# HG changeset patch
# User bulwahn
# Date 1289204743 -3600
# Node ID 552563ea330487f7e9b1e31c4cfbbb2a27148109
# Parent  718b44dbd74dc1974c0358b1e360fc78f8a99611
adding code and theory for smallvalue generators, but do not setup the interpretation yet

diff -r 718b44dbd74d -r 552563ea3304 src/HOL/IsaMakefile
--- a/src/HOL/IsaMakefile	Mon Nov 08 02:33:48 2010 +0100
+++ b/src/HOL/IsaMakefile	Mon Nov 08 09:25:43 2010 +0100
@@ -270,6 +270,7 @@
   Semiring_Normalization.thy \
   SetInterval.thy \
   Sledgehammer.thy \
+  Smallcheck.thy \
   SMT.thy \
   String.thy \
   Typerep.thy \
@@ -336,6 +337,7 @@
   Tools/Sledgehammer/sledgehammer_atp_reconstruct.ML \
   Tools/Sledgehammer/sledgehammer_atp_translate.ML \
   Tools/Sledgehammer/sledgehammer_util.ML \
+  Tools/smallvalue_generators.ML \
   Tools/SMT/smtlib_interface.ML \
   Tools/SMT/smt_builtin.ML \
   Tools/SMT/smt_monomorph.ML \
diff -r 718b44dbd74d -r 552563ea3304 src/HOL/Main.thy
--- a/src/HOL/Main.thy	Mon Nov 08 02:33:48 2010 +0100
+++ b/src/HOL/Main.thy	Mon Nov 08 09:25:43 2010 +0100
@@ -1,7 +1,7 @@
 header {* Main HOL *}
 
 theory Main
-imports Plain Record Predicate_Compile Nitpick
+imports Plain Record Predicate_Compile Smallcheck Nitpick
 begin
 
 text {*
diff -r 718b44dbd74d -r 552563ea3304 src/HOL/Smallcheck.thy
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Smallcheck.thy	Mon Nov 08 09:25:43 2010 +0100
@@ -0,0 +1,69 @@
+(* Author: Lukas Bulwahn, TU Muenchen *)
+
+header {* Another simple counterexample generator *}
+
+theory Smallcheck
+imports Quickcheck
+uses ("Tools/smallvalue_generators.ML")
+begin
+
+
+section {* small value generator type classes *}
+
+class small = term_of +
+fixes small :: "('a \<Rightarrow> term list option) \<Rightarrow> code_numeral \<Rightarrow> term list option"
+
+instantiation unit :: small
+begin
+
+definition "find_first f d = f ()"
+
+instance ..
+
+end
+
+instantiation int :: small
+begin
+
+function small' :: "(int => term list option) => int => int => term list option"
+where "small' f d i = (if d < i then None else (case f i of Some t => Some t | None => small' f d (i + 1)))"
+by pat_completeness auto
+
+termination 
+  by (relation "measure (%(_, d, i). nat (d + 1 - i))") auto
+
+definition "small f d = small' f (Code_Numeral.int_of d) (- (Code_Numeral.int_of d))"
+
+instance ..
+
+end
+
+instantiation prod :: (small, small) small
+begin
+
+definition
+  "small f d = small (%x. small (%y. f (x, y)) d) d"
+
+instance ..
+
+end
+
+section {* Defining combinators for any first-order data type *}
+
+definition catch_match :: "term list option => term list option => term list option"
+where
+  [code del]: "catch_match t1 t2 = (SOME t. t = t1 \<or> t = t2)"
+
+code_const catch_match 
+  (SML "(_) handle Match => _")
+
+use "Tools/smallvalue_generators.ML"
+
+(* We do not activate smallcheck yet. 
+setup {* Smallvalue_Generators.setup *}
+*)
+
+hide_fact catch_match_def
+hide_const (open) catch_match
+
+end
\ No newline at end of file
diff -r 718b44dbd74d -r 552563ea3304 src/HOL/Tools/smallvalue_generators.ML
--- /dev/null	Thu Jan 01 00:00:00 1970 +0000
+++ b/src/HOL/Tools/smallvalue_generators.ML	Mon Nov 08 09:25:43 2010 +0100
@@ -0,0 +1,249 @@
+(*  Title:      HOL/Tools/smallvalue_generators.ML
+    Author:     Lukas Bulwahn, TU Muenchen
+
+Generators for small values for various types.
+*)
+
+signature SMALLVALUE_GENERATORS =
+sig
+  val ensure_smallvalue_datatype: Datatype.config -> string list -> theory -> theory
+  val compile_generator_expr:
+    Proof.context -> term -> int -> term list option * (bool list * bool)
+  val put_counterexample: (unit -> int -> term list option)
+    -> Proof.context -> Proof.context
+  val setup: theory -> theory
+end;
+
+structure Smallvalue_Generators : SMALLVALUE_GENERATORS =
+struct
+
+(** general term functions **)
+
+fun dest_funT (Type ("fun",[S, T])) = (S, T)
+  | dest_funT T = raise TYPE ("dest_funT", [T], [])
+ 
+fun mk_fun_comp (t, u) =
+  let
+    val (_, B) = dest_funT (fastype_of t)
+    val (C, A) = dest_funT (fastype_of u)
+  in
+    Const(@{const_name "Fun.comp"}, (A --> B) --> (C --> A) --> C --> B) $ t $ u
+  end;
+
+fun mk_measure f =
+  let
+    val Type ("fun", [T, @{typ nat}]) = fastype_of f 
+  in
+    Const (@{const_name Wellfounded.measure},
+      (T --> @{typ nat}) --> HOLogic.mk_prodT (T, T) --> @{typ bool})
+    $ f
+  end
+
+fun mk_sumcases rT f (Type (@{type_name Sum_Type.sum}, [TL, TR])) =
+  let
+    val lt = mk_sumcases rT f TL
+    val rt = mk_sumcases rT f TR
+  in
+    SumTree.mk_sumcase TL TR rT lt rt
+  end
+  | mk_sumcases _ f T = f T
+
+
+(** abstract syntax **)
+
+val size = @{term "i :: code_numeral"}
+val size_pred = @{term "(i :: code_numeral) - 1"}
+val size_ge_zero = @{term "(i :: code_numeral) > 0"}
+fun test_function T = Free ("f", T --> @{typ "term list option"})
+
+fun mk_none_continuation (x, y) =
+  let
+    val (T as Type(@{type_name "option"}, [T'])) = fastype_of x
+  in
+    Const (@{const_name Option.option_case}, T --> (T' --> T) --> T --> T)
+      $ y $ Const (@{const_name Some}, T' --> T) $ x
+  end
+
+(** datatypes **)
+
+(* constructing smallvalue generator instances on datatypes *)
+
+exception FUNCTION_TYPE;
+
+val smallN = "small";
+
+fun smallT T = (T --> @{typ "Code_Evaluation.term list option"}) --> @{typ code_numeral}
+  --> @{typ "Code_Evaluation.term list option"}
+
+fun mk_equations thy descr vs tycos (names, auxnames) (Ts, Us) =
+  let
+    val smallsN = map (prefix (smallN ^ "_")) (names @ auxnames);
+    val smalls = map2 (fn name => fn T => Free (name, smallT T))
+      smallsN (Ts @ Us)
+    fun mk_small_call T =
+      let
+        val small = Const (@{const_name "Smallcheck.small_class.small"}, smallT T)        
+      in
+        (T, (fn t => small $ absdummy (T, t) $ size_pred))
+      end
+    fun mk_small_aux_call fTs (k, _) (tyco, Ts) =
+      let
+        val T = Type (tyco, Ts)
+        val _ = if not (null fTs) then raise FUNCTION_TYPE else ()
+        val small = nth smalls k
+      in
+        (T, (fn t => small $ absdummy (T, t) $ size_pred))
+      end
+    fun mk_consexpr simpleT (c, xs) =
+      let
+        val (Ts, fns) = split_list xs
+        val constr = Const (c, Ts ---> simpleT)
+        val bounds = map Bound (((length xs) - 1) downto 0)
+        val start_term = test_function simpleT $ (list_comb (constr, bounds))
+      in fold_rev (fn f => fn t => f t) fns start_term end
+    fun mk_rhs exprs =
+        @{term "If :: bool => term list option => term list option => term list option"}
+            $ size_ge_zero $ (foldr1 mk_none_continuation exprs) $ @{term "None :: term list option"}
+    val rhss =
+      Datatype_Aux.interpret_construction descr vs
+        { atyp = mk_small_call, dtyp = mk_small_aux_call }
+      |> (map o apfst) Type
+      |> map (fn (T, cs) => map (mk_consexpr T) cs)
+      |> map mk_rhs
+    val lhss = map2 (fn t => fn T => t $ test_function T $ size) smalls (Ts @ Us);
+    val eqs = map (HOLogic.mk_Trueprop o HOLogic.mk_eq) (lhss ~~ rhss)
+  in
+    (Ts @ Us ~~ (smallsN ~~ eqs))
+  end
+    
+val less_int_pred = @{lemma "i > 0 ==> Code_Numeral.nat_of ((i :: code_numeral) - 1) < Code_Numeral.nat_of i" by auto}
+
+fun gen_inst_state_tac ctxt rel st =
+  case Term.add_vars (prop_of st) [] of
+    [v as (_, T)] =>
+      let
+        val cert = Thm.cterm_of (ProofContext.theory_of ctxt)
+        val rel' = cert rel
+        val st' = Thm.incr_indexes (#maxidx (Thm.rep_cterm rel') + 1) st (*FIXME??*)
+      in        
+        PRIMITIVE (Drule.cterm_instantiate [(cert (Var v), rel')]) st'
+      end
+  | _ => Seq.empty;
+
+fun instantiate_smallvalue_datatype config descr vs tycos prfx (names, auxnames) (Ts, Us) thy =
+  let
+    val _ = Datatype_Aux.message config "Creating smallvalue generators ...";
+    val eqs = mk_equations thy descr vs tycos (names, auxnames) (Ts, Us)
+    fun my_relation_tac ctxt st =
+      let
+        val ((_ $ (_ $ rel)) :: tl) = prems_of st
+        val domT = (HOLogic.dest_setT (fastype_of rel))
+        fun mk_single_measure T = mk_fun_comp (@{term "Code_Numeral.nat_of"},
+            Const (@{const_name "Product_Type.snd"}, T --> @{typ "code_numeral"}))
+        val measure = mk_measure (mk_sumcases @{typ nat} mk_single_measure domT)
+      in
+        (Function_Common.apply_termination_rule ctxt 1
+        THEN gen_inst_state_tac ctxt measure) st
+      end
+    fun termination_tac ctxt = 
+      my_relation_tac ctxt
+      THEN rtac @{thm wf_measure} 1
+      THEN (REPEAT_DETERM (Simplifier.asm_full_simp_tac 
+        (HOL_basic_ss addsimps [@{thm in_measure}, @{thm o_def}, @{thm snd_conv},
+         @{thm nat_mono_iff}, less_int_pred] @ @{thms sum.cases}) 1))
+    fun pat_completeness_auto ctxt =
+      Pat_Completeness.pat_completeness_tac ctxt 1
+      THEN auto_tac (clasimpset_of ctxt)
+  in
+    thy
+    |> Class.instantiation (tycos, vs, @{sort small})
+    |> Function.add_function
+      (map (fn (T, (name, _)) =>
+          Syntax.no_syn (Binding.conceal (Binding.name name), SOME (smallT T))) eqs)
+        (map (pair (apfst Binding.conceal Attrib.empty_binding) o snd o snd) eqs)
+        Function_Common.default_config pat_completeness_auto
+    |> snd
+    |> Local_Theory.restore
+    |> (fn lthy => Function.prove_termination NONE (termination_tac lthy) lthy)
+    |> snd
+    |> Class.prove_instantiation_exit (K (Class.intro_classes_tac []))
+  end;
+
+fun ensure_smallvalue_datatype config raw_tycos thy =
+  let
+    val algebra = Sign.classes_of thy;
+    val (descr, raw_vs, tycos, prfx, (names, auxnames), raw_TUs) =
+      Datatype.the_descr thy raw_tycos;
+    val typerep_vs = (map o apsnd)
+      (curry (Sorts.inter_sort algebra) @{sort typerep}) raw_vs;
+    val smallvalue_insts = (map (rpair @{sort small}) o flat o maps snd o maps snd)
+      (Datatype_Aux.interpret_construction descr typerep_vs
+        { atyp = single, dtyp = (K o K o K) [] });
+    (*val term_of_insts = (map (rpair @{sort term_of}) o flat o maps snd o maps snd)
+      (Datatype_Aux.interpret_construction descr typerep_vs
+        { atyp = K [], dtyp = K o K });*)
+    val has_inst = exists (fn tyco =>
+      can (Sorts.mg_domain algebra tyco) @{sort small}) tycos;
+  in if has_inst then thy
+    else case Quickcheck_Generators.perhaps_constrain thy smallvalue_insts typerep_vs
+     of SOME constrain => (instantiate_smallvalue_datatype config descr
+          (map constrain typerep_vs) tycos prfx (names, auxnames)
+            ((pairself o map o map_atyps) (fn TFree v => TFree (constrain v)) raw_TUs) thy
+            handle FUNCTION_TYPE =>
+              (Datatype_Aux.message config
+                "Creation of smallvalue generators failed because the datatype contains a function type";
+              thy))
+      | NONE => thy
+  end;
+
+(** building and compiling generator expressions **)
+
+structure Counterexample = Proof_Data (
+  type T = unit -> int -> term list option
+  fun init _ () = error "Counterexample"
+);
+val put_counterexample = Counterexample.put;
+
+val target = "Quickcheck";
+
+fun mk_generator_expr thy prop Ts =
+  let
+    val bound_max = length Ts - 1;
+    val bounds = map Bound (bound_max downto 0)
+    val result = list_comb (prop, bounds);
+    val terms = HOLogic.mk_list @{typ term} (map2 HOLogic.mk_term_of Ts bounds);
+    val check =
+      @{term "Smallcheck.catch_match :: term list option => term list option => term list option"} $
+        (@{term "If :: bool => term list option => term list option => term list option"}
+        $ result $ @{term "None :: term list option"}
+        $ (@{term "Some :: term list => term list option"} $ terms))
+      $ @{term "None :: term list option"};
+    fun mk_small_closure (depth, T) t =
+      Const (@{const_name "Smallcheck.small_class.small"}, smallT T)
+        $ absdummy (T, t) $ depth
+  in Abs ("d", @{typ code_numeral}, fold_rev mk_small_closure (rev bounds ~~ Ts) check) end
+
+fun compile_generator_expr ctxt t =
+  let
+    val Ts = (map snd o fst o strip_abs) t;
+    val thy = ProofContext.theory_of ctxt
+  in if Quickcheck.report ctxt then
+    error "Compilation with reporting facility is not supported"
+  else
+    let
+      val t' = mk_generator_expr thy t Ts;
+      val compile = Code_Runtime.dynamic_value_strict
+        (Counterexample.get, put_counterexample, "Smallvalue_Generators.put_counterexample")
+        thy (SOME target) (fn proc => fn g => g #> (Option.map o map) proc) t' [];
+      val dummy_report = ([], false)
+    in compile #> rpair dummy_report end
+  end;
+
+(** setup **)
+
+val setup =
+  Datatype.interpretation ensure_smallvalue_datatype
+  #> Context.theory_map
+    (Quickcheck.add_generator ("small", compile_generator_expr));
+
+end;