author  wenzelm 
Mon, 28 Jun 1999 21:46:33 +0200  
changeset 6848  3d82756e1af5 
parent 6798  f6bc583a5776 
child 6853  80f88b762816 
permissions  rwrr 
5820  1 
(* Title: Pure/Isar/proof.ML 
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ID: $Id$ 

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Author: Markus Wenzel, TU Muenchen 

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Proof states and methods. 

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*) 

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signature PROOF = 

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sig 

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type context 

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type state 

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exception STATE of string * state 

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val context_of: state > context 

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val theory_of: state > theory 

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val sign_of: state > Sign.sg 

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val the_facts: state > thm list 
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val the_fact: state > thm 
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val goal_facts: (state > thm list) > state > state 
5820  19 
val use_facts: state > state 
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val reset_facts: state > state 

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val assert_backward: state > state 

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val enter_forward: state > state 

6529  23 
val verbose: bool ref 
5820  24 
val print_state: state > unit 
6776  25 
val level: state > int 
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type method 
6848  27 
val method: (thm list > tactic) > method 
5820  28 
val refine: (context > method) > state > state Seq.seq 
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val bind: (indexname * string) list > state > state 

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val bind_i: (indexname * term) list > state > state 

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val match_bind: (string list * string) list > state > state 
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val match_bind_i: (term list * term) list > state > state 

6091  33 
val have_thmss: string > context attribute list > 
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(thm list * context attribute list) list > state > state 

6848  35 
val assume: (int > tactic) > string > context attribute list > (string * string list) list 
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> state > state 

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val assume_i: (int > tactic) > string > context attribute list > (term * term list) list 

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> state > state 

5820  39 
val fix: (string * string option) list > state > state 
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val fix_i: (string * typ) list > state > state 

5936  41 
val theorem: bstring > theory attribute list > string * string list > theory > state 
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val theorem_i: bstring > theory attribute list > term * term list > theory > state 

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val lemma: bstring > theory attribute list > string * string list > theory > state 

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val lemma_i: bstring > theory attribute list > term * term list > theory > state 

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val chain: state > state 
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val from_facts: thm list > state > state 
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val show: string > context attribute list > string * string list > state > state 
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val show_i: string > context attribute list > term * term list > state > state 

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val have: string > context attribute list > string * string list > state > state 

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val have_i: string > context attribute list > term * term list > state > state 

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val begin_block: state > state 
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val next_block: state > state 

6404  53 
val end_block: state > state 
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val at_bottom: state > bool 

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val local_qed: (state > state Seq.seq) > ({kind: string, name: string, thm: thm} > unit) 
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> state > state Seq.seq 

6404  57 
val global_qed: (state > state Seq.seq) > bstring option 
6529  58 
> theory attribute list option > state > theory * {kind: string, name: string, thm: thm} 
5820  59 
end; 
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signature PROOF_PRIVATE = 

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sig 

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include PROOF 

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val put_data: Object.kind > ('a > Object.T) > 'a > state > state 

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end; 

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structure Proof: PROOF_PRIVATE = 

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struct 

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(** proof state **) 

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type context = ProofContext.context; 

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(* type goal *) 

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datatype kind = 

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Theorem of theory attribute list  (*toplevel theorem*) 

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Lemma of theory attribute list  (*toplevel lemma*) 

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Goal of context attribute list  (*intermediate result, solving subgoal*) 

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Aux of context attribute list ; (*intermediate result*) 

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val kind_name = 

6001  85 
fn Theorem _ => "theorem"  Lemma _ => "lemma"  Goal _ => "show"  Aux _ => "have"; 
5820  86 

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type goal = 

6848  88 
(kind * (*result kind*) 
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string * (*result name*) 

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cterm list * (*result assumptions*) 

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(int > tactic) list * (*tactics to solve result assumptions*) 

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term) * (*result statement*) 

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(thm list * (*use facts*) 

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thm); (*goal: subgoals ==> statement*) 

5820  95 

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(* type mode *) 

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datatype mode = Forward  ForwardChain  Backward; 

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val mode_name = 

6798  102 
enclose "`" "'" o 
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(fn Forward => "state"  ForwardChain => "chain"  Backward => "prove"); 

5820  104 

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(* type node *) 

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type node = 

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{context: context, 

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facts: thm list option, 
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mode: mode, 
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goal: goal option}; 

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fun make_node (context, facts, mode, goal) = 

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{context = context, facts = facts, mode = mode, goal = goal}: node; 

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(* datatype state *) 

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datatype state = 

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State of 

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node * (*current*) 

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node list; (*parents wrt. block structure*) 

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exception STATE of string * state; 

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fun err_malformed name state = 

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raise STATE (name ^ ": internal error  malformed proof state", state); 

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fun map_current f (State ({context, facts, mode, goal}, nodes)) = 

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State (make_node (f (context, facts, mode, goal)), nodes); 

133 

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fun init_state thy = 

5875  135 
State (make_node (ProofContext.init thy, None, Forward, None), []); 
5820  136 

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(** basic proof state operations **) 

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(* context *) 

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fun context_of (State ({context, ...}, _)) = context; 

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val theory_of = ProofContext.theory_of o context_of; 

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val sign_of = ProofContext.sign_of o context_of; 

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fun map_context f = map_current (fn (ctxt, facts, mode, goal) => (f ctxt, facts, mode, goal)); 

148 

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fun map_context_result f (state as State ({context, facts, mode, goal}, nodes)) = 

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let val (context', result) = f context 

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in (State (make_node (context', facts, mode, goal), nodes), result) end; 

152 

153 

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fun put_data kind f = map_context o ProofContext.put_data kind f; 

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val declare_term = map_context o ProofContext.declare_term; 

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val add_binds = map_context o ProofContext.add_binds_i; 

6790  157 
val auto_bind_goal = map_context o ProofContext.auto_bind_goal; 
6798  158 
val auto_bind_facts = map_context oo ProofContext.auto_bind_facts; 
6091  159 
val put_thms = map_context o ProofContext.put_thms; 
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val put_thmss = map_context o ProofContext.put_thmss; 

5820  161 

162 

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(* facts *) 

164 

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fun the_facts (State ({facts = Some facts, ...}, _)) = facts 

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 the_facts state = raise STATE ("No current facts available", state); 

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fun the_fact state = 
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(case the_facts state of 

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[fact] => fact 

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 _ => raise STATE ("Single fact expected", state)); 

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6848  173 
fun assert_facts state = (the_facts state; state); 
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5820  175 
fun put_facts facts state = 
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state 

177 
> map_current (fn (ctxt, _, mode, goal) => (ctxt, facts, mode, goal)) 

6798  178 
> put_thms ("facts", if_none facts []); 
5820  179 

180 
val reset_facts = put_facts None; 

181 

182 
fun have_facts (name, facts) state = 

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state 

184 
> put_facts (Some facts) 

6798  185 
> put_thms (name, facts); 
5820  186 

187 
fun these_facts (state, ths) = have_facts ths state; 

188 
fun fetch_facts (State ({facts, ...}, _)) = put_facts facts; 

189 

190 

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(* goal *) 

192 

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fun find_goal i (State ({goal = Some goal, ...}, _)) = (i, goal) 

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 find_goal i (State ({goal = None, ...}, node :: nodes)) = 

195 
find_goal (i + 1) (State (node, nodes)) 

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 find_goal _ (state as State (_, [])) = err_malformed "find_goal" state; 

197 

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fun put_goal goal = map_current (fn (ctxt, facts, mode, _) => (ctxt, facts, mode, goal)); 

199 

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fun map_goal f (State ({context, facts, mode, goal = Some goal}, nodes)) = 

201 
State (make_node (context, facts, mode, Some (f goal)), nodes) 

202 
 map_goal f (State (nd, node :: nodes)) = 

203 
let val State (node', nodes') = map_goal f (State (node, nodes)) 

204 
in State (nd, node' :: nodes') end 

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 map_goal _ state = state; 

206 

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fun goal_facts get state = 

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state 

209 
> map_goal (fn (result, (_, thm)) => (result, (get state, thm))); 

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fun use_facts state = 

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state 

213 
> goal_facts the_facts 

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> reset_facts; 

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(* mode *) 

218 

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fun get_mode (State ({mode, ...}, _)) = mode; 

220 
fun put_mode mode = map_current (fn (ctxt, facts, _, goal) => (ctxt, facts, mode, goal)); 

221 

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val enter_forward = put_mode Forward; 

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val enter_forward_chain = put_mode ForwardChain; 

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val enter_backward = put_mode Backward; 

225 

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fun assert_mode pred state = 

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let val mode = get_mode state in 

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if pred mode then state 

6731  229 
else raise STATE ("Illegal application of proof command in " ^ mode_name mode ^ " mode", state) 
5820  230 
end; 
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fun is_chain state = get_mode state = ForwardChain; 

233 
val assert_forward = assert_mode (equal Forward); 

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val assert_forward_or_chain = assert_mode (equal Forward orf equal ForwardChain); 

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val assert_backward = assert_mode (equal Backward); 

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237 

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(* blocks *) 

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6776  240 
fun level (State (_, nodes)) = length nodes; 
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5820  242 
fun open_block (State (node, nodes)) = State (node, node :: nodes); 
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fun new_block state = 

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state 

246 
> open_block 

247 
> put_goal None; 

248 

249 
fun close_block (State (_, node :: nodes)) = State (node, nodes) 

250 
 close_block state = raise STATE ("Unbalanced block parentheses", state); 

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(** print_state **) 

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6529  256 
val verbose = ProofContext.verbose; 
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6756  258 
fun print_facts _ None = () 
259 
 print_facts s (Some ths) = 

260 
Pretty.writeln (Pretty.big_list (s ^ " facts:") (map Display.pretty_thm ths)); 

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5820  262 
fun print_state (state as State ({context, facts, mode, goal = _}, nodes)) = 
263 
let 

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print_state: use begin_goal from Goals.current_goals_markers;
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val ref (_, _, begin_goal) = Goals.current_goals_markers; 
5820  265 

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fun levels_up 0 = "" 

267 
 levels_up i = " (" ^ string_of_int i ^ " levels up)"; 

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6848  269 
fun print_goal (i, ((kind, name, _, _, _), (goal_facts, thm))) = 
6756  270 
(print_facts "Using" (if null goal_facts then None else Some goal_facts); 
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writeln (kind_name kind ^ " " ^ quote name ^ levels_up (i div 2) ^ ":"); 

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print_state: use begin_goal from Goals.current_goals_markers;
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Locale.print_goals_marker begin_goal (! goals_limit) thm); 
6848  273 

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val ctxt_strings = ProofContext.strings_of_context context; 

5820  275 
in 
6262  276 
writeln ("Nesting level: " ^ string_of_int (length nodes div 2)); 
5820  277 
writeln ""; 
6798  278 
writeln (mode_name mode ^ " mode"); 
5993  279 
writeln ""; 
6529  280 
if ! verbose orelse mode = Forward then 
6848  281 
(if null ctxt_strings then () else (seq writeln ctxt_strings; writeln ""); 
6756  282 
print_facts "Current" facts; 
6529  283 
print_goal (find_goal 0 state)) 
6756  284 
else if mode = ForwardChain then print_facts "Picking" facts 
6529  285 
else print_goal (find_goal 0 state) 
5820  286 
end; 
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(** proof steps **) 

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(* datatype method *) 

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6848  294 
datatype method = Method of thm list > tactic; 
5820  295 
val method = Method; 
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297 

298 
(* refine goal *) 

299 

300 
fun check_sign sg state = 

301 
if Sign.subsig (sg, sign_of state) then state 

302 
else raise STATE ("Bad signature of result: " ^ Sign.str_of_sg sg, state); 

303 

304 
fun refine meth_fun (state as State ({context, ...}, _)) = 

6848  305 
let 
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val Method meth = meth_fun context; 

307 
val (_, (result, (facts, thm))) = find_goal 0 state; 

5820  308 

6848  309 
fun refn thm' = 
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state 

311 
> check_sign (Thm.sign_of_thm thm') 

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> map_goal (K (result, (facts, thm'))); 

313 
in Seq.map refn (meth facts thm) end; 

5820  314 

315 

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(* prepare result *) 

317 

318 
fun varify_frees names thm = 

319 
let 

320 
fun get_free x (None, t as Free (y, _)) = if x = y then Some t else None 

321 
 get_free _ (opt, _) = opt; 

322 

323 
fun find_free t x = foldl_aterms (get_free x) (None, t); 

324 

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val {sign, maxidx, prop, ...} = Thm.rep_thm thm; 

326 
val frees = map (Thm.cterm_of sign) (mapfilter (find_free prop) names); 

327 
in 

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thm 

329 
> Drule.forall_intr_list frees 

330 
> Drule.forall_elim_vars (maxidx + 1) 

331 
end; 

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6790  333 
fun varify_tfrees thm = 
334 
let 

335 
val {hyps, prop, ...} = Thm.rep_thm thm; 

336 
val frees = foldr Term.add_term_frees (prop :: hyps, []); 

337 
val leave_tfrees = foldr Term.add_term_tfree_names (frees, []); 

338 
in thm > Thm.varifyT' leave_tfrees end; 

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5820  340 
fun implies_elim_hyps thm = 
341 
foldl (uncurry Thm.implies_elim) (thm, map Thm.assume (Drule.cprems_of thm)); 

342 

6848  343 

5820  344 
fun prep_result state asms t raw_thm = 
345 
let 

346 
val ctxt = context_of state; 

347 
fun err msg = raise STATE (msg, state); 

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349 
val ngoals = Thm.nprems_of raw_thm; 

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val _ = 

351 
if ngoals = 0 then () 

352 
else (Locale.print_goals ngoals raw_thm; err (string_of_int ngoals ^ " unsolved goal(s)!")); 

353 

354 
val thm = 

355 
raw_thm RS Drule.rev_triv_goal 

356 
> implies_elim_hyps 

357 
> Drule.implies_intr_list asms 

6731  358 
> varify_frees (ProofContext.fixed_names ctxt) 
6790  359 
> varify_tfrees; 
5820  360 

361 
val {hyps, prop, sign, ...} = Thm.rep_thm thm; 

362 
val tsig = Sign.tsig_of sign; 

363 
in 

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(* FIXME 

365 
if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then 

366 
warning ("Proved a different theorem: " ^ Sign.string_of_term sign prop) 

367 
else (); 

368 
*) 

369 
if not (null hyps) then 

370 
err ("Additional hypotheses:\n" ^ cat_lines (map (Sign.string_of_term sign) hyps)) 

371 
(* FIXME else if not (Pattern.matches tsig (t, Logic.skip_flexpairs prop)) then 

372 
err ("Proved a different theorem: " ^ Sign.string_of_term sign prop) *) 

6790  373 
else (thm, prop) 
5820  374 
end; 
375 

376 

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(* prepare final result *) 

378 

379 
fun strip_flexflex thm = 

380 
Seq.hd (Thm.flexflex_rule thm) handle THM _ => thm; 

381 

382 
fun final_result state pre_thm = 

383 
let 

384 
val thm = 

385 
pre_thm 

386 
> strip_flexflex 

387 
> Thm.strip_shyps 

388 
> Drule.standard; 

389 

390 
val str_of_sort = Sign.str_of_sort (Thm.sign_of_thm thm); 

391 
val xshyps = Thm.extra_shyps thm; 

392 
in 

393 
if not (null xshyps) then 

394 
raise STATE ("Extra sort hypotheses: " ^ commas (map str_of_sort xshyps), state) 

395 
else thm 

396 
end; 

397 

398 

399 
(* solve goal *) 

400 

6848  401 
fun REV_RANGE _ [] = all_tac 
402 
 REV_RANGE k (tac :: tacs) = tac k THEN REV_RANGE (k  1) tacs; 

403 

404 
fun solve_goal rule tacs state = 

5820  405 
let 
6848  406 
val rev_tacs = rev tacs; 
407 
val n = length rev_tacs  1; 

408 

5820  409 
val (_, (result, (facts, thm))) = find_goal 0 state; 
6848  410 
val thms' = FIRSTGOAL (rtac rule THEN' (fn i => REV_RANGE (i + n) rev_tacs)) thm; 
5820  411 
in Seq.map (fn thm' => map_goal (K (result, (facts, thm'))) state) thms' end; 
412 

413 

414 

415 
(*** structured proof commands ***) 

416 

417 
(** context **) 

418 

419 
(* bind *) 

420 

421 
fun gen_bind f x state = 

422 
state 

423 
> assert_forward 

424 
> map_context (f x) 

425 
> reset_facts; 

426 

427 
val bind = gen_bind ProofContext.add_binds; 

428 
val bind_i = gen_bind ProofContext.add_binds_i; 

429 

430 
val match_bind = gen_bind ProofContext.match_binds; 

431 
val match_bind_i = gen_bind ProofContext.match_binds_i; 

432 

433 

6091  434 
(* have_thmss *) 
5820  435 

6091  436 
fun have_thmss name atts ths_atts state = 
5820  437 
state 
438 
> assert_forward 

6091  439 
> map_context_result (ProofContext.have_thmss (PureThy.default_name name) atts ths_atts) 
5820  440 
> these_facts; 
441 

442 

443 
(* fix *) 

444 

445 
fun gen_fix f xs state = 

446 
state 

447 
> assert_forward 

448 
> map_context (f xs) 

449 
> reset_facts; 

450 

451 
val fix = gen_fix ProofContext.fix; 

452 
val fix_i = gen_fix ProofContext.fix_i; 

453 

454 

455 
(* assume *) 

456 

6848  457 
fun gen_assume f tac name atts props state = 
5820  458 
state 
459 
> assert_forward 

6848  460 
> map_context_result (f tac (PureThy.default_name name) atts props) 
6798  461 
> (fn (st, (facts, prems)) => 
462 
(st, facts) 

463 
> these_facts 

464 
> put_thms ("prems", prems)); 

5820  465 

466 
val assume = gen_assume ProofContext.assume; 

467 
val assume_i = gen_assume ProofContext.assume_i; 

468 

469 

470 

471 
(** goals **) 

472 

473 
(* forward chaining *) 

474 

475 
fun chain state = 

476 
state 

477 
> assert_forward 

6848  478 
> assert_facts 
5820  479 
> enter_forward_chain; 
480 

481 
fun from_facts facts state = 

482 
state 

483 
> put_facts (Some facts) 

484 
> chain; 

485 

486 

487 
(* setup goals *) 

488 

5936  489 
fun setup_goal opt_block prepp kind name atts raw_propp state = 
5820  490 
let 
5936  491 
val (state', concl) = 
492 
state 

493 
> assert_forward_or_chain 

494 
> enter_forward 

495 
> opt_block 

496 
> map_context_result (fn c => prepp (c, raw_propp)); 

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497 
val cterm_of = Thm.cterm_of (sign_of state); 
5820  498 

6848  499 
val (casms, asm_tacs) = Library.split_list (ProofContext.assumptions (context_of state')); 
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500 
val cprems = map cterm_of (Logic.strip_imp_prems concl); 
6848  501 
val prem_tacs = replicate (length cprems) (K all_tac); 
502 

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503 
val prop = Logic.list_implies (map Thm.term_of casms, concl); 
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504 
val cprop = cterm_of prop; 
5820  505 
val thm = Drule.mk_triv_goal cprop; 
506 
in 

5936  507 
state' 
6848  508 
> put_goal (Some ((kind atts, (PureThy.default_name name), casms @ cprems, 
509 
asm_tacs @ prem_tacs, prop), ([], thm))) 

6790  510 
> auto_bind_goal prop 
5820  511 
> (if is_chain state then use_facts else reset_facts) 
512 
> new_block 

513 
> enter_backward 

514 
end; 

515 

516 

517 
(*global goals*) 

518 
fun global_goal prep kind name atts x thy = 

519 
setup_goal I prep kind name atts x (init_state thy); 

520 

5936  521 
val theorem = global_goal ProofContext.bind_propp Theorem; 
522 
val theorem_i = global_goal ProofContext.bind_propp_i Theorem; 

523 
val lemma = global_goal ProofContext.bind_propp Lemma; 

524 
val lemma_i = global_goal ProofContext.bind_propp_i Lemma; 

5820  525 

526 

527 
(*local goals*) 

528 
fun local_goal prep kind name atts x = 

529 
setup_goal open_block prep kind name atts x; 

530 

5936  531 
val show = local_goal ProofContext.bind_propp Goal; 
532 
val show_i = local_goal ProofContext.bind_propp_i Goal; 

533 
val have = local_goal ProofContext.bind_propp Aux; 

534 
val have_i = local_goal ProofContext.bind_propp_i Aux; 

5820  535 

536 

537 

538 
(** blocks **) 

539 

540 
(* begin_block *) 

541 

542 
fun begin_block state = 

543 
state 

544 
> assert_forward 

545 
> new_block 

546 
> reset_facts 

547 
> open_block; 

548 

549 

550 
(* next_block *) 

551 

552 
fun next_block state = 

553 
state 

554 
> assert_forward 

555 
> close_block 

556 
> new_block; 

557 

558 

559 

560 
(** conclusions **) 

561 

562 
(* current goal *) 

563 

564 
fun current_goal (State ({goal = Some goal, ...}, _)) = goal 

565 
 current_goal state = raise STATE ("No current goal!", state); 

566 

6404  567 
fun assert_current_goal true (state as State ({goal = None, ...}, _)) = 
568 
raise STATE ("No goal in this block!", state) 

569 
 assert_current_goal false (state as State ({goal = Some _, ...}, _)) = 

570 
raise STATE ("Goal present in this block!", state) 

571 
 assert_current_goal _ state = state; 

5820  572 

573 
fun assert_bottom true (state as State (_, _ :: _)) = 

574 
raise STATE ("Not at bottom of proof!", state) 

575 
 assert_bottom false (state as State (_, [])) = 

576 
raise STATE ("Already at bottom of proof!", state) 

577 
 assert_bottom _ state = state; 

578 

6404  579 
val at_bottom = can (assert_bottom true o close_block); 
580 

5820  581 

582 
(* finish proof *) 

583 

584 
fun check_finished state states = 

585 
(case Seq.pull states of 

586 
None => raise STATE ("Failed to finish proof", state) 

587 
 Some s_sq => Seq.cons s_sq); 

588 

6404  589 
fun finish_proof bot finalize state = 
5820  590 
state 
591 
> assert_forward 

592 
> close_block 

593 
> assert_bottom bot 

6404  594 
> assert_current_goal true 
595 
> finalize 

5820  596 
> check_finished state; 
597 

598 

6404  599 
(* end_block *) 
600 

601 
fun end_block state = 

602 
state 

603 
> assert_forward 

604 
> close_block 

605 
> assert_current_goal false 

606 
> close_block 

607 
> fetch_facts state; 

608 

609 

610 
(* local_qed *) 

5820  611 

6731  612 
fun finish_local print_result state = 
5820  613 
let 
6848  614 
val ((kind, name, asms, tacs, t), (_, raw_thm)) = current_goal state; 
6790  615 
val (result, result_prop) = prep_result state asms t raw_thm; 
5820  616 
val (atts, opt_solve) = 
617 
(case kind of 

6848  618 
Goal atts => (atts, solve_goal result tacs) 
5820  619 
 Aux atts => (atts, Seq.single) 
620 
 _ => raise STATE ("No local goal!", state)); 

621 
in 

6731  622 
print_result {kind = kind_name kind, name = name, thm = result}; 
5820  623 
state 
624 
> close_block 

6798  625 
> auto_bind_facts name [result_prop] 
6091  626 
> have_thmss name atts [Thm.no_attributes [result]] 
5820  627 
> opt_solve 
628 
end; 

629 

6731  630 
fun local_qed finalize print_result state = 
6404  631 
state 
632 
> finish_proof false finalize 

6731  633 
> (Seq.flat o Seq.map (finish_local print_result)); 
5820  634 

635 

6404  636 
(* global_qed *) 
5820  637 

638 
fun finish_global alt_name alt_atts state = 

639 
let 

6848  640 
val ((kind, def_name, asms, _, t), (_, raw_thm)) = current_goal state; 
6790  641 
val result = final_result state (#1 (prep_result state asms t raw_thm)); 
5820  642 

643 
val name = if_none alt_name def_name; 

644 
val atts = 

645 
(case kind of 

646 
Theorem atts => if_none alt_atts atts 

6091  647 
 Lemma atts => (if_none alt_atts atts) @ [Drule.tag_lemma] 
5820  648 
 _ => raise STATE ("No global goal!", state)); 
649 

6091  650 
val (thy', result') = PureThy.store_thm ((name, result), atts) (theory_of state); 
6529  651 
in (thy', {kind = kind_name kind, name = name, thm = result'}) end; 
5820  652 

6404  653 
fun global_qed finalize alt_name alt_atts state = 
5820  654 
state 
6404  655 
> finish_proof true finalize 
5820  656 
> Seq.hd 
657 
> finish_global alt_name alt_atts; 

658 

659 

660 
end; 