src/HOL/Tools/smallvalue_generators.ML
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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 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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(* static options *)
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val define_foundationally = false
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(** general term functions **)
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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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  in
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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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fun mk_undefined T = Const(@{const_name undefined}, T)
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(** abstract syntax **)
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fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => Code_Evaluation.term"});
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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", termifyT 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 "Smallcheck.orelse"}, T --> T --> T)
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      $ x $ y
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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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val full_smallN = "full_small";
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fun full_smallT T = (termifyT T --> @{typ "Code_Evaluation.term list option"})
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  --> @{typ code_numeral} --> @{typ "Code_Evaluation.term list option"}
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fun mk_equations thy descr vs tycos smalls (Ts, Us) =
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  let
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    fun mk_small_call T =
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      let
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        val small = Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T)        
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      in
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        (T, (fn t => small $
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          (HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
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          $ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, 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 $
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          (HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
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            $ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, 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 (fn x => Bound (2 * x + 1)) (((length xs) - 1) downto 0)
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        val term_bounds = map (fn x => Bound (2 * x)) (((length xs) - 1) downto 0)
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        val Eval_App = Const ("Code_Evaluation.App", HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
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        val Eval_Const = Const ("Code_Evaluation.Const", HOLogic.literalT --> @{typ typerep} --> HOLogic.termT)
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        val term = fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"}))
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          bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
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        val start_term = test_function simpleT $ 
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        (HOLogic.pair_const simpleT @{typ "unit => Code_Evaluation.term"}
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          $ (list_comb (constr, bounds)) $ absdummy (@{typ unit}, term))
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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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    eqs
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  end
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(* foundational definition with the function package *)
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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 mk_single_measure T = HOLogic.mk_comp (@{term "Code_Numeral.nat_of"},
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    Const (@{const_name "Product_Type.snd"}, T --> @{typ "code_numeral"}))
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fun mk_termination_measure T =
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  let
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    val T' = fst (HOLogic.dest_prodT (HOLogic.dest_setT T))
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  in
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    mk_measure (mk_sumcases @{typ nat} mk_single_measure T')
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  end
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fun termination_tac ctxt = 
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  Function_Relation.relation_tac ctxt mk_termination_measure 1
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  THEN rtac @{thm wf_measure} 1
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  THEN (REPEAT_DETERM (Simplifier.asm_full_simp_tac 
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    (HOL_basic_ss addsimps [@{thm in_measure}, @{thm o_def}, @{thm snd_conv},
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     @{thm nat_mono_iff}, less_int_pred] @ @{thms sum.cases}) 1))
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fun pat_completeness_auto ctxt =
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  Pat_Completeness.pat_completeness_tac ctxt 1
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  THEN auto_tac (clasimpset_of ctxt)    
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(* creating the instances *)
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fun instantiate_smallvalue_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
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  let
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    val _ = Datatype_Aux.message config "Creating smallvalue generators ...";
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    val smallsN = map (prefix (full_smallN ^ "_")) (names @ auxnames);
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  in
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    thy
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    |> Class.instantiation (tycos, vs, @{sort full_small})
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    |> (if define_foundationally then
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      let
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        val smalls = map2 (fn name => fn T => Free (name, full_smallT T)) smallsN (Ts @ Us)
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        val eqs = mk_equations thy descr vs tycos smalls (Ts, Us)
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      in
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        Function.add_function
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          (map (fn (name, T) =>
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              Syntax.no_syn (Binding.conceal (Binding.name name), SOME (full_smallT T)))
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                (smallsN ~~ (Ts @ Us)))
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            (map (pair (apfst Binding.conceal Attrib.empty_binding)) eqs)
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          Function_Common.default_config pat_completeness_auto
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        #> snd
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        #> Local_Theory.restore
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        #> (fn lthy => Function.prove_termination NONE (termination_tac lthy) lthy)
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        #> snd
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      end
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    else
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      fold_map (fn (name, T) => Local_Theory.define
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          ((Binding.conceal (Binding.name name), NoSyn),
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            (apfst Binding.conceal Attrib.empty_binding, mk_undefined (full_smallT T)))
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        #> apfst fst) (smallsN ~~ (Ts @ Us))
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      #> (fn (smalls, lthy) =>
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        let
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          val eqs_t = mk_equations thy descr vs tycos smalls (Ts, Us)
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          val eqs = map (fn eq => Goal.prove lthy ["f", "i"] [] eq
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            (fn _ => Skip_Proof.cheat_tac (ProofContext.theory_of lthy))) eqs_t
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        in
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          fold (fn (name, eq) => Local_Theory.note
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          ((Binding.conceal (Binding.qualify true prfx
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             (Binding.qualify true name (Binding.name "simps"))),
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             Code.add_default_eqn_attrib :: map (Attrib.internal o K)
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               [Simplifier.simp_add, Nitpick_Simps.add]), [eq]) #> snd) (smallsN ~~ eqs) lthy
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        end))
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    |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
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  end handle FUNCTION_TYPE =>
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    (Datatype_Aux.message config
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      "Creation of smallvalue generators failed because the datatype contains a function type";
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    thy)
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(** building and compiling generator expressions **)
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structure Counterexample = Proof_Data (
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  type T = unit -> int -> 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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val target = "Quickcheck";
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fun mk_generator_expr thy prop Ts =
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  let
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    val bound_max = length Ts - 1;
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    val bounds = map_index (fn (i, ty) =>
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      (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
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    val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);
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    val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);
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    val check =
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      @{term "Smallcheck.catch_match :: term list option => term list option => term list option"} $
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        (@{term "If :: bool => term list option => term list option => term list option"}
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        $ result $ @{term "None :: term list option"} $ (@{term "Some :: term list => term list option"} $ terms))
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      $ @{term "None :: term list option"};
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    fun mk_small_closure (_, _, i, T) t =
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      Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T)
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        $ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"}) 
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        $ absdummy (T, absdummy (@{typ "unit => term"}, t))) $ Bound i
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  in Abs ("d", @{typ code_numeral}, fold_rev mk_small_closure bounds check) end
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fun compile_generator_expr ctxt t =
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  let
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    val Ts = (map snd o fst o strip_abs) t;
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    val thy = ProofContext.theory_of ctxt
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  in if Config.get ctxt Quickcheck.report then
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    error "Compilation with reporting facility is not supported"
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  else
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    let
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      val t' = mk_generator_expr thy t Ts;
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      val compile = Code_Runtime.dynamic_value_strict
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        (Counterexample.get, put_counterexample, "Smallvalue_Generators.put_counterexample")
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        thy (SOME target) (fn proc => fn g => g #> (Option.map o map) proc) t' [];
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      val dummy_report = ([], false)
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    in compile #> rpair dummy_report end
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  end;
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(** setup **)
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val setup =
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  Datatype.interpretation
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    (Quickcheck_Generators.ensure_sort_datatype (@{sort full_small}, instantiate_smallvalue_datatype))
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  #> Context.theory_map
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    (Quickcheck.add_generator ("small", compile_generator_expr));
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end;