(* Title: HOL/Tools/smallvalue_generators.ML
Author: Lukas Bulwahn, TU Muenchen
Generators for small values for various types.
*)
signature SMALLVALUE_GENERATORS =
sig
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 **)
fun termifyT T = HOLogic.mk_prodT (T, @{typ "unit => Code_Evaluation.term"});
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", termifyT 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"}
val full_smallN = "full_small";
fun full_smallT T = (termifyT 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 (full_smallN ^ "_")) (names @ auxnames);
val smalls = map2 (fn name => fn T => Free (name, full_smallT T))
smallsN (Ts @ Us)
fun mk_small_call T =
let
val small = Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T)
in
(T, (fn t => small $
(HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
$ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, 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 $
(HOLogic.split_const (T, @{typ "unit => Code_Evaluation.term"}, @{typ "Code_Evaluation.term list option"})
$ absdummy (T, absdummy (@{typ "unit => Code_Evaluation.term"}, 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 (fn x => Bound (2 * x + 1)) (((length xs) - 1) downto 0)
val term_bounds = map (fn x => Bound (2 * x)) (((length xs) - 1) downto 0)
val Eval_App = Const ("Code_Evaluation.App", HOLogic.termT --> HOLogic.termT --> HOLogic.termT)
val Eval_Const = Const ("Code_Evaluation.Const", HOLogic.literalT --> @{typ typerep} --> HOLogic.termT)
val term = fold (fn u => fn t => Eval_App $ t $ (u $ @{term "()"}))
bounds (Eval_Const $ HOLogic.mk_literal c $ HOLogic.mk_typerep (Ts ---> simpleT))
val start_term = test_function simpleT $
(HOLogic.pair_const simpleT @{typ "unit => Code_Evaluation.term"}
$ (list_comb (constr, bounds)) $ absdummy (@{typ unit}, term))
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 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 mk_single_measure T = mk_fun_comp (@{term "Code_Numeral.nat_of"},
Const (@{const_name "Product_Type.snd"}, T --> @{typ "code_numeral"}))
fun mk_termination_measure T =
let
val T' = fst (HOLogic.dest_prodT (HOLogic.dest_setT T))
in
mk_measure (mk_sumcases @{typ nat} mk_single_measure T')
end
fun termination_tac ctxt =
Function_Relation.relation_tac ctxt mk_termination_measure 1
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 full_small})
|> Function.add_function
(map (fn (T, (name, _)) =>
Syntax.no_syn (Binding.conceal (Binding.name name), SOME (full_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 handle FUNCTION_TYPE =>
(Datatype_Aux.message config
"Creation of smallvalue generators failed because the datatype contains a function type";
thy)
(** 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_index (fn (i, ty) =>
(2 * (bound_max - i) + 1, 2 * (bound_max - i), 2 * i, ty)) Ts;
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 "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 (_, _, i, T) t =
Const (@{const_name "Smallcheck.full_small_class.full_small"}, full_smallT T)
$ (HOLogic.split_const (T, @{typ "unit => term"}, @{typ "term list option"})
$ absdummy (T, absdummy (@{typ "unit => term"}, t))) $ Bound i
in Abs ("d", @{typ code_numeral}, fold_rev mk_small_closure bounds 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
(Quickcheck_Generators.ensure_sort_datatype (@{sort full_small}, instantiate_smallvalue_datatype))
#> Context.theory_map
(Quickcheck.add_generator ("small", compile_generator_expr));
end;