author | bulwahn |
Mon, 08 Nov 2010 09:25:43 +0100 | |
changeset 40420 | 552563ea3304 |
child 40639 | f1f0e6adca0a |
permissions | -rw-r--r-- |
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(* Title: HOL/Tools/smallvalue_generators.ML |
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Author: Lukas Bulwahn, TU Muenchen |
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Generators for small values for various types. |
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*) |
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signature SMALLVALUE_GENERATORS = |
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sig |
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val ensure_smallvalue_datatype: Datatype.config -> string list -> theory -> theory |
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val compile_generator_expr: |
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Proof.context -> term -> int -> term list option * (bool list * bool) |
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val put_counterexample: (unit -> int -> term list option) |
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-> Proof.context -> Proof.context |
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val setup: theory -> theory |
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end; |
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structure Smallvalue_Generators : SMALLVALUE_GENERATORS = |
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struct |
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(** general term functions **) |
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fun dest_funT (Type ("fun",[S, T])) = (S, T) |
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| dest_funT T = raise TYPE ("dest_funT", [T], []) |
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fun mk_fun_comp (t, u) = |
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let |
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val (_, B) = dest_funT (fastype_of t) |
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val (C, A) = dest_funT (fastype_of u) |
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in |
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Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u |
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end; |
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fun mk_measure f = |
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let |
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val Type ("fun", [T, @{typ nat}]) = fastype_of f |
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Const (@{const_name Wellfounded.measure}, |
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(T --> @{typ nat}) --> HOLogic.mk_prodT (T, T) --> @{typ bool}) |
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$ f |
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end |
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fun mk_sumcases rT f (Type (@{type_name Sum_Type.sum}, [TL, TR])) = |
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let |
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val lt = mk_sumcases rT f TL |
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val rt = mk_sumcases rT f TR |
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in |
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SumTree.mk_sumcase TL TR rT lt rt |
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end |
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| mk_sumcases _ f T = f T |
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(** abstract syntax **) |
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val size = @{term "i :: code_numeral"} |
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val size_pred = @{term "(i :: code_numeral) - 1"} |
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val size_ge_zero = @{term "(i :: code_numeral) > 0"} |
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fun test_function T = Free ("f", T --> @{typ "term list option"}) |
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fun mk_none_continuation (x, y) = |
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let |
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val (T as Type(@{type_name "option"}, [T'])) = fastype_of x |
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in |
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Const (@{const_name Option.option_case}, T --> (T' --> T) --> T --> T) |
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$ y $ Const (@{const_name Some}, T' --> T) $ x |
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end |
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(** datatypes **) |
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(* constructing smallvalue generator instances on datatypes *) |
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exception FUNCTION_TYPE; |
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val smallN = "small"; |
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fun smallT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ code_numeral} |
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--> @{typ "Code_Evaluation.term list option"} |
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fun mk_equations thy descr vs tycos (names, auxnames) (Ts, Us) = |
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let |
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val smallsN = map (prefix (smallN ^ "_")) (names @ auxnames); |
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val smalls = map2 (fn name => fn T => Free (name, smallT T)) |
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smallsN (Ts @ Us) |
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fun mk_small_call T = |
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let |
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val small = Const (@{const_name "Smallcheck.small_class.small"}, smallT T) |
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in |
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(T, (fn t => small $ absdummy (T, t) $ size_pred)) |
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end |
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fun mk_small_aux_call fTs (k, _) (tyco, Ts) = |
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let |
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val T = Type (tyco, Ts) |
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val _ = if not (null fTs) then raise FUNCTION_TYPE else () |
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val small = nth smalls k |
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in |
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(T, (fn t => small $ absdummy (T, t) $ size_pred)) |
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end |
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fun mk_consexpr simpleT (c, xs) = |
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let |
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val (Ts, fns) = split_list xs |
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val constr = Const (c, Ts ---> simpleT) |
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val bounds = map Bound (((length xs) - 1) downto 0) |
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val start_term = test_function simpleT $ (list_comb (constr, bounds)) |
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in fold_rev (fn f => fn t => f t) fns start_term end |
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fun mk_rhs exprs = |
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@{term "If :: bool => term list option => term list option => term list option"} |
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$ size_ge_zero $ (foldr1 mk_none_continuation exprs) $ @{term "None :: term list option"} |
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val rhss = |
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Datatype_Aux.interpret_construction descr vs |
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{ atyp = mk_small_call, dtyp = mk_small_aux_call } |
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|> (map o apfst) Type |
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|> map (fn (T, cs) => map (mk_consexpr T) cs) |
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|> map mk_rhs |
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val lhss = map2 (fn t => fn T => t $ test_function T $ size) smalls (Ts @ Us); |
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val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss) |
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in |
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(Ts @ Us ~~ (smallsN ~~ eqs)) |
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end |
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val less_int_pred = @{lemma "i > 0 ==> Code_Numeral.nat_of ((i :: code_numeral) - 1) < Code_Numeral.nat_of i" by auto} |
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fun gen_inst_state_tac ctxt rel st = |
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case Term.add_vars (prop_of st) [] of |
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[v as (_, T)] => |
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let |
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val cert = Thm.cterm_of (ProofContext.theory_of ctxt) |
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val rel' = cert rel |
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val st' = Thm.incr_indexes (#maxidx (Thm.rep_cterm rel') + 1) st (*FIXME??*) |
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in |
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PRIMITIVE (Drule.cterm_instantiate [(cert (Var v), rel')]) st' |
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end |
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131 |
| _ => Seq.empty; |
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132 |
|
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133 |
fun instantiate_smallvalue_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy = |
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134 |
let |
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135 |
val _ = Datatype_Aux.message config "Creating smallvalue generators ..."; |
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136 |
val eqs = mk_equations thy descr vs tycos (names, auxnames) (Ts, Us) |
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137 |
fun my_relation_tac ctxt st = |
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138 |
let |
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139 |
val ((_ $ (_ $ rel)) :: tl) = prems_of st |
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140 |
val domT = (HOLogic.dest_setT (fastype_of rel)) |
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141 |
fun mk_single_measure T = mk_fun_comp (@{term "Code_Numeral.nat_of"}, |
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142 |
Const (@{const_name "Product_Type.snd"}, T --> @{typ "code_numeral"})) |
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143 |
val measure = mk_measure (mk_sumcases @{typ nat} mk_single_measure domT) |
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144 |
in |
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145 |
(Function_Common.apply_termination_rule ctxt 1 |
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146 |
THEN gen_inst_state_tac ctxt measure) st |
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147 |
end |
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148 |
fun termination_tac ctxt = |
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149 |
my_relation_tac ctxt |
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150 |
THEN rtac @{thm wf_measure} 1 |
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151 |
THEN (REPEAT_DETERM (Simplifier.asm_full_simp_tac |
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152 |
(HOL_basic_ss addsimps [@{thm in_measure}, @{thm o_def}, @{thm snd_conv}, |
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153 |
@{thm nat_mono_iff}, less_int_pred] @ @{thms sum.cases}) 1)) |
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154 |
fun pat_completeness_auto ctxt = |
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155 |
Pat_Completeness.pat_completeness_tac ctxt 1 |
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156 |
THEN auto_tac (clasimpset_of ctxt) |
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157 |
in |
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158 |
thy |
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159 |
|> Class.instantiation (tycos, vs, @{sort small}) |
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160 |
|> Function.add_function |
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161 |
(map (fn (T, (name, _)) => |
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162 |
Syntax.no_syn (Binding.conceal (Binding.name name), SOME (smallT T))) eqs) |
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163 |
(map (pair (apfst Binding.conceal Attrib.empty_binding) o snd o snd) eqs) |
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164 |
Function_Common.default_config pat_completeness_auto |
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165 |
|> snd |
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166 |
|> Local_Theory.restore |
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167 |
|> (fn lthy => Function.prove_termination NONE (termination_tac lthy) lthy) |
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168 |
|> snd |
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169 |
|> Class.prove_instantiation_exit (K (Class.intro_classes_tac [])) |
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170 |
end; |
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171 |
|
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172 |
fun ensure_smallvalue_datatype config raw_tycos thy = |
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173 |
let |
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174 |
val algebra = Sign.classes_of thy; |
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175 |
val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) = |
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176 |
Datatype.the_descr thy raw_tycos; |
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177 |
val typerep_vs = (map o apsnd) |
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178 |
(curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs; |
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179 |
val smallvalue_insts = (map (rpair @{sort small}) o flat o maps snd o maps snd) |
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180 |
(Datatype_Aux.interpret_construction descr typerep_vs |
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181 |
{ atyp = single, dtyp = (K o K o K) [] }); |
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182 |
(*val term_of_insts = (map (rpair @{sort term_of}) o flat o maps snd o maps snd) |
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183 |
(Datatype_Aux.interpret_construction descr typerep_vs |
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184 |
{ atyp = K [], dtyp = K o K });*) |
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185 |
val has_inst = exists (fn tyco => |
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186 |
can (Sorts.mg_domain algebra tyco) @{sort small}) tycos; |
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187 |
in if has_inst then thy |
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188 |
else case Quickcheck_Generators.perhaps_constrain thy smallvalue_insts typerep_vs |
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189 |
of SOME constrain => (instantiate_smallvalue_datatype config descr |
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190 |
(map constrain typerep_vs) tycos prfx (names, auxnames) |
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191 |
((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy |
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192 |
handle FUNCTION_TYPE => |
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193 |
(Datatype_Aux.message config |
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194 |
"Creation of smallvalue generators failed because the datatype contains a function type"; |
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195 |
thy)) |
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196 |
| NONE => thy |
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197 |
end; |
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198 |
|
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199 |
(** building and compiling generator expressions **) |
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200 |
|
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201 |
structure Counterexample = Proof_Data ( |
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202 |
type T = unit -> int -> term list option |
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203 |
fun init _ () = error "Counterexample" |
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204 |
); |
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205 |
val put_counterexample = Counterexample.put; |
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206 |
|
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207 |
val target = "Quickcheck"; |
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208 |
|
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209 |
fun mk_generator_expr thy prop Ts = |
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210 |
let |
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211 |
val bound_max = length Ts - 1; |
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212 |
val bounds = map Bound (bound_max downto 0) |
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213 |
val result = list_comb (prop, bounds); |
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214 |
val terms = HOLogic.mk_list @{typ term} (map2 HOLogic.mk_term_of Ts bounds); |
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215 |
val check = |
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216 |
@{term "Smallcheck.catch_match :: term list option => term list option => term list option"} $ |
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217 |
(@{term "If :: bool => term list option => term list option => term list option"} |
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218 |
$ result $ @{term "None :: term list option"} |
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219 |
$ (@{term "Some :: term list => term list option"} $ terms)) |
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220 |
$ @{term "None :: term list option"}; |
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221 |
fun mk_small_closure (depth, T) t = |
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222 |
Const (@{const_name "Smallcheck.small_class.small"}, smallT T) |
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223 |
$ absdummy (T, t) $ depth |
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224 |
in Abs ("d", @{typ code_numeral}, fold_rev mk_small_closure (rev bounds ~~ Ts) check) end |
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225 |
|
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226 |
fun compile_generator_expr ctxt t = |
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227 |
let |
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228 |
val Ts = (map snd o fst o strip_abs) t; |
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229 |
val thy = ProofContext.theory_of ctxt |
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230 |
in if Quickcheck.report ctxt then |
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231 |
error "Compilation with reporting facility is not supported" |
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232 |
else |
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233 |
let |
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234 |
val t' = mk_generator_expr thy t Ts; |
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235 |
val compile = Code_Runtime.dynamic_value_strict |
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236 |
(Counterexample.get, put_counterexample, "Smallvalue_Generators.put_counterexample") |
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237 |
thy (SOME target) (fn proc => fn g => g #> (Option.map o map) proc) t' []; |
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238 |
val dummy_report = ([], false) |
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239 |
in compile #> rpair dummy_report end |
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240 |
end; |
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241 |
|
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242 |
(** setup **) |
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243 |
|
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244 |
val setup = |
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245 |
Datatype.interpretation ensure_smallvalue_datatype |
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246 |
#> Context.theory_map |
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247 |
(Quickcheck.add_generator ("small", compile_generator_expr)); |
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248 |
|
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249 |
end; |