm_free_simps;
-
-goal UTerm.thy "!u. t~=Comb(t,u)";
-by (uterm_ind_tac "t" 1);
-by (rtac (Var_not_Comb RS allI) 1);
-by (rtac (Const_not_Comb RS allI) 1);
-by (asm_simp_tac uterm_free_ss 1);
-qed "t_not_Comb_t";
-
-goal UTerm.thy "!t. u~=Comb(t,u)";
-by (uterm_ind_tac "u" 1);
-by (rtac (Var_not_Comb RS allI) 1);
-by (rtac (Const_not_Comb RS allI) 1);
-by (asm_simp_tac uterm_free_ss 1);
-qed "u_not_Comb_u";
-
-
-(*** UTerm_rec -- by wf recursion on pred_sexp ***)
-
-val UTerm_rec_unfold =
- [UTerm_rec_def, wf_pred_sexp RS wf_trancl] MRS def_wfrec;
-
-(** conversion rules **)
-
-goalw UTerm.thy [VAR_def] "UTerm_rec(VAR(x),b,c,d) = b(x)";
-by (rtac (UTerm_rec_unfold RS trans) 1);
-by (simp_tac (HOL_ss addsimps [Case_In0]) 1);
-qed "UTerm_rec_VAR";
-
-goalw UTerm.thy [CONST_def] "UTerm_rec(CONST(x),b,c,d) = c(x)";
-by (rtac (UTerm_rec_unfold RS trans) 1);
-by (simp_tac (HOL_ss addsimps [Case_In0,Case_In1]) 1);
-qed "UTerm_rec_CONST";
-
-goalw UTerm.thy [COMB_def]
- "!!M N. [| M: sexp; N: sexp |] ==> \
-\ UTerm_rec(COMB(M,N), b, c, d) = \
-\ d(M, N, UTerm_rec(M,b,c,d), UTerm_rec(N,b,c,d))";
-by (rtac (UTerm_rec_unfold RS trans) 1);
-by (simp_tac (HOL_ss addsimps [Split,Case_In1]) 1);
-by (asm_simp_tac (pred_sexp_ss addsimps [In1_def]) 1);
-qed "UTerm_rec_COMB";
-
-(*** uterm_rec -- by UTerm_rec ***)
-
-val Rep_uterm_in_sexp =
- Rep_uterm RS (range_Leaf_subset_sexp RS uterm_subset_sexp RS subsetD);
-
-val uterm_rec_simps =
- uterm.intrs @
- [UTerm_rec_VAR, UTerm_rec_CONST, UTerm_rec_COMB,
- Abs_uterm_inverse, Rep_uterm_inverse,
- Rep_uterm, rangeI, inj_Leaf, Inv_f_f, Rep_uterm_in_sexp];
-val uterm_rec_ss = HOL_ss addsimps uterm_rec_simps;
-
-goalw UTerm.thy [uterm_rec_def, Var_def] "uterm_rec(Var(x),b,c,d) = b(x)";
-by (simp_tac uterm_rec_ss 1);
-qed "uterm_rec_Var";
-
-goalw UTerm.thy [uterm_rec_def, Const_def] "uterm_rec(Const(x),b,c,d) = c(x)";
-by (simp_tac uterm_rec_ss 1);
-qed "uterm_rec_Const";
-
-goalw UTerm.thy [uterm_rec_def, Comb_def]
- "uterm_rec(Comb(u,v),b,c,d) = d(u,v,uterm_rec(u,b,c,d),uterm_rec(v,b,c,d))";
-by (simp_tac uterm_rec_ss 1);
-qed "uterm_rec_Comb";
-
-val uterm_simps = [UTerm_rec_VAR, UTerm_rec_CONST, UTerm_rec_COMB,
- uterm_rec_Var, uterm_rec_Const, uterm_rec_Comb];
-val uterm_ss = uterm_free_ss addsimps uterm_simps;
-
-
-(**********)
-
-val uterm_rews = [uterm_rec_Var,uterm_rec_Const,uterm_rec_Comb,
- t_not_Comb_t,u_not_Comb_u,
- Const_not_Comb,Comb_not_Var,Var_not_Const,
- Comb_not_Const,Var_not_Comb,Const_not_Var,
- Var_Var_eq,Const_Const_eq,Comb_Comb_eq];
-