(* Author: Florian Haftmann, TU Muenchen *)

header {* A simple counterexample generator *}

theory Quickcheck

imports Random Code_Eval

begin

notation fcomp (infixl "o>" 60)

notation scomp (infixl "o\<rightarrow>" 60)

subsection {* The @{text random} class *}

class random = typerep +

  fixes random :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a \<times> (unit \<Rightarrow> term)) \<times> Random.seed"

subsection {* Quickcheck generator *}

ML {*

structure Quickcheck =

struct

open Quickcheck;

val eval_ref : (unit -> int -> int * int -> term list option * (int * int)) option ref = ref NONE;

val target = "Quickcheck";

fun mk_generator_expr thy prop tys =

  let

    val bound_max = length tys - 1;

    val bounds = map_index (fn (i, ty) =>

      (2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) tys;

    val result = list_comb (prop, map (fn (i, _, _, _) => Bound i) bounds);

    val terms = HOLogic.mk_list @{typ term} (map (fn (_, i, _, _) => Bound i $ @{term "()"}) bounds);

    val check = @{term "If \<Colon> bool \<Rightarrow> term list option \<Rightarrow> term list option \<Rightarrow> term list option"}

      $ result $ @{term "None \<Colon> term list option"} $ (@{term "Some \<Colon> term list \<Rightarrow> term list option "} $ terms);

    val return = @{term "Pair \<Colon> term list option \<Rightarrow> Random.seed \<Rightarrow> term list option \<times> Random.seed"};

    fun liftT T sT = sT --> HOLogic.mk_prodT (T, sT);

    fun mk_termtyp ty = HOLogic.mk_prodT (ty, @{typ "unit \<Rightarrow> term"});

    fun mk_scomp T1 T2 sT f g = Const (@{const_name scomp},

      liftT T1 sT --> (T1 --> liftT T2 sT) --> liftT T2 sT) $ f $ g;

    fun mk_split ty = Sign.mk_const thy

      (@{const_name split}, [ty, @{typ "unit \<Rightarrow> term"}, liftT @{typ "term list option"} @{typ Random.seed}]);

    fun mk_scomp_split ty t t' =

      mk_scomp (mk_termtyp ty) @{typ "term list option"} @{typ Random.seed} t

        (mk_split ty $ Abs ("", ty, Abs ("", @{typ "unit \<Rightarrow> term"}, t')));

    fun mk_bindclause (_, _, i, ty) = mk_scomp_split ty

      (Sign.mk_const thy (@{const_name random}, [ty]) $ Bound i);

  in Abs ("n", @{typ code_numeral}, fold_rev mk_bindclause bounds (return $ check)) end;

fun compile_generator_expr thy t =

  let

    val tys = (map snd o fst o strip_abs) t;

    val t' = mk_generator_expr thy t tys;

    val f = Code_ML.eval (SOME target) ("Quickcheck.eval_ref", eval_ref)

      (fn proc => fn g => fn s => g s #>> (Option.map o map) proc) thy t' [];

  in f #> Random_Engine.run end;

end

*}

setup {*

  Code_Target.extend_target (Quickcheck.target, (Code_ML.target_Eval, K I))

  #> Quickcheck.add_generator ("code", Quickcheck.compile_generator_expr o ProofContext.theory_of)

*}

subsection {* Fundamental types*}

instantiation bool :: random

begin

definition

  "random i = Random.range i o\<rightarrow>

    (\<lambda>k. Pair (if (k div 2 = 0) then Code_Eval.valtermify True else Code_Eval.valtermify False))"

instance ..

end

instantiation itself :: (typerep) random

begin

definition random_itself :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> ('a itself \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where

  "random_itself _ = Pair (Code_Eval.valtermify TYPE('a))"

instance ..

end

text {* Type @{typ "'a \<Rightarrow> 'b"} *}

ML {*

structure Random_Engine =

struct

open Random_Engine;

fun random_fun (T1 : typ) (T2 : typ) (eq : 'a -> 'a -> bool) (term_of : 'a -> term)

    (random : Random_Engine.seed -> ('b * (unit -> term)) * Random_Engine.seed)

    (random_split : Random_Engine.seed -> Random_Engine.seed * Random_Engine.seed)

    (seed : Random_Engine.seed) =

  let

    val (seed', seed'') = random_split seed;

    val state = ref (seed', [], Const (@{const_name undefined}, T1 --> T2));

    val fun_upd = Const (@{const_name fun_upd},

      (T1 --> T2) --> T1 --> T2 --> T1 --> T2);

    fun random_fun' x =

      let

        val (seed, fun_map, f_t) = ! state;

      in case AList.lookup (uncurry eq) fun_map x

       of SOME y => y

        | NONE => let

              val t1 = term_of x;

              val ((y, t2), seed') = random seed;

              val fun_map' = (x, y) :: fun_map;

              val f_t' = fun_upd $ f_t $ t1 $ t2 ();

              val _ = state := (seed', fun_map', f_t');

            in y end

      end;

    fun term_fun' () = #3 (! state);

  in ((random_fun', term_fun'), seed'') end;

end

*}

axiomatization random_fun_aux :: "typerep \<Rightarrow> typerep \<Rightarrow> ('a \<Rightarrow> 'a \<Rightarrow> bool) \<Rightarrow> ('a \<Rightarrow> term)

  \<Rightarrow> (Random.seed \<Rightarrow> ('b \<times> (unit \<Rightarrow> term)) \<times> Random.seed) \<Rightarrow> (Random.seed \<Rightarrow> Random.seed \<times> Random.seed)

  \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed"

code_const random_fun_aux (Quickcheck "Random'_Engine.random'_fun")

  -- {* With enough criminal energy this can be abused to derive @{prop False};

  for this reason we use a distinguished target @{text Quickcheck}

  not spoiling the regular trusted code generation *}

instantiation "fun" :: ("{eq, term_of}", "{type, random}") random

begin

definition random_fun :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (('a \<Rightarrow> 'b) \<times> (unit \<Rightarrow> term)) \<times> Random.seed" where

  "random n = random_fun_aux TYPEREP('a) TYPEREP('b) (op =) Code_Eval.term_of (random n) Random.split_seed"

instance ..

end

code_reserved Quickcheck Random_Engine

subsection {* Numeric types *}

instantiation nat :: random

begin

definition random_nat :: "code_numeral \<Rightarrow> Random.seed \<Rightarrow> (nat \<times> (unit \<Rightarrow> Code_Eval.term)) \<times> Random.seed" where

  "random_nat i = Random.range (i + 1) o\<rightarrow> (\<lambda>k. Pair (

     let n = Code_Numeral.nat_of k

     in (n, \<lambda>_. Code_Eval.term_of n)))"

instance ..

end

instantiation int :: random

begin

definition

  "random i = Random.range (2 * i + 1) o\<rightarrow> (\<lambda>k. Pair (

     let j = (if k \<ge> i then Code_Numeral.int_of (k - i) else - Code_Numeral.int_of (i - k))

     in (j, \<lambda>_. Code_Eval.term_of j)))"

instance ..

end

no_notation fcomp (infixl "o>" 60)

no_notation scomp (infixl "o\<rightarrow>" 60)

end