author  blanchet 
Wed, 22 Dec 2010 09:02:43 +0100  
changeset 41384  c4488b7cbe3b 
parent 41313  a96ac4d180b7 
child 41406  062490d081b9 
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 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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val atp_problem_weights : string problem > (string * real) list 
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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 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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s = @{const_name finite} orelse 
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(s <> @{const_name HOL.eq} andalso 
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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 _ => 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 close_universally phi = 
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let 
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fun term_vars bounds (ATerm (name as (s, _), tms)) = 
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(is_atp_variable s andalso not (member (op =) bounds name)) 
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? insert (op =) name 
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#> fold (term_vars bounds) tms 
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fun formula_vars bounds (AQuant (_, xs, phi)) = 
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formula_vars (xs @ bounds) phi 
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 formula_vars bounds (AConn (_, phis)) = fold (formula_vars bounds) phis 
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 formula_vars bounds (AAtom tm) = term_vars bounds tm 
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in 
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case formula_vars [] phi [] of [] => phi  xs => AQuant (AForall, xs, phi) 
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end 
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fun combformula_for_prop thy eq_as_iff = 
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let 
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fun do_term bs t ts = 
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combterm_from_term thy bs (Envir.eta_contract t) 
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>> AAtom > union (op =) ts 
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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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137 
 @{const HOL.disj} $ t1 $ t2 => do_conn bs AOr t1 t2 
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138 
 @{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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140 
if eq_as_iff then do_conn bs AIff t1 t2 else do_term bs t 
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141 
 _ => do_term bs t 
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142 
in do_formula [] end 
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143 

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val presimplify_term = prop_of o Meson.presimplify oo Skip_Proof.make_thm 
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145 

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146 
fun concealed_bound_name j = sledgehammer_weak_prefix ^ Int.toString j 
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147 
fun conceal_bounds Ts t = 
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148 
subst_bounds (map (Free o apfst concealed_bound_name) 
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149 
(0 upto length Ts  1 ~~ Ts), t) 
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150 
fun reveal_bounds Ts = 
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151 
subst_atomic (map (fn (j, T) => (Free (concealed_bound_name j, T), Bound j)) 
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152 
(0 upto length Ts  1 ~~ Ts)) 
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153 

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154 
(* Removes the lambdas from an equation of the form "t = (%x. u)". 
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(Cf. "extensionalize_theorem" in "Meson_Clausify".) *) 
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156 
fun extensionalize_term t = 
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157 
let 
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158 
fun aux j (@{const Trueprop} $ t') = @{const Trueprop} $ aux j t' 
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159 
 aux j (t as Const (s, Type (_, [Type (_, [_, T']), 
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160 
Type (_, [_, res_T])])) 
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161 
$ 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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163 
let val var_t = Var ((var_s, j), var_T) in 
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164 
Const (s, T' > T' > res_T) 
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165 
$ betapply (t2, var_t) $ subst_bound (var_t, t') 
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166 
> aux (j + 1) 
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167 
end 
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168 
else 
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169 
t 
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170 
 aux _ t = t 
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171 
in aux (maxidx_of_term t + 1) t end 
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172 

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173 
fun introduce_combinators_in_term ctxt kind t = 
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174 
let val thy = ProofContext.theory_of ctxt in 
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175 
if Meson.is_fol_term thy t then 
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176 
t 
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177 
else 
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178 
let 
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179 
fun aux Ts t = 
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180 
case t of 
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181 
@{const Not} $ t1 => @{const Not} $ aux Ts t1 
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182 
 (t0 as Const (@{const_name All}, _)) $ Abs (s, T, t') => 
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183 
t0 $ Abs (s, T, aux (T :: Ts) t') 
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184 
 (t0 as Const (@{const_name All}, _)) $ t1 => 
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185 
aux Ts (t0 $ eta_expand Ts t1 1) 
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186 
 (t0 as Const (@{const_name Ex}, _)) $ Abs (s, T, t') => 
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187 
t0 $ Abs (s, T, aux (T :: Ts) t') 
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188 
 (t0 as Const (@{const_name Ex}, _)) $ t1 => 
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189 
aux Ts (t0 $ eta_expand Ts t1 1) 
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190 
 (t0 as @{const HOL.conj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 
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191 
 (t0 as @{const HOL.disj}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 
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192 
 (t0 as @{const HOL.implies}) $ t1 $ t2 => t0 $ aux Ts t1 $ aux Ts t2 
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193 
 (t0 as Const (@{const_name HOL.eq}, Type (_, [@{typ bool}, _]))) 
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194 
$ t1 $ t2 => 
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195 
t0 $ aux Ts t1 $ aux Ts t2 
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196 
 _ => if not (exists_subterm (fn Abs _ => true  _ => false) t) then 
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197 
t 
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198 
else 
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199 
t > conceal_bounds Ts 
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200 
> Envir.eta_contract 
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201 
> cterm_of thy 
39890  202 
> Meson_Clausify.introduce_combinators_in_cterm 
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203 
> prop_of > Logic.dest_equals > snd 
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204 
> reveal_bounds Ts 
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205 
val (t, ctxt') = Variable.import_terms true [t] ctxt >> the_single 
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206 
in t > aux [] > singleton (Variable.export_terms ctxt' ctxt) end 
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207 
handle THM _ => 
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208 
(* A type variable of sort "{}" will make abstraction fail. *) 
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209 
if kind = Conjecture then HOLogic.false_const 
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210 
else HOLogic.true_const 
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211 
end 
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212 

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213 
(* Metis's use of "resolve_tac" freezes the schematic variables. We simulate the 
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214 
same in Sledgehammer to prevent the discovery of unreplable proofs. *) 
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215 
fun freeze_term t = 
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216 
let 
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217 
fun aux (t $ u) = aux t $ aux u 
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218 
 aux (Abs (s, T, t)) = Abs (s, T, aux t) 
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219 
 aux (Var ((s, i), T)) = 
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220 
Free (sledgehammer_weak_prefix ^ s ^ "_" ^ string_of_int i, T) 
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221 
 aux t = t 
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222 
in t > exists_subterm is_Var t ? aux end 
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223 

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224 
(* making fact and conjecture formulas *) 
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225 
fun make_formula ctxt eq_as_iff presimp name kind t = 
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226 
let 
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227 
val thy = ProofContext.theory_of ctxt 
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228 
val t = t > Envir.beta_eta_contract 
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229 
> transform_elim_term 
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230 
> Object_Logic.atomize_term thy 
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231 
val need_trueprop = (fastype_of t = HOLogic.boolT) 
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232 
val t = t > need_trueprop ? HOLogic.mk_Trueprop 
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233 
> extensionalize_term 
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234 
> presimp ? presimplify_term thy 
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235 
> perhaps (try (HOLogic.dest_Trueprop)) 
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236 
> introduce_combinators_in_term ctxt kind 
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237 
> kind <> Axiom ? freeze_term 
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238 
val (combformula, ctypes_sorts) = combformula_for_prop thy eq_as_iff t [] 
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239 
in 
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240 
{name = name, combformula = combformula, kind = kind, 
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241 
ctypes_sorts = ctypes_sorts} 
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242 
end 
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243 

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244 
fun make_fact ctxt eq_as_iff presimp ((name, _), th) = 
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245 
case make_formula ctxt eq_as_iff presimp name Axiom (prop_of th) of 
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246 
{combformula = AAtom (CombConst (("c_True", _), _, _)), ...} => NONE 
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247 
 formula => SOME formula 
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248 
fun make_conjecture ctxt ts = 
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249 
let val last = length ts  1 in 
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250 
map2 (fn j => make_formula ctxt true true (Int.toString j) 
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(if j = last then Conjecture else Hypothesis)) 
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(0 upto last) ts 
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end 
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(** Helper facts **) 
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fun fold_formula f (AQuant (_, _, phi)) = fold_formula f phi 
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 fold_formula f (AConn (_, phis)) = fold (fold_formula f) phis 
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 fold_formula f (AAtom tm) = f tm 
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fun count_term (ATerm ((s, _), tms)) = 
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(if is_atp_variable s then I 
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else Symtab.map_entry s (Integer.add 1)) 
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#> fold count_term tms 
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val count_formula = fold_formula count_term 
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val init_counters = 
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metis_helpers > map fst > sort_distinct string_ord > map (rpair 0) 
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> Symtab.make 
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fun get_helper_facts ctxt explicit_forall type_sys formulas = 
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let 
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val no_dangerous_types = types_dangerous_types type_sys 
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val ct = init_counters > fold count_formula formulas 
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fun is_used s = the (Symtab.lookup ct s) > 0 
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fun dub c needs_full_types (th, j) = 
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((c ^ "_" ^ string_of_int j ^ (if needs_full_types then "ft" else ""), 
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false), th) 
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fun make_facts eq_as_iff = map_filter (make_fact ctxt eq_as_iff false) 
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in 
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(metis_helpers 
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> filter (is_used o fst) 
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> maps (fn (c, (needs_full_types, ths)) => 
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if needs_full_types andalso not no_dangerous_types then 
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[] 
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else 
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ths ~~ (1 upto length ths) 
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> map (dub c needs_full_types) 
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> make_facts (not needs_full_types)), 
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if type_sys = Tags false then 
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let 
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fun var s = ATerm (`I s, []) 
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fun tag tm = ATerm (`I type_tag_name, [var "X", tm]) 
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in 
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[Fof (helper_prefix ^ ascii_of "ti_ti", Axiom, 
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AAtom (ATerm (`I "equal", [tag (tag (var "Y")), tag (var "Y")])) 
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> explicit_forall ? close_universally)] 
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end 
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else 
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[]) 
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end 
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fun translate_atp_fact ctxt = `(make_fact ctxt true 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 
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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 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 conjs = make_conjecture ctxt (hyp_ts @ [concl_t]) 
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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, (conjs, facts, class_rel_clauses, arity_clauses)) 
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end 
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fun tag_with_type ty t = ATerm (`I type_tag_name, [ty, t]) 
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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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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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fun formula_for_fo_literal (pos, t) = AAtom t > not pos ? mk_anot 
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(* Finite types such as "unit", "bool", "bool * bool", and "bool => bool" are 
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considered dangerous because their "exhaust" properties can easily lead to 
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unsound ATP proofs. The checks below are an (unsound) approximation of 
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finiteness. *) 
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349 

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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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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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 is_type_dangerous _ _ = false 
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and is_type_constr_dangerous ctxt s = 
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let val thy = ProofContext.theory_of ctxt in 
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case Datatype_Data.get_info thy s of 
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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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 NONE => 
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case Typedef.get_info ctxt s of 
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({rep_type, ...}, _) :: _ => is_type_dangerous ctxt rep_type 
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 [] => true 
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end 
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368 

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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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is_type_constr_dangerous ctxt (invert_const s') 
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 NONE => false) 
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 is_combtyp_dangerous _ _ = false 
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376 
fun should_tag_with_type ctxt (Tags full_types) ty = 
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377 
full_types orelse is_combtyp_dangerous ctxt ty 
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378 
 should_tag_with_type _ _ _ = false 
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379 

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380 
val fname_table = 
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381 
[("c_False", (0, ("c_fFalse", @{const_name Metis.fFalse}))), 
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382 
("c_True", (0, ("c_fTrue", @{const_name Metis.fTrue}))), 
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383 
("c_Not", (1, ("c_fNot", @{const_name Metis.fNot}))), 
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384 
("c_conj", (2, ("c_fconj", @{const_name Metis.fconj}))), 
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385 
("c_disj", (2, ("c_fdisj", @{const_name Metis.fdisj}))), 
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386 
("c_implies", (2, ("c_fimplies", @{const_name Metis.fimplies}))), 
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387 
("equal", (2, ("c_fequal", @{const_name Metis.fequal})))] 
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388 

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389 
fun fo_term_for_combterm ctxt type_sys = 
38282
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390 
let 
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391 
val thy = ProofContext.theory_of ctxt 
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392 
fun aux top_level u = 
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393 
let 
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394 
val (head, args) = strip_combterm_comb u 
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395 
val (x, ty_args) = 
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396 
case head of 
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397 
CombConst (name as (s, s'), _, ty_args) => 
41140
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398 
(case AList.lookup (op =) fname_table s of 
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399 
SOME (n, fname) => 
41150
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400 
(if top_level andalso length args = n then 
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401 
case s of 
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402 
"c_False" => ("$false", s') 
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403 
 "c_True" => ("$true", s') 
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404 
 _ => name 
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405 
else 
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406 
fname, []) 
41140
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407 
 NONE => 
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408 
case strip_prefix_and_unascii const_prefix s of 
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409 
NONE => (name, ty_args) 
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410 
 SOME s'' => 
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411 
let 
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412 
val s'' = invert_const s'' 
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413 
val ty_args = 
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414 
if needs_type_args thy type_sys s'' then ty_args else [] 
41150
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415 
in (name, ty_args) end) 
38282
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416 
 CombVar (name, _) => (name, []) 
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417 
 CombApp _ => raise Fail "impossible \"CombApp\"" 
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418 
val t = 
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419 
ATerm (x, map fo_term_for_combtyp ty_args @ map (aux false) args) 
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420 
val ty = combtyp_of u 
38282
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421 
in 
41138
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422 
t > (if should_tag_with_type ctxt type_sys ty then 
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423 
tag_with_type (fo_term_for_combtyp ty) 
41134  424 
else 
425 
I) 

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426 
end 
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427 
in aux true end 
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428 

41138
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429 
fun formula_for_combformula ctxt type_sys = 
38282
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430 
let 
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431 
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi) 
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432 
 aux (AConn (c, phis)) = AConn (c, map aux phis) 
41138
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433 
 aux (AAtom tm) = AAtom (fo_term_for_combterm ctxt type_sys tm) 
38282
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434 
in aux end 
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435 

41138
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436 
fun formula_for_fact ctxt type_sys 
40204
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standardize on "fact" terminology (vs. "axiom" or "theorem") in Sledgehammer  but keep "Axiom" in the lowerlevel "ATP_Problem" module
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437 
({combformula, ctypes_sorts, ...} : translated_formula) = 
38282
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438 
mk_ahorn (map (formula_for_fo_literal o fo_literal_for_type_literal) 
41137
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439 
(atp_type_literals_for_types type_sys ctypes_sorts)) 
41138
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440 
(formula_for_combformula ctxt type_sys combformula) 
38282
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441 

41138
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442 
fun problem_line_for_fact ctxt prefix type_sys (formula as {name, kind, ...}) = 
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443 
Fof (prefix ^ ascii_of name, kind, formula_for_fact ctxt type_sys formula) 
38282
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444 

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445 
fun problem_line_for_class_rel_clause (ClassRelClause {name, subclass, 
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446 
superclass, ...}) = 
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447 
let val ty_arg = ATerm (("T", "T"), []) in 
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448 
Fof (class_rel_clause_prefix ^ ascii_of name, Axiom, 
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449 
AConn (AImplies, [AAtom (ATerm (subclass, [ty_arg])), 
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450 
AAtom (ATerm (superclass, [ty_arg]))])) 
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451 
end 
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changeset

452 

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453 
fun fo_literal_for_arity_literal (TConsLit (c, t, args)) = 
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454 
(true, ATerm (c, [ATerm (t, map (fn arg => ATerm (arg, [])) args)])) 
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455 
 fo_literal_for_arity_literal (TVarLit (c, sort)) = 
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456 
(false, ATerm (c, [ATerm (sort, [])])) 
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diff
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457 

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changeset

458 
fun problem_line_for_arity_clause (ArityClause {name, conclLit, premLits, 
319c59682c51
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459 
...}) = 
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460 
Fof (arity_clause_prefix ^ ascii_of name, Axiom, 
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461 
mk_ahorn (map (formula_for_fo_literal o apfst not 
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462 
o fo_literal_for_arity_literal) premLits) 
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463 
(formula_for_fo_literal 
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464 
(fo_literal_for_arity_literal conclLit))) 
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diff
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465 

41138
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466 
fun problem_line_for_conjecture ctxt type_sys 
40114  467 
({name, kind, combformula, ...} : translated_formula) = 
38282
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468 
Fof (conjecture_prefix ^ name, kind, 
41138
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parents:
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diff
changeset

469 
formula_for_combformula ctxt type_sys combformula) 
38282
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parents:
diff
changeset

470 

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

471 
fun free_type_literals_for_conjecture type_sys 
40114  472 
({ctypes_sorts, ...} : translated_formula) = 
41137
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changeset

473 
ctypes_sorts > atp_type_literals_for_types type_sys 
8b634031b2a5
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changeset

474 
> map fo_literal_for_type_literal 
38282
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475 

39975
7c50d5ca5c04
avoid generating several formulas with the same name ("tfrees")
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diff
changeset

476 
fun problem_line_for_free_type j lit = 
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39954
diff
changeset

477 
Fof (tfree_prefix ^ string_of_int j, Hypothesis, formula_for_fo_literal lit) 
41313
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
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parents:
41211
diff
changeset

478 
fun problem_lines_for_free_types type_sys conjs = 
38282
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diff
changeset

479 
let 
41313
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

480 
val litss = map (free_type_literals_for_conjecture type_sys) conjs 
38282
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changeset

481 
val lits = fold (union (op =)) litss [] 
39975
7c50d5ca5c04
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parents:
39954
diff
changeset

482 
in map2 problem_line_for_free_type (0 upto length lits  1) lits end 
38282
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diff
changeset

483 

319c59682c51
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changeset

484 
(** "hBOOL" and "hAPP" **) 
319c59682c51
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diff
changeset

485 

319c59682c51
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486 
type const_info = {min_arity: int, max_arity: int, sub_level: bool} 
319c59682c51
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487 

319c59682c51
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488 
fun consider_term top_level (ATerm ((s, _), ts)) = 
39452  489 
(if is_atp_variable s then 
38282
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490 
I 
319c59682c51
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parents:
diff
changeset

491 
else 
319c59682c51
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parents:
diff
changeset

492 
let val n = length ts in 
319c59682c51
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parents:
diff
changeset

493 
Symtab.map_default 
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changeset

494 
(s, {min_arity = n, max_arity = 0, sub_level = false}) 
319c59682c51
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495 
(fn {min_arity, max_arity, sub_level} => 
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496 
{min_arity = Int.min (n, min_arity), 
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497 
max_arity = Int.max (n, max_arity), 
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changeset

498 
sub_level = sub_level orelse not top_level}) 
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499 
end) 
41138
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changeset

500 
#> fold (consider_term (top_level andalso s = type_tag_name)) ts 
38282
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501 
fun consider_formula (AQuant (_, _, phi)) = consider_formula phi 
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502 
 consider_formula (AConn (_, phis)) = fold consider_formula phis 
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parents:
diff
changeset

503 
 consider_formula (AAtom tm) = consider_term true tm 
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parents:
diff
changeset

504 

319c59682c51
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parents:
diff
changeset

505 
fun consider_problem_line (Fof (_, _, phi)) = consider_formula phi 
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parents:
diff
changeset

506 
fun consider_problem problem = fold (fold consider_problem_line o snd) problem 
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parents:
diff
changeset

507 

41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

508 
(* needed for helper facts if the problem otherwise does not involve equality *) 
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

509 
val equal_entry = ("equal", {min_arity = 2, max_arity = 2, sub_level = false}) 
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

510 

38282
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parents:
diff
changeset

511 
fun const_table_for_problem explicit_apply problem = 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

512 
if explicit_apply then 
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

513 
NONE 
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

514 
else 
41147
0e1903273712
fix translation of higherorder equality ("fequal") if "precise_overloaded_args" is "true"
blanchet
parents:
41145
diff
changeset

515 
SOME (Symtab.empty > Symtab.default equal_entry > consider_problem problem) 
38282
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diff
changeset

516 

41134  517 
fun min_arity_of thy type_sys NONE s = 
41138
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implemented partiallytyped "tags" type encoding
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diff
changeset

518 
(if s = "equal" orelse s = type_tag_name orelse 
38282
319c59682c51
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parents:
diff
changeset

519 
String.isPrefix type_const_prefix s orelse 
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parents:
diff
changeset

520 
String.isPrefix class_prefix s then 
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blanchet
parents:
diff
changeset

521 
16383 (* large number *) 
38748  522 
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
blanchet
parents:
41134
diff
changeset

523 
SOME s' => num_atp_type_args thy type_sys (invert_const s') 
38282
319c59682c51
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parents:
diff
changeset

524 
 NONE => 0) 
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parents:
diff
changeset

525 
 min_arity_of _ _ (SOME the_const_tab) s = 
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parents:
diff
changeset

526 
case Symtab.lookup the_const_tab s of 
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parents:
diff
changeset

527 
SOME ({min_arity, ...} : const_info) => min_arity 
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diff
changeset

528 
 NONE => 0 
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parents:
diff
changeset

529 

319c59682c51
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blanchet
parents:
diff
changeset

530 
fun full_type_of (ATerm ((s, _), [ty, _])) = 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
41137
diff
changeset

531 
if s = type_tag_name then SOME ty else NONE 
eb80538166b6
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parents:
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diff
changeset

532 
 full_type_of _ = NONE 
38282
319c59682c51
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parents:
diff
changeset

533 

319c59682c51
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parents:
diff
changeset

534 
fun list_hAPP_rev _ t1 [] = t1 
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blanchet
parents:
diff
changeset

535 
 list_hAPP_rev NONE t1 (t2 :: ts2) = 
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move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

536 
ATerm (`I "hAPP", [list_hAPP_rev NONE t1 ts2, t2]) 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

537 
 list_hAPP_rev (SOME ty) t1 (t2 :: ts2) = 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

538 
case full_type_of t2 of 
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
41137
diff
changeset

539 
SOME ty2 => 
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
41137
diff
changeset

540 
let val ty' = ATerm (`make_fixed_type_const @{type_name fun}, 
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

541 
[ty2, ty]) in 
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
41137
diff
changeset

542 
ATerm (`I "hAPP", 
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

543 
[tag_with_type ty' (list_hAPP_rev (SOME ty') t1 ts2), t2]) 
eb80538166b6
implemented partiallytyped "tags" type encoding
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parents:
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diff
changeset

544 
end 
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

545 
 NONE => list_hAPP_rev NONE t1 (t2 :: ts2) 
38282
319c59682c51
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blanchet
parents:
diff
changeset

546 

41134  547 
fun repair_applications_in_term thy type_sys const_tab = 
38282
319c59682c51
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parents:
diff
changeset

548 
let 
319c59682c51
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blanchet
parents:
diff
changeset

549 
fun aux opt_ty (ATerm (name as (s, _), ts)) = 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

550 
if s = type_tag_name then 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

551 
case ts of 
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blanchet
parents:
diff
changeset

552 
[t1, t2] => ATerm (name, [aux NONE t1, aux (SOME t1) t2]) 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
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diff
changeset

553 
 _ => raise Fail "malformed type tag" 
38282
319c59682c51
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parents:
diff
changeset

554 
else 
319c59682c51
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blanchet
parents:
diff
changeset

555 
let 
319c59682c51
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blanchet
parents:
diff
changeset

556 
val ts = map (aux NONE) ts 
41134  557 
val (ts1, ts2) = chop (min_arity_of thy type_sys const_tab s) ts 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

558 
in list_hAPP_rev opt_ty (ATerm (name, ts1)) (rev ts2) end 
319c59682c51
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parents:
diff
changeset

559 
in aux NONE end 
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parents:
diff
changeset

560 

319c59682c51
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blanchet
parents:
diff
changeset

561 
fun boolify t = ATerm (`I "hBOOL", [t]) 
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parents:
diff
changeset

562 

319c59682c51
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blanchet
parents:
diff
changeset

563 
(* True if the constant ever appears outside of the toplevel position in 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

564 
literals, or if it appears with different arities (e.g., because of different 
319c59682c51
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blanchet
parents:
diff
changeset

565 
type instantiations). If false, the constant always receives all of its 
319c59682c51
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parents:
diff
changeset

566 
arguments and is used as a predicate. *) 
319c59682c51
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blanchet
parents:
diff
changeset

567 
fun is_predicate NONE s = 
38589
b03f8fe043ec
added "max_relevant_per_iter" option to Sledgehammer
blanchet
parents:
38518
diff
changeset

568 
s = "equal" orelse s = "$false" orelse s = "$true" orelse 
b03f8fe043ec
added "max_relevant_per_iter" option to Sledgehammer
blanchet
parents:
38518
diff
changeset

569 
String.isPrefix type_const_prefix s orelse String.isPrefix class_prefix s 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

570 
 is_predicate (SOME the_const_tab) s = 
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move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

571 
case Symtab.lookup the_const_tab s of 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

572 
SOME {min_arity, max_arity, sub_level} => 
319c59682c51
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blanchet
parents:
diff
changeset

573 
not sub_level andalso min_arity = max_arity 
319c59682c51
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parents:
diff
changeset

574 
 NONE => false 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

575 

41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

576 
fun repair_predicates_in_term pred_const_tab (t as ATerm ((s, _), ts)) = 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

577 
if s = type_tag_name then 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

578 
case ts of 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

579 
[_, t' as ATerm ((s', _), _)] => 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

580 
if is_predicate pred_const_tab s' then t' else boolify t 
41138
eb80538166b6
implemented partiallytyped "tags" type encoding
blanchet
parents:
41137
diff
changeset

581 
 _ => raise Fail "malformed type tag" 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

582 
else 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

583 
t > not (is_predicate pred_const_tab s) ? boolify 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

584 

41134  585 
fun repair_formula thy explicit_forall type_sys const_tab = 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

586 
let 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
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parents:
41138
diff
changeset

587 
val pred_const_tab = case type_sys of Tags _ => NONE  _ => const_tab 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

588 
fun aux (AQuant (q, xs, phi)) = AQuant (q, xs, aux phi) 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

589 
 aux (AConn (c, phis)) = AConn (c, map aux phis) 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

590 
 aux (AAtom tm) = 
41134  591 
AAtom (tm > repair_applications_in_term thy type_sys const_tab 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

592 
> repair_predicates_in_term pred_const_tab) 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

593 
in aux #> explicit_forall ? close_universally end 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

594 

41134  595 
fun repair_problem_line thy explicit_forall type_sys const_tab 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

596 
(Fof (ident, kind, phi)) = 
41134  597 
Fof (ident, kind, repair_formula thy explicit_forall type_sys const_tab phi) 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

598 
fun repair_problem thy = map o apsnd o map ooo repair_problem_line thy 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

599 

41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

600 
fun dest_Fof (Fof z) = z 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

601 

41157  602 
val factsN = "Relevant facts" 
603 
val class_relsN = "Class relationships" 

604 
val aritiesN = "Arity declarations" 

605 
val helpersN = "Helper facts" 

606 
val conjsN = "Conjectures" 

41313
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

607 
val free_typesN = "Type variables" 
41157  608 

609 
fun offset_of_heading_in_problem _ [] j = j 

610 
 offset_of_heading_in_problem needle ((heading, lines) :: problem) j = 

611 
if heading = needle then j 

612 
else offset_of_heading_in_problem needle problem (j + length lines) 

613 

41134  614 
fun prepare_atp_problem ctxt readable_names explicit_forall type_sys 
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

615 
explicit_apply hyp_ts concl_t facts = 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

616 
let 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

617 
val thy = ProofContext.theory_of ctxt 
41313
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

618 
val (fact_names, (conjs, facts, class_rel_clauses, arity_clauses)) = 
41134  619 
translate_formulas ctxt type_sys hyp_ts concl_t facts 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

620 
(* Reordering these might or might not confuse the proof reconstruction 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

621 
code or the SPASS Flotter hack. *) 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

622 
val problem = 
41157  623 
[(factsN, map (problem_line_for_fact ctxt fact_prefix type_sys) facts), 
624 
(class_relsN, map problem_line_for_class_rel_clause class_rel_clauses), 

625 
(aritiesN, map problem_line_for_arity_clause arity_clauses), 

626 
(helpersN, []), 

41313
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

627 
(conjsN, map (problem_line_for_conjecture ctxt type_sys) conjs), 
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

628 
(free_typesN, problem_lines_for_free_types type_sys conjs)] 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

629 
val const_tab = const_table_for_problem explicit_apply problem 
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

630 
val problem = 
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

631 
problem > repair_problem thy explicit_forall type_sys const_tab 
41157  632 
val helper_lines = 
41145
a5ee3b8e5a90
improve partially tagged encoding by adding a helper fact that coalesces consecutive "ti" tags
blanchet
parents:
41140
diff
changeset

633 
get_helper_facts ctxt explicit_forall type_sys 
a5ee3b8e5a90
improve partially tagged encoding by adding a helper fact that coalesces consecutive "ti" tags
blanchet
parents:
41140
diff
changeset

634 
(maps (map (#3 o dest_Fof) o snd) problem) 
41157  635 
>> map (problem_line_for_fact ctxt helper_prefix type_sys 
636 
#> repair_problem_line thy explicit_forall type_sys const_tab) 

637 
> op @ 

41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

638 
val (problem, pool) = 
41157  639 
problem > AList.update (op =) (helpersN, helper_lines) 
41140
9c68004b8c9d
added Sledgehammer support for higherorder propositional reasoning
blanchet
parents:
41138
diff
changeset

640 
> nice_atp_problem readable_names 
38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

641 
in 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

642 
(problem, 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

643 
case pool of SOME the_pool => snd the_pool  NONE => Symtab.empty, 
41157  644 
offset_of_heading_in_problem conjsN problem 0, 
645 
fact_names > Vector.fromList) 

38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

646 
end 
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
blanchet
parents:
diff
changeset

647 

41313
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

648 
(* FUDGE *) 
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

649 
val conj_weight = 0.0 
a96ac4d180b7
optionally supply constant weights to E  turned off by default until properly parameterized
blanchet
parents:
41211
diff
changeset

650 
val hyp_weight = 0.05 
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651 
val fact_min_weight = 0.1 
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652 
val fact_max_weight = 1.0 
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653 

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654 
fun add_term_weights weight (ATerm (s, tms)) = 
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655 
(not (is_atp_variable s) andalso s <> "equal") ? Symtab.default (s, weight) 
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656 
#> fold (add_term_weights weight) tms 
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657 
fun add_problem_line_weights weight (Fof (_, _, phi)) = 
41384  658 
fold_formula (add_term_weights weight) phi 
41313
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659 

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660 
fun add_conjectures_weights [] = I 
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661 
 add_conjectures_weights conjs = 
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662 
let val (hyps, conj) = split_last conjs in 
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663 
add_problem_line_weights conj_weight conj 
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664 
#> fold (add_problem_line_weights hyp_weight) hyps 
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665 
end 
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666 

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667 
fun add_facts_weights facts = 
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668 
let 
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669 
val num_facts = length facts 
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670 
fun weight_of j = 
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671 
fact_min_weight + (fact_max_weight  fact_min_weight) * Real.fromInt j 
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672 
/ Real.fromInt num_facts 
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673 
in 
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674 
map weight_of (0 upto num_facts  1) ~~ facts 
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675 
> fold (uncurry add_problem_line_weights) 
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676 
end 
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677 

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678 
(* Weights are from 0.0 (most important) to 1.0 (least important). *) 
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679 
fun atp_problem_weights problem = 
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680 
Symtab.empty 
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681 
> add_conjectures_weights (these (AList.lookup (op =) problem conjsN)) 
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682 
> add_facts_weights (these (AList.lookup (op =) problem factsN)) 
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683 
> Symtab.dest 
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684 

38282
319c59682c51
move Sledgehammer's HOL > FOL translation to separate file (sledgehammer_translate.ML)
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685 
end; 