author  blanchet 
Wed, 15 Dec 2010 11:26:28 +0100  
changeset 41138  eb80538166b6 
parent 41137  8b634031b2a5 
child 41140  9c68004b8c9d 
permissions  rwrr 
40114  1 
(* Title: HOL/Tools/Sledgehammer/sledgehammer_atp_translate.ML 
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Author: Fabian Immler, TU Muenchen 
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Author: Makarius 
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Author: Jasmin Blanchette, TU Muenchen 
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Translation of HOL to FOL for Sledgehammer. 
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*) 
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40068  9 
signature SLEDGEHAMMER_ATP_TRANSLATE = 
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sig 
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type 'a problem = 'a ATP_Problem.problem 
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type translated_formula 
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datatype type_system = 
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Tags of bool  

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Preds of bool  

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Const_Args  

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No_Types 

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val precise_overloaded_args : bool Unsynchronized.ref 
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val fact_prefix : string 
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val conjecture_prefix : string 
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val is_fully_typed : type_system > bool 
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val types_dangerous_types : type_system > bool 
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val num_atp_type_args : theory > type_system > string > int 
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val translate_atp_fact : 
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Proof.context > (string * 'a) * thm 
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> translated_formula option * ((string * 'a) * thm) 
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val prepare_atp_problem : 
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Proof.context > bool > bool > type_system > bool > term list > term 
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> (translated_formula option * ((string * 'a) * thm)) list 
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> string problem * string Symtab.table * int * (string * 'a) list vector 
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end; 
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structure Sledgehammer_ATP_Translate (*### : SLEDGEHAMMER_ATP_TRANSLATE *) = 
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struct 
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open ATP_Problem 
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open Metis_Translate 
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open Sledgehammer_Util 
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(* FIXME: Remove references once appropriate defaults have been determined 
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empirically. *) 
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val precise_overloaded_args = Unsynchronized.ref false 
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val fact_prefix = "fact_" 
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val conjecture_prefix = "conj_" 
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val helper_prefix = "help_" 
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val class_rel_clause_prefix = "clrel_"; 
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val arity_clause_prefix = "arity_" 
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val tfree_prefix = "tfree_" 
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(* Freshness almost guaranteed! *) 
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val sledgehammer_weak_prefix = "Sledgehammer:" 
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type translated_formula = 
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{name: string, 
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kind: kind, 
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combformula: (name, combterm) formula, 
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ctypes_sorts: typ list} 
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datatype type_system = 
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Tags of bool  

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Preds of bool  

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Const_Args  

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No_Types 

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fun is_fully_typed (Tags full_types) = full_types 

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 is_fully_typed (Preds full_types) = full_types 

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 is_fully_typed _ = false 

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fun types_dangerous_types (Tags _) = true 
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 types_dangerous_types (Preds _) = true 
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 types_dangerous_types _ = false 
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(* This is an approximation. If it returns "true" for a constant that isn't 
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overloaded (i.e., that has one uniform definition), needless clutter is 
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generated; if it returns "false" for an overloaded constant, the ATP gets a 
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license to do unsound reasoning if the type system is "overloaded_args". *) 
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fun is_overloaded thy s = 
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not (!precise_overloaded_args) orelse 
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length (Defs.specifications_of (Theory.defs_of thy) s) > 1 
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fun needs_type_args thy type_sys s = 
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case type_sys of 
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Tags full_types => not full_types andalso is_overloaded thy s 
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 Preds full_types => is_overloaded thy s (* FIXME: could be more precise *) 
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 Const_Args => is_overloaded thy s 
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 No_Types => false 
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fun num_atp_type_args thy type_sys s = 
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if needs_type_args thy type_sys s then num_type_args thy s else 0 
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fun atp_type_literals_for_types type_sys Ts = 
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if type_sys = No_Types then [] else type_literals_for_types Ts 
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fun mk_anot phi = AConn (ANot, [phi]) 
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fun mk_aconn c phi1 phi2 = AConn (c, [phi1, phi2]) 
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fun mk_ahorn [] phi = phi 
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 mk_ahorn (phi :: phis) psi = 
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AConn (AImplies, [fold (mk_aconn AAnd) phis phi, psi]) 
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fun combformula_for_prop thy = 
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let 
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val do_term = combterm_from_term thy 
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fun do_quant bs q s T t' = 
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let val s = Name.variant (map fst bs) s in 
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do_formula ((s, T) :: bs) t' 
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#>> (fn phi => AQuant (q, [`make_bound_var s], phi)) 
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end 
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and do_conn bs c t1 t2 = 
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do_formula bs t1 ##>> do_formula bs t2 
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#>> (fn (phi1, phi2) => AConn (c, [phi1, phi2])) 
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and do_formula bs t = 
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case t of 
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@{const Not} $ t1 => 
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do_formula bs t1 #>> (fn phi => AConn (ANot, [phi])) 
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 Const (@{const_name All}, _) $ Abs (s, T, t') => 
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do_quant bs AForall s T t' 
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 Const (@{const_name Ex}, _) $ Abs (s, T, t') => 
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do_quant bs AExists s T t' 
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 @{const HOL.conj} $ t1 $ t2 => do_conn bs AAnd t1 t2 
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 @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2 
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 @{const HOL.implies} $ t1 $ t2 => do_conn bs AImplies t1 t2 
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 Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _])) $ t1 $ t2 => 
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do_conn bs AIff t1 t2 
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 _ => (fn ts => do_term bs (Envir.eta_contract t) 
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>> AAtom > union (op =) ts) 
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in do_formula [] end 
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val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm 
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fun concealed_bound_name j = sledgehammer_weak_prefix ^ Int.toString j 
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fun conceal_bounds Ts t = 
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subst_bounds (map (Free o apfst concealed_bound_name) 
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(0 upto length Ts  1 ~~ Ts), t) 
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fun reveal_bounds Ts = 
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subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j)) 
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(0 upto length Ts  1 ~~ Ts)) 
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140 

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141 
(* Removes the lambdas from an equation of the form "t = (%x. u)". 
39890  142 
(Cf. "extensionalize_theorem" in "Meson_Clausify".) *) 
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143 
fun extensionalize_term t = 
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144 
let 
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145 
fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t' 
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146 
 aux j (t as Const (s, Type (_, [Type (_, [_, T']), 
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147 
Type (_, [_, res_T])])) 
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148 
$ t2 $ Abs (var_s, var_T, t')) = 
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if s = @{const_name HOL.eq} orelse s = @{const_name "=="} then 
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150 
let val var_t = Var ((var_s, j), var_T) in 
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151 
Const (s, T' > T' > res_T) 
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152 
$ betapply (t2, var_t) $ subst_bound (var_t, t') 
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153 
> aux (j + 1) 
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154 
end 
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155 
else 
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156 
t 
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157 
 aux _ t = t 
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158 
in aux (maxidx_of_term t + 1) t end 
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159 

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160 
fun introduce_combinators_in_term ctxt kind t = 
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161 
let val thy = ProofContext.theory_of ctxt in 
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162 
if Meson.is_fol_term thy t then 
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163 
t 
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164 
else 
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165 
let 
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166 
fun aux Ts t = 
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167 
case t of 
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168 
@{const Not} $ t1 => @{const Not} $ aux Ts t1 
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169 
 (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') => 
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170 
t0 $ Abs (s, T, aux (T :: Ts) t') 
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171 
 (t0 as Const (@{const_name All}, _)) $ t1 => 
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aux Ts (t0 $ eta_expand Ts t1 1) 
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173 
 (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') => 
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174 
t0 $ Abs (s, T, aux (T :: Ts) t') 
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 (t0 as Const (@{const_name Ex}, _)) $ t1 => 
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176 
aux Ts (t0 $ eta_expand Ts t1 1) 
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 (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 
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 (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 
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 (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 
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 (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _]))) 
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$ t1 $ t2 => 
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182 
t0 $ aux Ts t1 $ aux Ts t2 
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183 
 _ => if not (exists_subterm (fn Abs _ => true  _ => false) t) then 
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184 
t 
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185 
else 
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186 
t > conceal_bounds Ts 
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187 
> Envir.eta_contract 
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188 
> cterm_of thy 
39890  189 
> Meson_Clausify.introduce_combinators_in_cterm 
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190 
> prop_of > Logic.dest_equals > snd 
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191 
> reveal_bounds Ts 
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192 
val (t, ctxt') = Variable.import_terms true [t] ctxt >> the_single 
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193 
in t > aux [] > singleton (Variable.export_terms ctxt' ctxt) end 
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194 
handle THM _ => 
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195 
(* A type variable of sort "{}" will make abstraction fail. *) 
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196 
if kind = Conjecture then HOLogic.false_const 
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197 
else HOLogic.true_const 
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198 
end 
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199 

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200 
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the 
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201 
same in Sledgehammer to prevent the discovery of unreplable proofs. *) 
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202 
fun freeze_term t = 
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203 
let 
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204 
fun aux (t $ u) = aux t $ aux u 
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205 
 aux (Abs (s, T, t)) = Abs (s, T, aux t) 
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206 
 aux (Var ((s, i), T)) = 
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207 
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T) 
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208 
 aux t = t 
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209 
in t > exists_subterm is_Var t ? aux end 
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210 

38604  211 
(* "Object_Logic.atomize_term" isn't as powerful as it could be; for example, 
212 
it leaves metaequalities over "prop"s alone. *) 

38605  213 
val atomize_term = 
214 
let 

215 
fun aux (@{const Trueprop} $ t1) = t1 

216 
 aux (Const (@{const_name all}, _) $ Abs (s, T, t')) = 

217 
HOLogic.all_const T $ Abs (s, T, aux t') 

218 
 aux (@{const "==>"} $ t1 $ t2) = HOLogic.mk_imp (pairself aux (t1, t2)) 

219 
 aux (Const (@{const_name "=="}, Type (_, [@{typ prop}, _])) $ t1 $ t2) = 

220 
HOLogic.eq_const HOLogic.boolT $ aux t1 $ aux t2 

221 
 aux (Const (@{const_name "=="}, Type (_, [T, _])) $ t1 $ t2) = 

222 
HOLogic.eq_const T $ t1 $ t2 

223 
 aux _ = raise Fail "aux" 

224 
in perhaps (try aux) end 

38604  225 

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226 
(* making fact and conjecture formulas *) 
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227 
fun make_formula ctxt presimp name kind t = 
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228 
let 
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229 
val thy = ProofContext.theory_of ctxt 
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230 
val t = t > Envir.beta_eta_contract 
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231 
> transform_elim_term 
38604  232 
> atomize_term 
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233 
val need_trueprop = (fastype_of t = HOLogic.boolT) 
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234 
val t = t > need_trueprop ? HOLogic.mk_Trueprop 
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235 
> extensionalize_term 
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236 
> presimp ? presimplify_term thy 
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237 
> perhaps (try (HOLogic.dest_Trueprop)) 
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238 
> introduce_combinators_in_term ctxt kind 
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239 
> kind <> Axiom ? freeze_term 
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240 
val (combformula, ctypes_sorts) = combformula_for_prop thy t [] 
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241 
in 
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242 
{name = name, combformula = combformula, kind = kind, 
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243 
ctypes_sorts = ctypes_sorts} 
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244 
end 
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245 

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246 
fun make_fact ctxt presimp ((name, _), th) = 
38618  247 
case make_formula ctxt presimp name Axiom (prop_of th) of 
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248 
{combformula = AAtom (CombConst (("c_True", _), _, _)), ...} => NONE 
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249 
 formula => SOME formula 
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250 
fun make_conjecture ctxt ts = 
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251 
let val last = length ts  1 in 
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252 
map2 (fn j => make_formula ctxt true (Int.toString j) 
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253 
(if j = last then Conjecture else Hypothesis)) 
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254 
(0 upto last) ts 
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255 
end 
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256 

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257 
(** Helper facts **) 
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258 

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259 
fun count_combterm (CombConst ((s, _), _, _)) = 
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260 
Symtab.map_entry s (Integer.add 1) 
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261 
 count_combterm (CombVar _) = I 
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262 
 count_combterm (CombApp (t1, t2)) = fold count_combterm [t1, t2] 
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263 
fun count_combformula (AQuant (_, _, phi)) = count_combformula phi 
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264 
 count_combformula (AConn (_, phis)) = fold count_combformula phis 
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 count_combformula (AAtom tm) = count_combterm tm 
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fun count_translated_formula ({combformula, ...} : translated_formula) = 
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count_combformula combformula 
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268 

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val optional_helpers = 
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[(["c_COMBI"], @{thms Meson.COMBI_def}), 
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(["c_COMBK"], @{thms Meson.COMBK_def}), 
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(["c_COMBB"], @{thms Meson.COMBB_def}), 
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(["c_COMBC"], @{thms Meson.COMBC_def}), 
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(["c_COMBS"], @{thms Meson.COMBS_def})] 
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val optional_fully_typed_helpers = 
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[(["c_True", "c_False", "c_If"], @{thms True_or_False}), 
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(["c_If"], @{thms if_True if_False})] 
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val mandatory_helpers = @{thms Metis.fequal_def} 
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279 

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val init_counters = 
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[optional_helpers, optional_fully_typed_helpers] > maps (maps fst) 
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> sort_distinct string_ord > map (rpair 0) > Symtab.make 
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283 

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fun get_helper_facts ctxt is_FO type_sys conjectures facts = 
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let 
40069  286 
val ct = 
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fold (fold count_translated_formula) [conjectures, facts] init_counters 
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fun is_needed c = the (Symtab.lookup ct c) > 0 
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fun baptize th = ((Thm.get_name_hint th, false), th) 
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in 
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(optional_helpers 
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> is_fully_typed type_sys ? append optional_fully_typed_helpers 
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> maps (fn (ss, ths) => 
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if exists is_needed ss then map baptize ths else [])) @ 
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(if is_FO then [] else map baptize mandatory_helpers) 
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> map_filter (make_fact ctxt false) 
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297 
end 
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298 

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fun translate_atp_fact ctxt = `(make_fact ctxt true) 
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fun translate_formulas ctxt type_sys hyp_ts concl_t rich_facts = 
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let 
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val thy = ProofContext.theory_of ctxt 
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val fact_ts = map (prop_of o snd o snd) rich_facts 
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val (facts, fact_names) = 
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rich_facts 
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> map_filter (fn (NONE, _) => NONE 
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 (SOME fact, (name, _)) => SOME (fact, name)) 
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> ListPair.unzip 
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(* Remove existing facts from the conjecture, as this can dramatically 
39005  311 
boost an ATP's performance (for some reason). *) 
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val hyp_ts = hyp_ts > filter_out (member (op aconv) fact_ts) 
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val goal_t = Logic.list_implies (hyp_ts, concl_t) 
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val is_FO = Meson.is_fol_term thy goal_t 
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val subs = tfree_classes_of_terms [goal_t] 
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val supers = tvar_classes_of_terms fact_ts 
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val tycons = type_consts_of_terms thy (goal_t :: fact_ts) 
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(* TFrees in the conjecture; TVars in the facts *) 
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val conjectures = make_conjecture ctxt (hyp_ts @ [concl_t]) 
41134  320 
val helper_facts = get_helper_facts ctxt is_FO type_sys conjectures facts 
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val (supers', arity_clauses) = 
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if type_sys = No_Types then ([], []) 
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else make_arity_clauses thy tycons supers 
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val class_rel_clauses = make_class_rel_clauses thy subs supers' 
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in 
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(fact_names > map single > Vector.fromList, 
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327 
(conjectures, facts, helper_facts, class_rel_clauses, arity_clauses)) 
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328 
end 
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329 

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fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t]) 
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331 

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fun fo_term_for_combtyp (CombTVar name) = ATerm (name, []) 
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 fo_term_for_combtyp (CombTFree name) = ATerm (name, []) 
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 fo_term_for_combtyp (CombType (name, tys)) = 
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ATerm (name, map fo_term_for_combtyp tys) 
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336 

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fun fo_literal_for_type_literal (TyLitVar (class, name)) = 
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(true, ATerm (class, [ATerm (name, [])])) 
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 fo_literal_for_type_literal (TyLitFree (class, name)) = 
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(true, ATerm (class, [ATerm (name, [])])) 
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341 

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fun formula_for_fo_literal (pos, t) = AAtom t > not pos ? mk_anot 
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343 

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(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are 
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345 
considered dangerous because their "exhaust" properties can easily lead to 
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346 
unsound ATP proofs. The checks below are an (unsound) approximation of 
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347 
finiteness. *) 
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348 

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fun is_dtyp_dangerous _ (Datatype_Aux.DtTFree _) = true 
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 is_dtyp_dangerous ctxt (Datatype_Aux.DtType (s, Us)) = 
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is_type_constr_dangerous ctxt s andalso forall (is_dtyp_dangerous ctxt) Us 
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 is_dtyp_dangerous _ (Datatype_Aux.DtRec _) = false 
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353 
and is_type_dangerous ctxt (Type (s, Ts)) = 
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is_type_constr_dangerous ctxt s andalso forall (is_type_dangerous ctxt) Ts 
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355 
 is_type_dangerous ctxt _ = false 
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356 
and is_type_constr_dangerous ctxt s = 
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357 
let val thy = ProofContext.theory_of ctxt in 
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358 
case Datatype_Data.get_info thy s of 
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359 
SOME {descr, ...} => 
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forall (fn (_, (_, _, constrs)) => 
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forall (forall (is_dtyp_dangerous ctxt) o snd) constrs) descr 
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362 
 NONE => 
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363 
case Typedef.get_info ctxt s of 
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364 
({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type 
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365 
 [] => true 
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366 
end 
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367 

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fun is_combtyp_dangerous ctxt (CombType ((s, _), tys)) = 
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(case strip_prefix_and_unascii type_const_prefix s of 
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SOME s' => forall (is_combtyp_dangerous ctxt) tys andalso 
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371 
is_type_constr_dangerous ctxt (invert_const s') 
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372 
 NONE => false) 
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 is_combtyp_dangerous _ _ = false 
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374 

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fun should_tag_with_type ctxt (Tags full_types) ty = 
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376 
full_types orelse is_combtyp_dangerous ctxt ty 
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377 
 should_tag_with_type _ _ _ = false 
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378 

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379 
fun fo_term_for_combterm ctxt type_sys = 
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380 
let 
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381 
val thy = ProofContext.theory_of ctxt 
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382 
fun aux top_level u = 
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383 
let 
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384 
val (head, args) = strip_combterm_comb u 
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385 
val (x, ty_args) = 
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386 
case head of 
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387 
CombConst (name as (s, s'), _, ty_args) => 
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388 
(case strip_prefix_and_unascii const_prefix s of 
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389 
NONE => 
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390 
if s = "equal" then 
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391 
if top_level andalso length args = 2 then (name, []) 
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392 
else (("c_fequal", @{const_name Metis.fequal}), ty_args) 
30bedf58b177
implemented new type system encoding "overload_args", which is more lightweight than "const_args" (the unsound default) and hopefully almost as sound
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393 
else 
30bedf58b177
implemented new type system encoding "overload_args", which is more lightweight than "const_args" (the unsound default) and hopefully almost as sound
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394 
(name, ty_args) 
30bedf58b177
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395 
 SOME s'' => 
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396 
let 
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397 
val s'' = invert_const s'' 
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398 
val ty_args = 
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399 
if needs_type_args thy type_sys s'' then ty_args else [] 
30bedf58b177
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400 
in 
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diff
changeset

401 
if top_level then 
30bedf58b177
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diff
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402 
case s of 
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403 
"c_False" => (("$false", s'), []) 
30bedf58b177
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404 
 "c_True" => (("$true", s'), []) 
30bedf58b177
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405 
 _ => (name, ty_args) 
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406 
else 
30bedf58b177
implemented new type system encoding "overload_args", which is more lightweight than "const_args" (the unsound default) and hopefully almost as sound
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407 
(name, ty_args) 
30bedf58b177
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408 
end) 
38282
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409 
 CombVar (name, _) => (name, []) 
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410 
 CombApp _ => raise Fail "impossible \"CombApp\"" 
41138
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diff
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411 
val t = 
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412 
ATerm (x, map fo_term_for_combtyp ty_args @ map (aux false) args) 
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413 
val ty = combtyp_of u 
38282
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414 
in 
41138
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415 
t > (if should_tag_with_type ctxt type_sys ty then 
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416 
tag_with_type (fo_term_for_combtyp ty) 
41134  417 
else 
418 
I) 

38282
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419 
end 
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420 
in aux true end 
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421 

41138
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422 
fun formula_for_combformula ctxt type_sys = 
38282
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423 
let 
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424 
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi) 
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425 
 aux (AConn (c, phis)) = AConn (c, map aux phis) 
41138
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426 
 aux (AAtom tm) = AAtom (fo_term_for_combterm ctxt type_sys tm) 
38282
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427 
in aux end 
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428 

41138
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429 
fun formula_for_fact ctxt type_sys 
40204
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430 
({combformula, ctypes_sorts, ...} : translated_formula) = 
38282
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431 
mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal) 
41137
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432 
(atp_type_literals_for_types type_sys ctypes_sorts)) 
41138
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433 
(formula_for_combformula ctxt type_sys combformula) 
38282
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434 

41138
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435 
fun problem_line_for_fact ctxt prefix type_sys (formula as {name, kind, ...}) = 
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436 
Fof (prefix ^ ascii_of name, kind, formula_for_fact ctxt type_sys formula) 
38282
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437 

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438 
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass, 
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439 
superclass, ...}) = 
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440 
let val ty_arg = ATerm (("T", "T"), []) in 
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441 
Fof (class_rel_clause_prefix ^ ascii_of name, Axiom, 
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442 
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])), 
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443 
AAtom (ATerm (superclass, [ty_arg]))])) 
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444 
end 
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445 

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446 
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) = 
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447 
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)])) 
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448 
 fo_literal_for_arity_literal (TVarLit (c, sort)) = 
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449 
(false, ATerm (c, [ATerm (sort, [])])) 
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450 

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451 
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits, 
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452 
...}) = 
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453 
Fof (arity_clause_prefix ^ ascii_of name, Axiom, 
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454 
mk_ahorn (map (formula_for_fo_literal o apfst not 
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455 
o fo_literal_for_arity_literal) premLits) 
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456 
(formula_for_fo_literal 
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457 
(fo_literal_for_arity_literal conclLit))) 
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458 

41138
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459 
fun problem_line_for_conjecture ctxt type_sys 
40114  460 
({name, kind, combformula, ...} : translated_formula) = 
38282
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461 
Fof (conjecture_prefix ^ name, kind, 
41138
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462 
formula_for_combformula ctxt type_sys combformula) 
38282
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463 

41137
8b634031b2a5
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464 
fun free_type_literals_for_conjecture type_sys 
40114  465 
({ctypes_sorts, ...} : translated_formula) = 
41137
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466 
ctypes_sorts > atp_type_literals_for_types type_sys 
8b634031b2a5
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467 
> map fo_literal_for_type_literal 
38282
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468 

39975
7c50d5ca5c04
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469 
fun problem_line_for_free_type j lit = 
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470 
Fof (tfree_prefix ^ string_of_int j, Hypothesis, formula_for_fo_literal lit) 
41137
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implemented "no_types" encoding, which is too unsound to be useful but can come in handy for evaluations
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parents:
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changeset

471 
fun problem_lines_for_free_types type_sys conjectures = 
38282
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472 
let 
41137
8b634031b2a5
implemented "no_types" encoding, which is too unsound to be useful but can come in handy for evaluations
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parents:
41136
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changeset

473 
val litss = map (free_type_literals_for_conjecture type_sys) conjectures 
38282
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474 
val lits = fold (union (op =)) litss [] 
39975
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diff
changeset

475 
in map2 problem_line_for_free_type (0 upto length lits  1) lits end 
38282
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changeset

476 

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diff
changeset

477 
(** "hBOOL" and "hAPP" **) 
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diff
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478 

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479 
type const_info = {min_arity: int, max_arity: int, sub_level: bool} 
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480 

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481 
fun consider_term top_level (ATerm ((s, _), ts)) = 
39452  482 
(if is_atp_variable s then 
38282
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483 
I 
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484 
else 
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changeset

485 
let val n = length ts in 
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diff
changeset

486 
Symtab.map_default 
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487 
(s, {min_arity = n, max_arity = 0, sub_level = false}) 
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488 
(fn {min_arity, max_arity, sub_level} => 
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489 
{min_arity = Int.min (n, min_arity), 
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490 
max_arity = Int.max (n, max_arity), 
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changeset

491 
sub_level = sub_level orelse not top_level}) 
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492 
end) 
41138
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changeset

493 
#> fold (consider_term (top_level andalso s = type_tag_name)) ts 
38282
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494 
fun consider_formula (AQuant (_, _, phi)) = consider_formula phi 
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495 
 consider_formula (AConn (_, phis)) = fold consider_formula phis 
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496 
 consider_formula (AAtom tm) = consider_term true tm 
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diff
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497 

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changeset

498 
fun consider_problem_line (Fof (_, _, phi)) = consider_formula phi 
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499 
fun consider_problem problem = fold (fold consider_problem_line o snd) problem 
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diff
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500 

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diff
changeset

501 
fun const_table_for_problem explicit_apply problem = 
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changeset

502 
if explicit_apply then NONE 
319c59682c51
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changeset

503 
else SOME (Symtab.empty > consider_problem problem) 
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504 

41134  505 
fun min_arity_of thy type_sys NONE s = 
41138
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changeset

506 
(if s = "equal" orelse s = type_tag_name orelse 
38282
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507 
String.isPrefix type_const_prefix s orelse 
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508 
String.isPrefix class_prefix s then 
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diff
changeset

509 
16383 (* large number *) 
38748  510 
else case strip_prefix_and_unascii const_prefix s of 
41136
30bedf58b177
implemented new type system encoding "overload_args", which is more lightweight than "const_args" (the unsound default) and hopefully almost as sound
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parents:
41134
diff
changeset

511 
SOME s' => num_atp_type_args thy type_sys (invert_const s') 
38282
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512 
 NONE => 0) 
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513 
 min_arity_of _ _ (SOME the_const_tab) s = 
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514 
case Symtab.lookup the_const_tab s of 
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515 
SOME ({min_arity, ...} : const_info) => min_arity 
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516 
 NONE => 0 
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diff
changeset

517 

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518 
fun full_type_of (ATerm ((s, _), [ty, _])) = 
41138
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519 
if s = type_tag_name then SOME ty else NONE 
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520 
 full_type_of _ = NONE 
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521 

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522 
fun list_hAPP_rev _ t1 [] = t1 
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523 
 list_hAPP_rev NONE t1 (t2 :: ts2) = 
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524 
ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2]) 
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525 
 list_hAPP_rev (SOME ty) t1 (t2 :: ts2) = 
41138
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diff
changeset

526 
case full_type_of t2 of 
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diff
changeset

527 
SOME ty2 => 
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changeset

528 
let val ty' = ATerm (`make_fixed_type_const @{type_name fun}, 
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parents:
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diff
changeset

529 
[ty2, ty]) in 
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parents:
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diff
changeset

530 
ATerm (`I "hAPP", 
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implemented partiallytyped "tags" type encoding
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diff
changeset

531 
[tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2]) 
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diff
changeset

532 
end 
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diff
changeset

533 
 NONE => list_hAPP_rev NONE t1 (t2 :: ts2) 
38282
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534 

41134  535 
fun repair_applications_in_term thy type_sys const_tab = 
38282
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536 
let 
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537 
fun aux opt_ty (ATerm (name as (s, _), ts)) = 
41138
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diff
changeset

538 
if s = type_tag_name then 
38282
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changeset

539 
case ts of 
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540 
[t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2]) 
41138
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diff
changeset

541 
 _ => raise Fail "malformed type tag" 
38282
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542 
else 
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changeset

543 
let 
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544 
val ts = map (aux NONE) ts 
41134  545 
val (ts1, ts2) = chop (min_arity_of thy type_sys const_tab s) ts 
38282
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546 
in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end 
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changeset

547 
in aux NONE end 
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diff
changeset

548 

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changeset

549 
fun boolify t = ATerm (`I "hBOOL", [t]) 
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diff
changeset

550 

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diff
changeset

551 
(* True if the constant ever appears outside of the toplevel position in 
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diff
changeset

552 
literals, or if it appears with different arities (e.g., because of different 
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changeset

553 
type instantiations). If false, the constant always receives all of its 
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554 
arguments and is used as a predicate. *) 
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changeset

555 
fun is_predicate NONE s = 
38589
b03f8fe043ec
added "max_relevant_per_iter" option to Sledgehammer
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38518
diff
changeset

556 
s = "equal" orelse s = "$false" orelse s = "$true" orelse 
b03f8fe043ec
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diff
changeset

557 
String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s 
38282
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558 
 is_predicate (SOME the_const_tab) s = 
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559 
case Symtab.lookup the_const_tab s of 
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560 
SOME {min_arity, max_arity, sub_level} => 
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561 
not sub_level andalso min_arity = max_arity 
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changeset

562 
 NONE => false 
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changeset

563 

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changeset

564 
fun repair_predicates_in_term const_tab (t as ATerm ((s, _), ts)) = 
41138
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changeset

565 
if s = type_tag_name then 
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changeset

566 
case ts of 
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567 
[_, t' as ATerm ((s', _), _)] => 
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568 
if is_predicate const_tab s' then t' else boolify t 
41138
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implemented partiallytyped "tags" type encoding
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diff
changeset

569 
 _ => raise Fail "malformed type tag" 
38282
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changeset

570 
else 
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571 
t > not (is_predicate const_tab s) ? boolify 
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changeset

572 

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changeset

573 
fun close_universally phi = 
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changeset

574 
let 
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575 
fun term_vars bounds (ATerm (name as (s, _), tms)) = 
39452  576 
(is_atp_variable s andalso not (member (op =) bounds name)) 
38282
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changeset

577 
? insert (op =) name 
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changeset

578 
#> fold (term_vars bounds) tms 
38678
1bf1e21d3136
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diff
changeset

579 
fun formula_vars bounds (AQuant (_, xs, phi)) = 
38282
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changeset

580 
formula_vars (xs @ bounds) phi 
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diff
changeset

581 
 formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis 
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parents:
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changeset

582 
 formula_vars bounds (AAtom tm) = term_vars bounds tm 
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diff
changeset

583 
in 
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changeset

584 
case formula_vars [] phi [] of [] => phi  xs => AQuant (AForall, xs, phi) 
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changeset

585 
end 
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changeset

586 

41134  587 
fun repair_formula thy explicit_forall type_sys const_tab = 
38282
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diff
changeset

588 
let 
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changeset

589 
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi) 
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changeset

590 
 aux (AConn (c, phis)) = AConn (c, map aux phis) 
319c59682c51
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changeset

591 
 aux (AAtom tm) = 
41134  592 
AAtom (tm > repair_applications_in_term thy type_sys const_tab 
38282
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changeset

593 
> repair_predicates_in_term const_tab) 
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diff
changeset

594 
in aux #> explicit_forall ? close_universally end 
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diff
changeset

595 

41134  596 
fun repair_problem_line thy explicit_forall type_sys const_tab 
38282
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diff
changeset

597 
(Fof (ident, kind, phi)) = 
41134  598 
Fof (ident, kind, repair_formula thy explicit_forall type_sys const_tab phi) 
38282
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changeset

599 
fun repair_problem_with_const_table thy = 
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diff
changeset

600 
map o apsnd o map ooo repair_problem_line thy 
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changeset

601 

41134  602 
fun repair_problem thy explicit_forall type_sys explicit_apply problem = 
603 
repair_problem_with_const_table thy explicit_forall type_sys 

38282
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parents:
diff
changeset

604 
(const_table_for_problem explicit_apply problem) problem 
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parents:
diff
changeset

605 

41134  606 
fun prepare_atp_problem ctxt readable_names explicit_forall type_sys 
40204
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diff
changeset

607 
explicit_apply hyp_ts concl_t facts = 
38282
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diff
changeset

608 
let 
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diff
changeset

609 
val thy = ProofContext.theory_of ctxt 
40204
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parents:
40145
diff
changeset

610 
val (fact_names, (conjectures, facts, helper_facts, class_rel_clauses, 
da97d75e20e6
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parents:
40145
diff
changeset

611 
arity_clauses)) = 
41134  612 
translate_formulas ctxt type_sys hyp_ts concl_t facts 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
41137
diff
changeset

613 
val fact_lines = map (problem_line_for_fact ctxt fact_prefix type_sys) facts 
38282
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parents:
diff
changeset

614 
val helper_lines = 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
41137
diff
changeset

615 
map (problem_line_for_fact ctxt helper_prefix type_sys) helper_facts 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
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parents:
diff
changeset

616 
val conjecture_lines = 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

617 
map (problem_line_for_conjecture ctxt type_sys) conjectures 
41137
8b634031b2a5
implemented "no_types" encoding, which is too unsound to be useful but can come in handy for evaluations
blanchet
parents:
41136
diff
changeset

618 
val tfree_lines = problem_lines_for_free_types type_sys conjectures 
38282
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parents:
diff
changeset

619 
val class_rel_lines = 
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parents:
diff
changeset

620 
map problem_line_for_class_rel_clause class_rel_clauses 
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blanchet
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diff
changeset

621 
val arity_lines = map problem_line_for_arity_clause arity_clauses 
319c59682c51
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blanchet
parents:
diff
changeset

622 
(* Reordering these might or might not confuse the proof reconstruction 
319c59682c51
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blanchet
parents:
diff
changeset

623 
code or the SPASS Flotter hack. *) 
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blanchet
parents:
diff
changeset

624 
val problem = 
40204
da97d75e20e6
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blanchet
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diff
changeset

625 
[("Relevant facts", fact_lines), 
38282
319c59682c51
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parents:
diff
changeset

626 
("Class relationships", class_rel_lines), 
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blanchet
parents:
diff
changeset

627 
("Arity declarations", arity_lines), 
319c59682c51
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blanchet
parents:
diff
changeset

628 
("Helper facts", helper_lines), 
319c59682c51
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blanchet
parents:
diff
changeset

629 
("Conjectures", conjecture_lines), 
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blanchet
parents:
diff
changeset

630 
("Type variables", tfree_lines)] 
41134  631 
> repair_problem thy explicit_forall type_sys explicit_apply 
39452  632 
val (problem, pool) = nice_atp_problem readable_names problem 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

633 
val conjecture_offset = 
40204
da97d75e20e6
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blanchet
parents:
40145
diff
changeset

634 
length fact_lines + length class_rel_lines + length arity_lines 
38282
319c59682c51
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diff
changeset

635 
+ length helper_lines 
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parents:
diff
changeset

636 
in 
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parents:
diff
changeset

637 
(problem, 
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parents:
diff
changeset

638 
case pool of SOME the_pool => snd the_pool  NONE => Symtab.empty, 
40204
da97d75e20e6
standardize on "fact" terminology (vs. "axiom" or "theorem") in Sledgehammer  but keep "Axiom" in the lowerlevel "ATP_Problem" module
blanchet
parents:
40145
diff
changeset

639 
conjecture_offset, fact_names) 
38282
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diff
changeset

640 
end 
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parents:
diff
changeset

641 

319c59682c51
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diff
changeset

642 
end; 