author  bulwahn 
Mon, 30 May 2011 17:55:34 +0200  
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permissions  rwrr 
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(* Title: HOL/Tools/Quickcheck/narrowing_generators.ML 
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Author: Lukas Bulwahn, TU Muenchen 
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Narrowingbased counterexample generation. 
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*) 
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signature NARROWING_GENERATORS = 
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sig 
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val compile_generator_expr: 

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Proof.context > (term * term list) list > int list > term list option * Quickcheck.report option 
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val put_counterexample: (unit > term list option) > Proof.context > Proof.context 
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val finite_functions : bool Config.T 
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val overlord : bool Config.T 
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val setup: theory > theory 
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end; 

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structure Narrowing_Generators : NARROWING_GENERATORS = 
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struct 
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(* configurations *) 
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val finite_functions = Attrib.setup_config_bool @{binding quickcheck_finite_functions} (K true) 
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val overlord = Attrib.setup_config_bool @{binding quickcheck_narrowing_overlord} (K false) 
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(* partial_term_of instances *) 
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fun mk_partial_term_of (x, T) = 
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Const (@{const_name Quickcheck_Narrowing.partial_term_of_class.partial_term_of}, 
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Term.itselfT T > @{typ narrowing_term} > @{typ Code_Evaluation.term}) 
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$ Const ("TYPE", Term.itselfT T) $ x 
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(** formal definition **) 
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fun add_partial_term_of tyco raw_vs thy = 
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let 
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val vs = map (fn (v, _) => (v, @{sort typerep})) raw_vs; 
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val ty = Type (tyco, map TFree vs); 
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val lhs = Const (@{const_name partial_term_of}, 
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Term.itselfT ty > @{typ narrowing_term} > @{typ Code_Evaluation.term}) 
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$ Free ("x", Term.itselfT ty) $ Free ("t", @{typ narrowing_term}); 
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val rhs = @{term "undefined :: Code_Evaluation.term"}; 
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val eq = HOLogic.mk_Trueprop (HOLogic.mk_eq (lhs, rhs)); 
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fun triv_name_of t = (fst o dest_Free o fst o strip_comb o fst 
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o HOLogic.dest_eq o HOLogic.dest_Trueprop) t ^ "_triv"; 
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in 
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thy 
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> Class.instantiation ([tyco], vs, @{sort partial_term_of}) 
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> `(fn lthy => Syntax.check_term lthy eq) 
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> (fn eq => Specification.definition (NONE, ((Binding.name (triv_name_of eq), []), eq))) 
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> snd 
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> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) 
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end; 
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fun ensure_partial_term_of (tyco, (raw_vs, _)) thy = 
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let 
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val need_inst = not (can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort partial_term_of}) 
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andalso can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort typerep}; 
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in if need_inst then add_partial_term_of tyco raw_vs thy else thy end; 
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(** code equations for datatypes **) 
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fun mk_partial_term_of_eq thy ty (i, (c, (_, tys))) = 
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let 
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val frees = map Free (Name.names Name.context "a" (map (K @{typ narrowing_term}) tys)) 
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val narrowing_term = @{term "Quickcheck_Narrowing.Ctr"} $ HOLogic.mk_number @{typ code_int} i 
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$ (HOLogic.mk_list @{typ narrowing_term} (rev frees)) 
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val rhs = fold (fn u => fn t => @{term "Code_Evaluation.App"} $ t $ u) 
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(map mk_partial_term_of (frees ~~ tys)) 
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(@{term "Code_Evaluation.Const"} $ HOLogic.mk_literal c $ HOLogic.mk_typerep (tys > ty)) 
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val insts = 
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map (SOME o Thm.cterm_of thy o map_types Logic.unvarifyT_global o Logic.varify_global) 
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[Free ("ty", Term.itselfT ty), narrowing_term, rhs] 
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val cty = Thm.ctyp_of thy ty; 
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in 
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@{thm partial_term_of_anything} 
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> Drule.instantiate' [SOME cty] insts 
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> Thm.varifyT_global 
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end 
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fun add_partial_term_of_code tyco raw_vs raw_cs thy = 
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let 
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val algebra = Sign.classes_of thy; 
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val vs = map (fn (v, sort) => 
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(v, curry (Sorts.inter_sort algebra) @{sort typerep} sort)) raw_vs; 
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val ty = Type (tyco, map TFree vs); 
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val cs = (map o apsnd o apsnd o map o map_atyps) 
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(fn TFree (v, _) => TFree (v, (the o AList.lookup (op =) vs) v)) raw_cs; 
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val const = AxClass.param_of_inst thy (@{const_name partial_term_of}, tyco); 
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val var_insts = map (SOME o Thm.cterm_of thy o map_types Logic.unvarifyT_global o Logic.varify_global) 
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[Free ("ty", Term.itselfT ty), @{term "Quickcheck_Narrowing.Var p tt"}, 
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@{term "Code_Evaluation.Free (STR ''_'')"} $ HOLogic.mk_typerep ty] 
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val var_eq = 
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@{thm partial_term_of_anything} 
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> Drule.instantiate' [SOME (Thm.ctyp_of thy ty)] var_insts 
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> Thm.varifyT_global 
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val eqs = var_eq :: map_index (mk_partial_term_of_eq thy ty) cs; 
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in 
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thy 
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> Code.del_eqns const 
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> fold Code.add_eqn eqs 
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end; 
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fun ensure_partial_term_of_code (tyco, (raw_vs, cs)) thy = 
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let 
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val has_inst = can (Sorts.mg_domain (Sign.classes_of thy) tyco) @{sort partial_term_of}; 
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in if has_inst then add_partial_term_of_code tyco raw_vs cs thy else thy end; 
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110 
(* narrowing generators *) 
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111 

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112 
(** narrowing specific names and types **) 
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113 

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114 
exception FUNCTION_TYPE; 
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115 

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116 
val narrowingN = "narrowing"; 
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117 

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fun narrowingT T = 
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@{typ Quickcheck_Narrowing.code_int} > Type (@{type_name Quickcheck_Narrowing.cons}, [T]) 
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120 

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fun mk_empty T = Const (@{const_name Quickcheck_Narrowing.empty}, narrowingT T) 
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122 

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fun mk_cons c T = Const (@{const_name Quickcheck_Narrowing.cons}, T > narrowingT T) $ Const (c, T) 
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124 

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125 
fun mk_apply (T, t) (U, u) = 
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126 
let 
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127 
val (_, U') = dest_funT U 
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128 
in 
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(U', Const (@{const_name Quickcheck_Narrowing.apply}, 
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130 
narrowingT U > narrowingT T > narrowingT U') $ u $ t) 
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131 
end 
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132 

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133 
fun mk_sum (t, u) = 
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134 
let 
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135 
val T = fastype_of t 
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136 
in 
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137 
Const (@{const_name Quickcheck_Narrowing.sum}, T > T > T) $ t $ u 
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138 
end 
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139 

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140 
(** deriving narrowing instances **) 
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141 

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142 
fun mk_equations descr vs tycos narrowings (Ts, Us) = 
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143 
let 
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144 
fun mk_call T = 
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(T, Const (@{const_name "Quickcheck_Narrowing.narrowing_class.narrowing"}, narrowingT T)) 
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146 
fun mk_aux_call fTs (k, _) (tyco, Ts) = 
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147 
let 
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148 
val T = Type (tyco, Ts) 
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val _ = if not (null fTs) then raise FUNCTION_TYPE else () 
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150 
in 
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151 
(T, nth narrowings k) 
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152 
end 
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153 
fun mk_consexpr simpleT (c, xs) = 
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154 
let 
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155 
val Ts = map fst xs 
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156 
in snd (fold mk_apply xs (Ts > simpleT, mk_cons c (Ts > simpleT))) end 
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157 
fun mk_rhs exprs = foldr1 mk_sum exprs 
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158 
val rhss = 
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159 
Datatype_Aux.interpret_construction descr vs 
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160 
{ atyp = mk_call, dtyp = mk_aux_call } 
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161 
> (map o apfst) Type 
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162 
> map (fn (T, cs) => map (mk_consexpr T) cs) 
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163 
> map mk_rhs 
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164 
val lhss = narrowings 
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val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss) 
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166 
in 
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167 
eqs 
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168 
end 
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169 

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170 
fun instantiate_narrowing_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy = 
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171 
let 
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172 
val _ = Datatype_Aux.message config "Creating narrowing generators ..."; 
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173 
val narrowingsN = map (prefix (narrowingN ^ "_")) (names @ auxnames); 
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174 
in 
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175 
thy 
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176 
> Class.instantiation (tycos, vs, @{sort narrowing}) 
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177 
> Quickcheck_Common.define_functions 
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(fn narrowings => mk_equations descr vs tycos narrowings (Ts, Us), NONE) 
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prfx [] narrowingsN (map narrowingT (Ts @ Us)) 
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180 
> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) 
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181 
end; 
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182 

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183 
(* testing framework *) 
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184 

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185 
val target = "Haskell" 
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186 

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187 
(** invocation of Haskell interpreter **) 
41905  188 

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189 
val narrowing_engine = File.read (Path.explode "~~/src/HOL/Tools/Quickcheck/Narrowing_Engine.hs") 
41905  190 

191 
fun exec verbose code = 

192 
ML_Context.exec (fn () => Secure.use_text ML_Env.local_context (0, "generated code") verbose code) 

193 

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fun with_overlord_dir name f = 
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195 
let 
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196 
val path = Path.append (Path.explode "~/.isabelle") (Path.basic (name ^ serial_string ())) 
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197 
val _ = Isabelle_System.mkdirs path; 
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198 
in Exn.release (Exn.capture f path) end; 
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199 

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200 
fun value ctxt (get, put, put_ml) (code, value) size = 
41905  201 
let 
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202 
val tmp_prefix = "Quickcheck_Narrowing" 
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203 
val with_tmp_dir = 
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204 
if Config.get ctxt overlord then with_overlord_dir else Isabelle_System.with_tmp_dir 
41905  205 
fun run in_path = 
206 
let 

207 
val code_file = Path.append in_path (Path.basic "Code.hs") 

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208 
val narrowing_engine_file = Path.append in_path (Path.basic "Narrowing_Engine.hs") 
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val main_file = Path.append in_path (Path.basic "Main.hs") 
210 
val main = "module Main where {\n\n" ^ 

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"import Narrowing_Engine;\n" ^ 
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"import Code;\n\n" ^ 
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"main = Narrowing_Engine.depthCheck " ^ string_of_int size ^ " (Code.value ())\n\n" ^ 
41905  214 
"}\n" 
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val code' = prefix "module Code where {\n\ndata Typerep = Typerep String [Typerep];\n" 
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(unprefix "module Code where {" code) 
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217 
val _ = File.write code_file code' 
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218 
val _ = File.write narrowing_engine_file narrowing_engine 
41905  219 
val _ = File.write main_file main 
41946  220 
val executable = File.shell_path (Path.append in_path (Path.basic "isa_lsc")) 
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221 
val cmd = "( exec \"$ISABELLE_GHC\" fglasgowexts " ^ 
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(space_implode " " (map File.shell_path [code_file, narrowing_engine_file, main_file])) ^ 
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223 
" o " ^ executable ^ "; ) && " ^ executable 
41905  224 
in 
225 
bash_output cmd 

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226 
end 
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227 
val result = with_tmp_dir tmp_prefix run 
41905  228 
val output_value = the_default "NONE" 
229 
(try (snd o split_last o filter_out (fn s => s = "") o split_lines o fst) result) 

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> translate_string (fn s => if s = "\\" then "\\\\" else s) 
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val ml_code = "\nval _ = Context.set_thread_data (SOME (Context.map_proof (" ^ put_ml 
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^ " (fn () => " ^ output_value ^ ")) (ML_Context.the_generic_context ())))"; 

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val ctxt' = ctxt 

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> put (fn () => error ("Bad evaluation for " ^ quote put_ml)) 

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> Context.proof_map (exec false ml_code); 

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in get ctxt' () end; 

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fun evaluation cookie thy evaluator vs_t args size = 
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let 
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val ctxt = Proof_Context.init_global thy; 
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val (program_code, value_name) = evaluator vs_t; 
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val value_code = space_implode " " 

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(value_name :: "()" :: map (enclose "(" ")") args); 

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in Exn.interruptible_capture (value ctxt cookie (program_code, value_code)) size end; 
41905  245 

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fun dynamic_value_strict cookie thy postproc t args size = 
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let 
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fun evaluator naming program ((_, vs_ty), t) deps = 

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evaluation cookie thy (Code_Target.evaluator thy target naming program deps) (vs_ty, t) args size; 
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in Exn.release (Code_Thingol.dynamic_value thy (Exn.map_result o postproc) evaluator t) end; 
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(** counterexample generator **) 
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structure Counterexample = Proof_Data 
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( 
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type T = unit > term list option 

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fun init _ () = error "Counterexample" 
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) 
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val put_counterexample = Counterexample.put 
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fun finitize_functions t = 
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let 
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val ((names, Ts), t') = apfst split_list (strip_abs t) 
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fun mk_eval_ffun dT rT = 
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Const (@{const_name "Quickcheck_Narrowing.eval_ffun"}, 
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Type (@{type_name "Quickcheck_Narrowing.ffun"}, [dT, rT]) > dT > rT) 
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fun mk_eval_cfun dT rT = 
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Const (@{const_name "Quickcheck_Narrowing.eval_cfun"}, 
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Type (@{type_name "Quickcheck_Narrowing.cfun"}, [rT]) > dT > rT) 
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fun eval_function (T as Type (@{type_name fun}, [dT, rT])) = 
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let 
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val (rt', rT') = eval_function rT 
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in 
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case dT of 
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Type (@{type_name fun}, _) => 
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(fn t => absdummy (dT, rt' (mk_eval_cfun dT rT' $ incr_boundvars 1 t $ Bound 0)), 
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Type (@{type_name "Quickcheck_Narrowing.cfun"}, [rT'])) 
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 _ => (fn t => absdummy (dT, rt' (mk_eval_ffun dT rT' $ incr_boundvars 1 t $ Bound 0)), 
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Type (@{type_name "Quickcheck_Narrowing.ffun"}, [dT, rT'])) 
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end 
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 eval_function T = (I, T) 
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val (tt, Ts') = split_list (map eval_function Ts) 
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val t'' = subst_bounds (map2 (fn f => fn x => f x) (rev tt) (map_index (Bound o fst) Ts), t') 
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in 
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list_abs (names ~~ Ts', t'') 
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end 
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fun compile_generator_expr ctxt [(t, eval_terms)] [_, size] = 
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let 
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val thy = Proof_Context.theory_of ctxt 
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val t' = list_abs_free (Term.add_frees t [], t) 
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val t'' = if Config.get ctxt finite_functions then finitize_functions t' else t' 
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fun ensure_testable t = 
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Const (@{const_name Quickcheck_Narrowing.ensure_testable}, fastype_of t > fastype_of t) $ t 
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val result = dynamic_value_strict 
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(Counterexample.get, Counterexample.put, "Narrowing_Generators.put_counterexample") 
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thy (Option.map o map) (ensure_testable t'') [] size 
41905  299 
in 
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(result, NONE) 
41905  301 
end; 
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(* setup *) 
41905  304 

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val setup = 

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Code.datatype_interpretation ensure_partial_term_of 
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#> Code.datatype_interpretation ensure_partial_term_of_code 
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#> Datatype.interpretation (Quickcheck_Common.ensure_sort_datatype 
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(((@{sort typerep}, @{sort term_of}), @{sort narrowing}), instantiate_narrowing_datatype)) 
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#> Context.theory_map 
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(Quickcheck.add_generator ("narrowing", compile_generator_expr)) 
41905  312 

313 
end; 