File intuitionistic.ML

(*  Title:      Tools/intuitionistic.ML
    Author:     Stefan Berghofer, TU Muenchen

Simple intuitionistic proof search.
*)

signature INTUITIONISTIC =
sig
  val prover_tac: Proof.context -> int option -> int -> tactic
  val method_setup: bstring -> theory -> theory
end;

structure Intuitionistic: INTUITIONISTIC =
struct

(* main tactic *)

local

val remdups_tac = SUBGOAL (fn (g, i) =>
  let val prems = Logic.strip_assums_hyp g in
    REPEAT_DETERM_N (length prems - length (distinct op aconv prems))
    (Tactic.ematch_tac [Drule.remdups_rl] i THEN Tactic.eq_assume_tac i)
  end);

fun REMDUPS tac = tac THEN_ALL_NEW remdups_tac;

val bires_tac = Tactic.biresolution_from_nets_tac ContextRules.orderlist;

fun safe_step_tac ctxt =
  ContextRules.Swrap ctxt
   (eq_assume_tac ORELSE'
    bires_tac true (ContextRules.netpair_bang ctxt));

fun unsafe_step_tac ctxt =
  ContextRules.wrap ctxt
   (assume_tac APPEND'
    bires_tac false (ContextRules.netpair_bang ctxt) APPEND'
    bires_tac false (ContextRules.netpair ctxt));

fun step_tac ctxt i =
  REPEAT_DETERM1 (REMDUPS (safe_step_tac ctxt) i) ORELSE
  REMDUPS (unsafe_step_tac ctxt) i;

fun intprover_tac ctxt gs d lim = SUBGOAL (fn (g, i) => if d > lim then no_tac else
  let
    val ps = Logic.strip_assums_hyp g;
    val c = Logic.strip_assums_concl g;
  in
    if member (fn ((ps1, c1), (ps2, c2)) =>
        c1 aconv c2 andalso
        length ps1 = length ps2 andalso
        gen_eq_set (op aconv) (ps1, ps2)) gs (ps, c) then no_tac
    else (step_tac ctxt THEN_ALL_NEW intprover_tac ctxt ((ps, c) :: gs) (d + 1) lim) i
  end);

in

fun prover_tac ctxt opt_lim =
  SELECT_GOAL (DEEPEN (2, the_default 20 opt_lim) (intprover_tac ctxt [] 0) 4 1);

end;


(* method setup *)

local

val introN = "intro";
val elimN = "elim";
val destN = "dest";
val ruleN = "rule";

fun modifier name kind kind' att =
  Args.$$$ name |-- (kind >> K NONE || kind' |-- OuterParse.nat --| Args.colon >> SOME)
    >> (pair (I: Proof.context -> Proof.context) o att);

val modifiers =
 [modifier destN Args.bang_colon Args.bang ContextRules.dest_bang,
  modifier destN Args.colon (Scan.succeed ()) ContextRules.dest,
  modifier elimN Args.bang_colon Args.bang ContextRules.elim_bang,
  modifier elimN Args.colon (Scan.succeed ()) ContextRules.elim,
  modifier introN Args.bang_colon Args.bang ContextRules.intro_bang,
  modifier introN Args.colon (Scan.succeed ()) ContextRules.intro,
  Args.del -- Args.colon >> K (I, ContextRules.rule_del)];

val method =
  Method.bang_sectioned_args' modifiers (Scan.lift (Scan.option OuterParse.nat))
    (fn n => fn prems => fn ctxt => METHOD (fn facts =>
      HEADGOAL (Method.insert_tac (prems @ facts) THEN'
      ObjectLogic.atomize_prems_tac THEN' prover_tac ctxt n)));

in

fun method_setup name = Method.add_method (name, method, "intuitionistic proof search");

end;

end;