(* Title: HOL/TPTP/CASC_Setup.thy
Author: Jasmin Blanchette
Copyright 2011
Setup for Isabelle, Nitpick, and Refute for participating at CASC in the THF and
TNT divisions. This theory file should be loaded by the Isabelle theory files
generated by Geoff Sutcliffe's TPTP2X tool from the original THF0 files.
*)
theory CASC_Setup
imports Complex_Main
uses "../ex/sledgehammer_tactics.ML"
begin
consts
is_int :: "'a \<Rightarrow> bool"
is_rat :: "'a \<Rightarrow> bool"
overloading rat_is_int \<equiv> "is_int :: rat \<Rightarrow> bool"
begin
definition "rat_is_int (q\<Colon>rat) \<longleftrightarrow> (\<exists>n\<Colon>int. q = of_int n)"
end
overloading real_is_int \<equiv> "is_int :: real \<Rightarrow> bool"
begin
definition "real_is_int (x\<Colon>real) \<longleftrightarrow> x \<in> \<int>"
end
overloading real_is_rat \<equiv> "is_rat :: real \<Rightarrow> bool"
begin
definition "real_is_rat (x\<Colon>real) \<longleftrightarrow> x \<in> \<rat>"
end
consts
to_int :: "'a \<Rightarrow> int"
to_rat :: "'a \<Rightarrow> rat"
to_real :: "'a \<Rightarrow> real"
overloading rat_to_int \<equiv> "to_int :: rat \<Rightarrow> int"
begin
definition "rat_to_int (q\<Colon>rat) = floor q"
end
overloading real_to_int \<equiv> "to_int :: real \<Rightarrow> int"
begin
definition "real_to_int (x\<Colon>real) = floor x"
end
overloading int_to_rat \<equiv> "to_rat :: int \<Rightarrow> rat"
begin
definition "int_to_rat (n\<Colon>int) = (of_int n\<Colon>rat)"
end
overloading real_to_rat \<equiv> "to_rat :: real \<Rightarrow> rat"
begin
definition "real_to_rat (x\<Colon>real) = (inv real x\<Colon>rat)"
end
overloading int_to_real \<equiv> "to_real :: int \<Rightarrow> real"
begin
definition "int_to_real (n\<Colon>int) = real n"
end
overloading rat_to_real \<equiv> "to_real :: rat \<Rightarrow> real"
begin
definition "rat_to_real (x\<Colon>rat) = (of_rat x\<Colon>real)"
end
declare
rat_is_int_def [simp]
real_is_int_def [simp]
real_is_rat_def [simp]
rat_to_int_def [simp]
real_to_int_def [simp]
int_to_rat_def [simp]
real_to_rat_def [simp]
int_to_real_def [simp]
rat_to_real_def [simp]
lemma to_rat_is_int [intro, simp]: "is_int (to_rat (n\<Colon>int))"
by (metis int_to_rat_def rat_is_int_def)
lemma to_real_is_int [intro, simp]: "is_int (to_real (n\<Colon>int))"
by (metis Ints_real_of_int int_to_real_def real_is_int_def)
lemma to_real_is_rat [intro, simp]: "is_rat (to_real (q\<Colon>rat))"
by (metis Rats_of_rat rat_to_real_def real_is_rat_def)
lemma inj_of_rat [intro, simp]: "inj (of_rat\<Colon>rat\<Rightarrow>real)"
by (metis injI of_rat_eq_iff rat_to_real_def)
declare [[smt_oracle]]
refute_params [maxtime = 10000, no_assms, expect = genuine]
nitpick_params [timeout = none, card = 1-50, verbose, dont_box, no_assms,
batch_size = 1, expect = genuine]
ML {* Proofterm.proofs := 0 *}
ML {*
fun SOLVE_TIMEOUT seconds name tac st =
let
val result =
TimeLimit.timeLimit (Time.fromSeconds seconds)
(fn () => SINGLE (SOLVE tac) st) ()
handle TimeLimit.TimeOut => NONE
| ERROR _ => NONE
in
(case result of
NONE => (warning ("FAILURE: " ^ name); Seq.empty)
| SOME st' => (warning ("SUCCESS: " ^ name); Seq.single st'))
end
*}
ML {*
fun isabellep_tac ctxt max_secs =
SOLVE_TIMEOUT (max_secs div 10) "smt" (ALLGOALS (SMT_Solver.smt_tac ctxt []))
ORELSE
SOLVE_TIMEOUT (max_secs div 5) "sledgehammer"
(ALLGOALS (Sledgehammer_Tactics.sledgehammer_as_oracle_tac ctxt []
Sledgehammer_Filter.no_relevance_override))
ORELSE
SOLVE_TIMEOUT (max_secs div 10) "simp" (ALLGOALS (asm_full_simp_tac (simpset_of ctxt)))
ORELSE
SOLVE_TIMEOUT (max_secs div 20) "blast" (ALLGOALS (blast_tac ctxt))
ORELSE
SOLVE_TIMEOUT (max_secs div 10) "auto" (auto_tac ctxt
THEN ALLGOALS (Sledgehammer_Tactics.sledgehammer_as_oracle_tac ctxt []
Sledgehammer_Filter.no_relevance_override))
ORELSE
SOLVE_TIMEOUT (max_secs div 10) "metis"
(ALLGOALS (Metis_Tactic.metis_tac [] ATP_Problem_Generate.lam_liftingN ctxt []))
ORELSE
SOLVE_TIMEOUT (max_secs div 10) "fast" (ALLGOALS (fast_tac ctxt))
ORELSE
SOLVE_TIMEOUT (max_secs div 20) "best" (ALLGOALS (best_tac ctxt))
ORELSE
SOLVE_TIMEOUT (max_secs div 20) "arith" (ALLGOALS (Arith_Data.arith_tac ctxt))
ORELSE
SOLVE_TIMEOUT (max_secs div 10) "force" (ALLGOALS (force_tac ctxt))
ORELSE
SOLVE_TIMEOUT max_secs "fastforce" (ALLGOALS (fast_force_tac ctxt))
*}
method_setup isabellep = {*
Scan.lift (Scan.optional Parse.nat 6000) >>
(fn m => fn ctxt => SIMPLE_METHOD (isabellep_tac ctxt m))
*} "combination of Isabelle provers and oracles for CASC"
end