author  lcp 
Mon, 31 Oct 1994 17:55:43 +0100  
changeset 668  0d0923eb0f0d 
parent 655  9748dbcd4157 
child 708  8422e50adce0 
permissions  rwrr 
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(* Title: Pure/drule.ML 
0  2 
ID: $Id$ 
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory 
0  4 
Copyright 1993 University of Cambridge 
5 

6 
Derived rules and other operations on theorems and theories 

7 
*) 

8 

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infix 0 RS RSN RL RLN MRS MRL COMP; 
0  10 

11 
signature DRULE = 

12 
sig 

13 
structure Thm : THM 

14 
local open Thm in 

668  15 
val add_defs : (string * string) list > theory > theory 
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val add_defs_i : (string * term) list > theory > theory 

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val asm_rl : thm 

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val assume_ax : theory > string > thm 

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val COMP : thm * thm > thm 

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val compose : thm * int * thm > thm list 

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val cterm_instantiate : (cterm*cterm)list > thm > thm 

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val cut_rl : thm 

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val equal_abs_elim : cterm > thm > thm 

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val equal_abs_elim_list: cterm list > thm > thm 
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val eq_thm : thm * thm > bool 
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val eq_thm_sg : thm * thm > bool 

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val flexpair_abs_elim_list: cterm list > thm > thm 
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val forall_intr_list : cterm list > thm > thm 
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val forall_intr_frees : thm > thm 

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val forall_elim_list : cterm list > thm > thm 

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val forall_elim_var : int > thm > thm 

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val forall_elim_vars : int > thm > thm 

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val implies_elim_list : thm > thm list > thm 

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val implies_intr_list : cterm list > thm > thm 

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val MRL : thm list list * thm list > thm list 

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val MRS : thm list * thm > thm 

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val pprint_cterm : cterm > pprint_args > unit 

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val pprint_ctyp : ctyp > pprint_args > unit 

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val pprint_theory : theory > pprint_args > unit 

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val pprint_thm : thm > pprint_args > unit 

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val pretty_thm : thm > Sign.Syntax.Pretty.T 

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val print_cterm : cterm > unit 

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val print_ctyp : ctyp > unit 

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val print_goals : int > thm > unit 

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val print_goals_ref : (int > thm > unit) ref 

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val print_syntax : theory > unit 

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val print_sign : theory > unit 

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val print_axioms : theory > unit 

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val print_theory : theory > unit 

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val print_thm : thm > unit 

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val prth : thm > thm 

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val prthq : thm Sequence.seq > thm Sequence.seq 

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val prths : thm list > thm list 

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val read_instantiate : (string*string)list > thm > thm 

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val read_instantiate_sg: Sign.sg > (string*string)list > thm > thm 
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val read_insts : 
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Sign.sg > (indexname > typ option) * (indexname > sort option) 
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> (indexname > typ option) * (indexname > sort option) 
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> (string*string)list 
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> (indexname*ctyp)list * (cterm*cterm)list 
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val reflexive_thm : thm 
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val revcut_rl : thm 

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val rewrite_goal_rule : bool*bool > (meta_simpset > thm > thm option) 

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> meta_simpset > int > thm > thm 
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val rewrite_goals_rule: thm list > thm > thm 
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val rewrite_rule : thm list > thm > thm 
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val RS : thm * thm > thm 

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val RSN : thm * (int * thm) > thm 

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val RL : thm list * thm list > thm list 

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val RLN : thm list * (int * thm list) > thm list 

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val show_hyps : bool ref 

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val size_of_thm : thm > int 

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val standard : thm > thm 

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val string_of_cterm : cterm > string 

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val string_of_ctyp : ctyp > string 

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val string_of_thm : thm > string 

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val symmetric_thm : thm 

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val thin_rl : thm 

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val transitive_thm : thm 

0  80 
val triv_forall_equality: thm 
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val types_sorts: thm > (indexname> typ option) * (indexname> sort option) 

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val zero_var_indexes : thm > thm 
0  83 
end 
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end; 

85 

668  86 

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functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE = 
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struct 
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structure Thm = Thm; 

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structure Sign = Thm.Sign; 

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structure Type = Sign.Type; 

575  92 
structure Syntax = Sign.Syntax; 
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structure Pretty = Syntax.Pretty 

400  94 
structure Symtab = Sign.Symtab; 
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0  96 
local open Thm 
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in 

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(**** Extend Theories ****) 
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(** add constant definitions **) 

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(* all_axioms_of *) 

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(*results may contain duplicates!*) 

106 

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fun ancestry_of thy = 

108 
thy :: flat (map ancestry_of (parents_of thy)); 

109 

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val all_axioms_of = flat o map axioms_of o ancestry_of; 

111 

112 

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(* clash_types, clash_consts *) 

114 

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(*check if types have common instance (ignoring sorts)*) 

116 

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fun clash_types ty1 ty2 = 

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let 

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val ty1' = Type.varifyT ty1; 

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val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2); 

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in 

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Type.raw_unify (ty1', ty2') 

123 
end; 

124 

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fun clash_consts (c1, ty1) (c2, ty2) = 

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c1 = c2 andalso clash_types ty1 ty2; 

127 

128 

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(* clash_defns *) 

130 

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fun clash_defn c_ty (name, tm) = 

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let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in 

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if clash_consts c_ty (c, ty') then Some (name, ty') else None 

134 
end handle TERM _ => None; 

135 

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fun clash_defns c_ty axms = 

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distinct (mapfilter (clash_defn c_ty) axms); 

138 

139 

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(* dest_defn *) 

141 

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fun dest_defn tm = 

143 
let 

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fun err msg = raise_term msg [tm]; 

145 

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val (lhs, rhs) = Logic.dest_equals tm 

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handle TERM _ => err "Not a metaequality (==)"; 

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val (head, args) = strip_comb lhs; 

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val (c, ty) = dest_Const head 

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handle TERM _ => err "Head of lhs not a constant"; 

151 

655  152 
fun occs_const (Const c_ty') = (c_ty' = (c, ty)) 
561  153 
 occs_const (Abs (_, _, t)) = occs_const t 
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 occs_const (t $ u) = occs_const t orelse occs_const u 

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 occs_const _ = false; 

641  156 

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val show_frees = commas_quote o map (fst o dest_Free); 

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val show_tfrees = commas_quote o map fst; 

159 

160 
val lhs_dups = duplicates args; 

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val rhs_extras = gen_rems (op =) (term_frees rhs, args); 

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val rhs_extrasT = gen_rems (op =) (term_tfrees rhs, typ_tfrees ty); 

561  163 
in 
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if not (forall is_Free args) then 

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err "Arguments of lhs have to be variables" 

641  166 
else if not (null lhs_dups) then 
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err ("Duplicate variables on lhs: " ^ show_frees lhs_dups) 

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else if not (null rhs_extras) then 

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err ("Extra variables on rhs: " ^ show_frees rhs_extras) 

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else if not (null rhs_extrasT) then 

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err ("Extra type variables on rhs: " ^ show_tfrees rhs_extrasT) 

561  172 
else if occs_const rhs then 
655  173 
err ("Constant to be defined occurs on rhs") 
561  174 
else (c, ty) 
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end; 

176 

177 

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(* check_defn *) 

179 

641  180 
fun err_in_defn name msg = 
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(writeln msg; error ("The error(s) above occurred in definition " ^ quote name)); 

561  182 

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fun check_defn sign (axms, (name, tm)) = 

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let 

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fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block 

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[Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sign ty])); 

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fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn; 

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fun show_defns c = commas o map (show_defn c); 

190 

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val (c, ty) = dest_defn tm 

641  192 
handle TERM (msg, _) => err_in_defn name msg; 
561  193 
val defns = clash_defns (c, ty) axms; 
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in 

195 
if not (null defns) then 

641  196 
err_in_defn name ("Definition of " ^ show_const (c, ty) ^ 
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" clashes with " ^ show_defns c defns) 
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else (name, tm) :: axms 

199 
end; 

200 

201 

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(* add_defs *) 

203 

204 
fun ext_defns prep_axm raw_axms thy = 

205 
let 

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val axms = map (prep_axm (sign_of thy)) raw_axms; 

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val all_axms = all_axioms_of thy; 

208 
in 

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foldl (check_defn (sign_of thy)) (all_axms, axms); 

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add_axioms_i axms thy 

211 
end; 

212 

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val add_defs_i = ext_defns cert_axm; 

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val add_defs = ext_defns read_axm; 

215 

216 

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(**** More derived rules and operations on theorems ****) 
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(** reading of instantiations **) 
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fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v 
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 _ => error("Lexical error in variable name " ^ quote (implode cs)); 
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fun absent ixn = 
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error("No such variable in term: " ^ Syntax.string_of_vname ixn); 
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fun inst_failure ixn = 
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error("Instantiation of " ^ Syntax.string_of_vname ixn ^ " fails"); 
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fun read_insts sign (rtypes,rsorts) (types,sorts) insts = 
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let val {tsig,...} = Sign.rep_sg sign 
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fun split([],tvs,vs) = (tvs,vs) 
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 split((sv,st)::l,tvs,vs) = (case explode sv of 
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"'"::cs => split(l,(indexname cs,st)::tvs,vs) 
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 cs => split(l,tvs,(indexname cs,st)::vs)); 
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val (tvs,vs) = split(insts,[],[]); 
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fun readT((a,i),st) = 
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let val ixn = ("'" ^ a,i); 
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val S = case rsorts ixn of Some S => S  None => absent ixn; 
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val T = Sign.read_typ (sign,sorts) st; 
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in if Type.typ_instance(tsig,T,TVar(ixn,S)) then (ixn,T) 
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else inst_failure ixn 
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end 
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val tye = map readT tvs; 
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fun add_cterm ((cts,tye), (ixn,st)) = 
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let val T = case rtypes ixn of 
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Some T => typ_subst_TVars tye T 
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 None => absent ixn; 
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val (ct,tye2) = read_def_cterm (sign,types,sorts) (st,T); 
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val cv = cterm_of sign (Var(ixn,typ_subst_TVars tye2 T)) 
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in ((cv,ct)::cts,tye2 @ tye) end 
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val (cterms,tye') = foldl add_cterm (([],tye), vs); 
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in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', cterms) end; 
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(*** Printing of theories, theorems, etc. ***) 
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(*If false, hypotheses are printed as dots*) 
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val show_hyps = ref true; 
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fun pretty_thm th = 
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let val {sign, hyps, prop,...} = rep_thm th 
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val hsymbs = if null hyps then [] 
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else if !show_hyps then 
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[Pretty.brk 2, 
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Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)] 
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else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @ 
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[Pretty.str"]"]; 
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in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end; 
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val string_of_thm = Pretty.string_of o pretty_thm; 
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val pprint_thm = Pretty.pprint o Pretty.quote o pretty_thm; 
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(** Toplevel commands for printing theorems **) 
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val print_thm = writeln o string_of_thm; 
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fun prth th = (print_thm th; th); 
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(*Print and return a sequence of theorems, separated by blank lines. *) 
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284 
fun prthq thseq = 
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285 
(Sequence.prints (fn _ => print_thm) 100000 thseq; thseq); 
229
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286 

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287 
(*Print and return a list of theorems, separated by blank lines. *) 
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288 
fun prths ths = (print_list_ln print_thm ths; ths); 
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289 

252
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290 

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291 
(* other printing commands *) 
229
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292 

252
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293 
fun pprint_ctyp cT = 
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294 
let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end; 
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295 

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296 
fun string_of_ctyp cT = 
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297 
let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end; 
229
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298 

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299 
val print_ctyp = writeln o string_of_ctyp; 
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300 

252
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301 
fun pprint_cterm ct = 
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302 
let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end; 
229
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303 

252
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304 
fun string_of_cterm ct = 
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305 
let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end; 
229
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306 

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307 
val print_cterm = writeln o string_of_cterm; 
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308 

252
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309 

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310 
(* print theory *) 
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311 

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312 
val pprint_theory = Sign.pprint_sg o sign_of; 
229
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313 

575  314 
val print_syntax = Syntax.print_syntax o syn_of; 
315 

385  316 
val print_sign = Sign.print_sg o sign_of; 
317 

318 
fun print_axioms thy = 

252
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319 
let 
400  320 
val {sign, new_axioms, ...} = rep_theory thy; 
321 
val axioms = Symtab.dest new_axioms; 

229
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322 

385  323 
fun prt_axm (a, t) = Pretty.block [Pretty.str (a ^ ":"), Pretty.brk 1, 
324 
Pretty.quote (Sign.pretty_term sign t)]; 

252
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325 
in 
385  326 
Pretty.writeln (Pretty.big_list "additional axioms:" (map prt_axm axioms)) 
252
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327 
end; 
229
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328 

385  329 
fun print_theory thy = (print_sign thy; print_axioms thy); 
330 

229
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331 

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332 

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333 
(** Print thm A1,...,An/B in "goal style"  premises as numbered subgoals **) 
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334 

641  335 
(* get type_env, sort_env of term *) 
336 

337 
local 

338 
open Syntax; 

339 

340 
fun ins_entry (x, y) [] = [(x, [y])] 

341 
 ins_entry (x, y) ((pair as (x', ys')) :: pairs) = 

342 
if x = x' then (x', y ins ys') :: pairs 

343 
else pair :: ins_entry (x, y) pairs; 

344 

345 
fun add_type_env (Free (x, T), env) = ins_entry (T, x) env 

346 
 add_type_env (Var (xi, T), env) = ins_entry (T, string_of_vname xi) env 

347 
 add_type_env (Abs (_, _, t), env) = add_type_env (t, env) 

348 
 add_type_env (t $ u, env) = add_type_env (u, add_type_env (t, env)) 

349 
 add_type_env (_, env) = env; 

350 

351 
fun add_sort_env (Type (_, Ts), env) = foldr add_sort_env (Ts, env) 

352 
 add_sort_env (TFree (x, S), env) = ins_entry (S, x) env 

353 
 add_sort_env (TVar (xi, S), env) = ins_entry (S, string_of_vname xi) env; 

354 

355 
val sort = map (apsnd sort_strings); 

356 
in 

357 
fun type_env t = sort (add_type_env (t, [])); 

358 
fun sort_env t = rev (sort (it_term_types add_sort_env (t, []))); 

359 
end; 

360 

361 

362 
(* print_goals *) 

363 

364 
fun print_goals maxgoals state = 

365 
let 

366 
open Syntax; 

367 

368 
val {sign, prop, ...} = rep_thm state; 

369 

370 
val pretty_term = Sign.pretty_term sign; 

371 
val pretty_typ = Sign.pretty_typ sign; 

372 
val pretty_sort = Sign.pretty_sort; 

373 

374 
fun pretty_vars prtf (X, vs) = Pretty.block 

375 
[Pretty.block (Pretty.commas (map Pretty.str vs)), 

376 
Pretty.str " ::", Pretty.brk 1, prtf X]; 

229
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377 

641  378 
fun print_list _ _ [] = () 
379 
 print_list name prtf lst = 

380 
(writeln ""; Pretty.writeln (Pretty.big_list name (map prtf lst))); 

381 

382 

383 
fun print_goals (_, []) = () 

384 
 print_goals (n, A :: As) = (Pretty.writeln (Pretty.blk (0, 

385 
[Pretty.str (" " ^ string_of_int n ^ ". "), pretty_term A])); 

386 
print_goals (n + 1, As)); 

387 

388 
val print_ffpairs = 

389 
print_list "Flexflex pairs:" (pretty_term o Logic.mk_flexpair); 

390 

391 
val print_types = print_list "Types:" (pretty_vars pretty_typ) o type_env; 

392 
val print_sorts = print_list "Sorts:" (pretty_vars pretty_sort) o sort_env; 

393 

394 

395 
val (tpairs, As, B) = Logic.strip_horn prop; 

396 
val ngoals = length As; 

397 

398 
val orig_no_freeTs = ! show_no_free_types; 

399 
val orig_sorts = ! show_sorts; 

400 

401 
fun restore () = 

402 
(show_no_free_types := orig_no_freeTs; show_sorts := orig_sorts); 

403 
in 

404 
(show_no_free_types := true; show_sorts := false; 

405 

406 
Pretty.writeln (pretty_term B); 

407 

408 
if ngoals = 0 then writeln "No subgoals!" 

409 
else if ngoals > maxgoals then 

410 
(print_goals (1, take (maxgoals, As)); 

411 
writeln ("A total of " ^ string_of_int ngoals ^ " subgoals...")) 

412 
else print_goals (1, As); 

413 

414 
print_ffpairs tpairs; 

415 

416 
if orig_sorts then 

417 
(print_types prop; print_sorts prop) 

418 
else if ! show_types then 

419 
print_types prop 

420 
else ()) 

421 
handle exn => (restore (); raise exn); 

422 
restore () 

423 
end; 

424 

229
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425 

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426 
(*"hook" for user interfaces: allows print_goals to be replaced*) 
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427 
val print_goals_ref = ref print_goals; 
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428 

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429 
(*** Find the type (sort) associated with a (T)Var or (T)Free in a term 
0  430 
Used for establishing default types (of variables) and sorts (of 
431 
type variables) when reading another term. 

432 
Index 1 indicates that a (T)Free rather than a (T)Var is wanted. 

433 
***) 

434 

435 
fun types_sorts thm = 

436 
let val {prop,hyps,...} = rep_thm thm; 

252
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437 
val big = list_comb(prop,hyps); (* bogus term! *) 
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438 
val vars = map dest_Var (term_vars big); 
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439 
val frees = map dest_Free (term_frees big); 
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440 
val tvars = term_tvars big; 
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441 
val tfrees = term_tfrees big; 
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442 
fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i)); 
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443 
fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); 
0  444 
in (typ,sort) end; 
445 

446 
(** Standardization of rules **) 

447 

448 
(*Generalization over a list of variables, IGNORING bad ones*) 

449 
fun forall_intr_list [] th = th 

450 
 forall_intr_list (y::ys) th = 

252
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451 
let val gth = forall_intr_list ys th 
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452 
in forall_intr y gth handle THM _ => gth end; 
0  453 

454 
(*Generalization over all suitable Free variables*) 

455 
fun forall_intr_frees th = 

456 
let val {prop,sign,...} = rep_thm th 

457 
in forall_intr_list 

252
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458 
(map (cterm_of sign) (sort atless (term_frees prop))) 
0  459 
th 
460 
end; 

461 

462 
(*Replace outermost quantified variable by Var of given index. 

463 
Could clash with Vars already present.*) 

252
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464 
fun forall_elim_var i th = 
0  465 
let val {prop,sign,...} = rep_thm th 
466 
in case prop of 

252
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467 
Const("all",_) $ Abs(a,T,_) => 
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468 
forall_elim (cterm_of sign (Var((a,i), T))) th 
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469 
 _ => raise THM("forall_elim_var", i, [th]) 
0  470 
end; 
471 

472 
(*Repeat forall_elim_var until all outer quantifiers are removed*) 

252
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473 
fun forall_elim_vars i th = 
0  474 
forall_elim_vars i (forall_elim_var i th) 
252
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475 
handle THM _ => th; 
0  476 

477 
(*Specialization over a list of cterms*) 

478 
fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th); 

479 

480 
(* maps [A1,...,An], B to [ A1;...;An ] ==> B *) 

481 
fun implies_intr_list cAs th = foldr (uncurry implies_intr) (cAs,th); 

482 

483 
(* maps [ A1;...;An ] ==> B and [A1,...,An] to B *) 

484 
fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths); 

485 

486 
(*Reset Var indexes to zero, renaming to preserve distinctness*) 

252
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487 
fun zero_var_indexes th = 
0  488 
let val {prop,sign,...} = rep_thm th; 
489 
val vars = term_vars prop 

490 
val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars) 

252
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491 
val inrs = add_term_tvars(prop,[]); 
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492 
val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); 
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493 
val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms') 
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494 
val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye; 
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495 
fun varpairs([],[]) = [] 
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496 
 varpairs((var as Var(v,T)) :: vars, b::bs) = 
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497 
let val T' = typ_subst_TVars tye T 
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498 
in (cterm_of sign (Var(v,T')), 
7532f95d7f44
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diff
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499 
cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs) 
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500 
end 
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diff
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501 
 varpairs _ = raise TERM("varpairs", []); 
0  502 
in instantiate (ctye, varpairs(vars,rev bs)) th end; 
503 

504 

505 
(*Standard form of objectrule: no hypotheses, Frees, or outer quantifiers; 

506 
all generality expressed by Vars having index 0.*) 

507 
fun standard th = 

508 
let val {maxidx,...} = rep_thm th 

252
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diff
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509 
in varifyT (zero_var_indexes (forall_elim_vars(maxidx+1) 
0  510 
(forall_intr_frees(implies_intr_hyps th)))) 
511 
end; 

512 

252
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513 
(*Assume a new formula, read following the same conventions as axioms. 
0  514 
Generalizes over Free variables, 
515 
creates the assumption, and then strips quantifiers. 

516 
Example is [ ALL x:?A. ?P(x) ] ==> [ ?P(?a) ] 

252
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diff
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517 
[ !(A,P,a)[ ALL x:A. P(x) ] ==> [ P(a) ] ] *) 
0  518 
fun assume_ax thy sP = 
519 
let val sign = sign_of thy 

252
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520 
val prop = Logic.close_form (term_of (read_cterm sign 
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diff
changeset

521 
(sP, propT))) 
229
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changeset

522 
in forall_elim_vars 0 (assume (cterm_of sign prop)) end; 
0  523 

252
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524 
(*Resolution: exactly one resolvent must be produced.*) 
0  525 
fun tha RSN (i,thb) = 
526 
case Sequence.chop (2, biresolution false [(false,tha)] i thb) of 

527 
([th],_) => th 

528 
 ([],_) => raise THM("RSN: no unifiers", i, [tha,thb]) 

529 
 _ => raise THM("RSN: multiple unifiers", i, [tha,thb]); 

530 

531 
(*resolution: P==>Q, Q==>R gives P==>R. *) 

532 
fun tha RS thb = tha RSN (1,thb); 

533 

534 
(*For joining lists of rules*) 

252
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535 
fun thas RLN (i,thbs) = 
0  536 
let val resolve = biresolution false (map (pair false) thas) i 
537 
fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => [] 

538 
in flat (map resb thbs) end; 

539 

540 
fun thas RL thbs = thas RLN (1,thbs); 

541 

11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

542 
(*Resolve a list of rules against bottom_rl from right to left; 
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

543 
makes proof trees*) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

544 
fun rls MRS bottom_rl = 
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

545 
let fun rs_aux i [] = bottom_rl 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

546 
 rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls) 
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

547 
in rs_aux 1 rls end; 
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

548 

d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

549 
(*As above, but for rule lists*) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

550 
fun rlss MRL bottom_rls = 
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

551 
let fun rs_aux i [] = bottom_rls 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

552 
 rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss) 
11
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

553 
in rs_aux 1 rlss end; 
d0e17c42dbb4
Added MRS, MRL from ZF/ROOT.ML. These support forward proof, resolving a
lcp
parents:
0
diff
changeset

554 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

555 
(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R 
0  556 
with no lifting or renaming! Q may contain ==> or metaquants 
557 
ALWAYS deletes premise i *) 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

558 
fun compose(tha,i,thb) = 
0  559 
Sequence.list_of_s (bicompose false (false,tha,0) i thb); 
560 

561 
(*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*) 

562 
fun tha COMP thb = 

563 
case compose(tha,1,thb) of 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

564 
[th] => th 
0  565 
 _ => raise THM("COMP", 1, [tha,thb]); 
566 

567 
(*Instantiate theorem th, reading instantiations under signature sg*) 

568 
fun read_instantiate_sg sg sinsts th = 

569 
let val ts = types_sorts th; 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

570 
in instantiate (read_insts sg ts ts sinsts) th end; 
0  571 

572 
(*Instantiate theorem th, reading instantiations under theory of th*) 

573 
fun read_instantiate sinsts th = 

574 
read_instantiate_sg (#sign (rep_thm th)) sinsts th; 

575 

576 

577 
(*Lefttoright replacements: tpairs = [...,(vi,ti),...]. 

578 
Instantiates distinct Vars by terms, inferring type instantiations. *) 

579 
local 

580 
fun add_types ((ct,cu), (sign,tye)) = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

581 
let val {sign=signt, t=t, T= T, ...} = rep_cterm ct 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

582 
and {sign=signu, t=u, T= U, ...} = rep_cterm cu 
0  583 
val sign' = Sign.merge(sign, Sign.merge(signt, signu)) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

584 
val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye) 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

585 
handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u]) 
0  586 
in (sign', tye') end; 
587 
in 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

588 
fun cterm_instantiate ctpairs0 th = 
0  589 
let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[])) 
590 
val tsig = #tsig(Sign.rep_sg sign); 

591 
fun instT(ct,cu) = let val inst = subst_TVars tye 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

592 
in (cterm_fun inst ct, cterm_fun inst cu) end 
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

593 
fun ctyp2 (ix,T) = (ix, ctyp_of sign T) 
0  594 
in instantiate (map ctyp2 tye, map instT ctpairs0) th end 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

595 
handle TERM _ => 
0  596 
raise THM("cterm_instantiate: incompatible signatures",0,[th]) 
597 
 TYPE _ => raise THM("cterm_instantiate: types", 0, [th]) 

598 
end; 

599 

600 

601 
(** theorem equality test is exported and used by BEST_FIRST **) 

602 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

603 
(*equality of theorems uses equality of signatures and 
0  604 
the aconvertible test for terms*) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

605 
fun eq_thm (th1,th2) = 
0  606 
let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

607 
and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

608 
in Sign.eq_sg (sg1,sg2) andalso 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

609 
aconvs(hyps1,hyps2) andalso 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

610 
prop1 aconv prop2 
0  611 
end; 
612 

613 
(*Do the two theorems have the same signature?*) 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

614 
fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); 
0  615 

616 
(*Useful "distance" function for BEST_FIRST*) 

617 
val size_of_thm = size_of_term o #prop o rep_thm; 

618 

619 

620 
(*** MetaRewriting Rules ***) 

621 

622 

623 
val reflexive_thm = 

385  624 
let val cx = cterm_of Sign.pure (Var(("x",0),TVar(("'a",0),logicS))) 
0  625 
in Thm.reflexive cx end; 
626 

627 
val symmetric_thm = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

628 
let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT) 
0  629 
in standard(Thm.implies_intr_hyps(Thm.symmetric(Thm.assume xy))) end; 
630 

631 
val transitive_thm = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

632 
let val xy = read_cterm Sign.pure ("x::'a::logic == y",propT) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

633 
val yz = read_cterm Sign.pure ("y::'a::logic == z",propT) 
0  634 
val xythm = Thm.assume xy and yzthm = Thm.assume yz 
635 
in standard(Thm.implies_intr yz (Thm.transitive xythm yzthm)) end; 

636 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

637 
(** Below, a "conversion" has type cterm > thm **) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

638 

4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

639 
val refl_cimplies = reflexive (cterm_of Sign.pure implies); 
0  640 

641 
(*In [A1,...,An]==>B, rewrite the selected A's only  for rewrite_goals_tac*) 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

642 
(*Do not rewrite flexflex pairs*) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

643 
fun goals_conv pred cv = 
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

644 
let fun gconv i ct = 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

645 
let val (A,B) = Thm.dest_cimplies ct 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

646 
val (thA,j) = case term_of A of 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

647 
Const("=?=",_)$_$_ => (reflexive A, i) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

648 
 _ => (if pred i then cv A else reflexive A, i+1) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

649 
in combination (combination refl_cimplies thA) (gconv j B) end 
229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

650 
handle TERM _ => reflexive ct 
0  651 
in gconv 1 end; 
652 

653 
(*Use a conversion to transform a theorem*) 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

654 
fun fconv_rule cv th = equal_elim (cv (cprop_of th)) th; 
0  655 

656 
(*rewriting conversion*) 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

657 
fun rew_conv mode prover mss = rewrite_cterm mode mss prover; 
0  658 

659 
(*Rewrite a theorem*) 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

660 
fun rewrite_rule thms = 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

661 
fconv_rule (rew_conv (true,false) (K(K None)) (Thm.mss_of thms)); 
0  662 

663 
(*Rewrite the subgoals of a proof state (represented by a theorem) *) 

664 
fun rewrite_goals_rule thms = 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

665 
fconv_rule (goals_conv (K true) (rew_conv (true,false) (K(K None)) 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

666 
(Thm.mss_of thms))); 
0  667 

668 
(*Rewrite the subgoal of a proof state (represented by a theorem) *) 

214
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

669 
fun rewrite_goal_rule mode prover mss i thm = 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

670 
if 0 < i andalso i <= nprems_of thm 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

671 
then fconv_rule (goals_conv (fn j => j=i) (rew_conv mode prover mss)) thm 
ed6a3e2b1a33
added new parameter to the simplification tactics which indicates if
nipkow
parents:
211
diff
changeset

672 
else raise THM("rewrite_goal_rule",i,[thm]); 
0  673 

674 

675 
(** Derived rules mainly for METAHYPS **) 

676 

677 
(*Given the term "a", takes (%x.t)==(%x.u) to t[a/x]==u[a/x]*) 

678 
fun equal_abs_elim ca eqth = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

679 
let val {sign=signa, t=a, ...} = rep_cterm ca 
0  680 
and combth = combination eqth (reflexive ca) 
681 
val {sign,prop,...} = rep_thm eqth 

682 
val (abst,absu) = Logic.dest_equals prop 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

683 
val cterm = cterm_of (Sign.merge (sign,signa)) 
0  684 
in transitive (symmetric (beta_conversion (cterm (abst$a)))) 
685 
(transitive combth (beta_conversion (cterm (absu$a)))) 

686 
end 

687 
handle THM _ => raise THM("equal_abs_elim", 0, [eqth]); 

688 

689 
(*Calling equal_abs_elim with multiple terms*) 

690 
fun equal_abs_elim_list cts th = foldr (uncurry equal_abs_elim) (rev cts, th); 

691 

692 
local 

693 
open Logic 

694 
val alpha = TVar(("'a",0), []) (* type ?'a::{} *) 

695 
fun err th = raise THM("flexpair_inst: ", 0, [th]) 

696 
fun flexpair_inst def th = 

697 
let val {prop = Const _ $ t $ u, sign,...} = rep_thm th 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

698 
val cterm = cterm_of sign 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

699 
fun cvar a = cterm(Var((a,0),alpha)) 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

700 
val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)] 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

701 
def 
0  702 
in equal_elim def' th 
703 
end 

704 
handle THM _ => err th  bind => err th 

705 
in 

706 
val flexpair_intr = flexpair_inst (symmetric flexpair_def) 

707 
and flexpair_elim = flexpair_inst flexpair_def 

708 
end; 

709 

710 
(*Version for flexflex pairs  this supports lifting.*) 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

711 
fun flexpair_abs_elim_list cts = 
0  712 
flexpair_intr o equal_abs_elim_list cts o flexpair_elim; 
713 

714 

715 
(*** Some useful metatheorems ***) 

716 

717 
(*The rule V/V, obtains assumption solving for eresolve_tac*) 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

718 
val asm_rl = trivial(read_cterm Sign.pure ("PROP ?psi",propT)); 
0  719 

720 
(*Metalevel cut rule: [ V==>W; V ] ==> W *) 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

721 
val cut_rl = trivial(read_cterm Sign.pure 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

722 
("PROP ?psi ==> PROP ?theta", propT)); 
0  723 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

724 
(*Generalized elim rule for one conclusion; cut_rl with reversed premises: 
0  725 
[ PROP V; PROP V ==> PROP W ] ==> PROP W *) 
726 
val revcut_rl = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

727 
let val V = read_cterm Sign.pure ("PROP V", propT) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

728 
and VW = read_cterm Sign.pure ("PROP V ==> PROP W", propT); 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

729 
in standard (implies_intr V 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

730 
(implies_intr VW 
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

731 
(implies_elim (assume VW) (assume V)))) 
0  732 
end; 
733 

668  734 
(*for deleting an unwanted assumption*) 
735 
val thin_rl = 

736 
let val V = read_cterm Sign.pure ("PROP V", propT) 

737 
and W = read_cterm Sign.pure ("PROP W", propT); 

738 
in standard (implies_intr V (implies_intr W (assume W))) 

739 
end; 

740 

0  741 
(* (!!x. PROP ?V) == PROP ?V Allows removal of redundant parameters*) 
742 
val triv_forall_equality = 

229
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

743 
let val V = read_cterm Sign.pure ("PROP V", propT) 
4002c4cd450c
Pure: MAJOR CHANGE. Moved ML types ctyp and cterm and their associated
lcp
parents:
214
diff
changeset

744 
and QV = read_cterm Sign.pure ("!!x::'a. PROP V", propT) 
385  745 
and x = read_cterm Sign.pure ("x", TFree("'a",logicS)); 
0  746 
in standard (equal_intr (implies_intr QV (forall_elim x (assume QV))) 
252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

747 
(implies_intr V (forall_intr x (assume V)))) 
0  748 
end; 
749 

750 
end 

751 
end; 

252
7532f95d7f44
removed eq_sg, pprint_sg, print_sg (now in sign.ML);
wenzelm
parents:
229
diff
changeset

752 