isabelle: comparison src/HOL/Tools/refute.ML

equal deleted inserted replaced

-:9f655a6bffd8
+:5b4b0e4e5205
-(*  Title:      HOL/Tools/refute.ML
-Author:     Tjark Weber, TU Muenchen
-Finite model generation for HOL formulas, using a SAT solver.
-*)
-(* ------------------------------------------------------------------------- *)
-(* Declares the 'REFUTE' signature as well as a structure 'Refute'.          *)
-(* Documentation is available in the Isabelle/Isar theory 'HOL/Refute.thy'.  *)
-(* ------------------------------------------------------------------------- *)
-signature REFUTE =
-sig
-exception REFUTE of string * string
-(* ------------------------------------------------------------------------- *)
-(* Model/interpretation related code (translation HOL -> propositional logic *)
-(* ------------------------------------------------------------------------- *)
-type params
-type interpretation
-type model
-type arguments
-exception MAXVARS_EXCEEDED
-val add_interpreter : string -> (Proof.context -> model -> arguments -> term ->
-(interpretation * model * arguments) option) -> theory -> theory
-val add_printer : string -> (Proof.context -> model -> typ ->
-interpretation -> (int -> bool) -> term option) -> theory -> theory
-val interpret : Proof.context -> model -> arguments -> term ->
-(interpretation * model * arguments)
-val print : Proof.context -> model -> typ -> interpretation -> (int -> bool) -> term
-val print_model : Proof.context -> model -> (int -> bool) -> string
-(* ------------------------------------------------------------------------- *)
-(* Interface                                                                 *)
-(* ------------------------------------------------------------------------- *)
-val set_default_param  : (string * string) -> theory -> theory
-val get_default_param  : Proof.context -> string -> string option
-val get_default_params : Proof.context -> (string * string) list
-val actual_params      : Proof.context -> (string * string) list -> params
-val find_model :
-Proof.context -> params -> term list -> term -> bool -> string
-(* tries to find a model for a formula: *)
-val satisfy_term :
-Proof.context -> (string * string) list -> term list -> term -> string
-(* tries to find a model that refutes a formula: *)
-val refute_term :
-Proof.context -> (string * string) list -> term list -> term -> string
-val refute_goal :
-Proof.context -> (string * string) list -> thm -> int -> string
-val setup : theory -> theory
-(* ------------------------------------------------------------------------- *)
-(* Additional functions used by Nitpick (to be factored out)                 *)
-(* ------------------------------------------------------------------------- *)
-val get_classdef : theory -> string -> (string * term) option
-val norm_rhs : term -> term
-val get_def : theory -> string * typ -> (string * term) option
-val get_typedef : theory -> typ -> (string * term) option
-val is_IDT_constructor : theory -> string * typ -> bool
-val is_IDT_recursor : theory -> string * typ -> bool
-val is_const_of_class: theory -> string * typ -> bool
-val string_of_typ : typ -> string
-end;
-structure Refute : REFUTE =
-struct
-open Prop_Logic;
-(* We use 'REFUTE' only for internal error conditions that should    *)
-(* never occur in the first place (i.e. errors caused by bugs in our *)
-(* code).  Otherwise (e.g. to indicate invalid input data) we use    *)
-(* 'error'.                                                          *)
-exception REFUTE of string * string;  (* ("in function", "cause") *)
-(* should be raised by an interpreter when more variables would be *)
-(* required than allowed by 'maxvars'                              *)
-exception MAXVARS_EXCEEDED;
-(* ------------------------------------------------------------------------- *)
-(* TREES                                                                     *)
-(* ------------------------------------------------------------------------- *)
-(* ------------------------------------------------------------------------- *)
-(* tree: implements an arbitrarily (but finitely) branching tree as a list   *)
-(*       of (lists of ...) elements                                          *)
-(* ------------------------------------------------------------------------- *)
-datatype 'a tree =
-Leaf of 'a
-| Node of ('a tree) list;
-(* ('a -> 'b) -> 'a tree -> 'b tree *)
-fun tree_map f tr =
-case tr of
-Leaf x  => Leaf (f x)
-| Node xs => Node (map (tree_map f) xs);
-(* ('a * 'b -> 'a) -> 'a * ('b tree) -> 'a *)
-fun tree_foldl f =
-let
-fun itl (e, Leaf x)  = f(e,x)
-| itl (e, Node xs) = Library.foldl (tree_foldl f) (e,xs)
-in
-itl
-end;
-(* 'a tree * 'b tree -> ('a * 'b) tree *)
-fun tree_pair (t1, t2) =
-case t1 of
-Leaf x =>
-(case t2 of
-Leaf y => Leaf (x,y)
-| Node _ => raise REFUTE ("tree_pair",
-"trees are of different height (second tree is higher)"))
-| Node xs =>
-(case t2 of
-(* '~~' will raise an exception if the number of branches in   *)
-(* both trees is different at the current node                 *)
-Node ys => Node (map tree_pair (xs ~~ ys))
-| Leaf _  => raise REFUTE ("tree_pair",
-"trees are of different height (first tree is higher)"));
-(* ------------------------------------------------------------------------- *)
-(* params: parameters that control the translation into a propositional      *)
-(*         formula/model generation                                          *)
-(*                                                                           *)
-(* The following parameters are supported (and required (!), except for      *)
-(* "sizes" and "expect"):                                                    *)
-(*                                                                           *)
-(* Name          Type    Description                                         *)
-(*                                                                           *)
-(* "sizes"       (string * int) list                                         *)
-(*                       Size of ground types (e.g. 'a=2), or depth of IDTs. *)
-(* "minsize"     int     If >0, minimal size of each ground type/IDT depth.  *)
-(* "maxsize"     int     If >0, maximal size of each ground type/IDT depth.  *)
-(* "maxvars"     int     If >0, use at most 'maxvars' Boolean variables      *)
-(*                       when transforming the term into a propositional     *)
-(*                       formula.                                            *)
-(* "maxtime"     int     If >0, terminate after at most 'maxtime' seconds.   *)
-(* "satsolver"   string  SAT solver to be used.                              *)
-(* "no_assms"    bool    If "true", assumptions in structured proofs are     *)
-(*                       not considered.                                     *)
-(* "expect"      string  Expected result ("genuine", "potential", "none", or *)
-(*                       "unknown").                                         *)
-(* ------------------------------------------------------------------------- *)
-type params =
-{
-sizes    : (string * int) list,
-minsize  : int,
-maxsize  : int,
-maxvars  : int,
-maxtime  : int,
-satsolver: string,
-no_assms : bool,
-expect   : string
-};
-(* ------------------------------------------------------------------------- *)
-(* interpretation: a term's interpretation is given by a variable of type    *)
-(*                 'interpretation'                                          *)
-(* ------------------------------------------------------------------------- *)
-type interpretation =
-prop_formula list tree;
-(* ------------------------------------------------------------------------- *)
-(* model: a model specifies the size of types and the interpretation of      *)
-(*        terms                                                              *)
-(* ------------------------------------------------------------------------- *)
-type model =
-(typ * int) list * (term * interpretation) list;
-(* ------------------------------------------------------------------------- *)
-(* arguments: additional arguments required during interpretation of terms   *)
-(* ------------------------------------------------------------------------- *)
-type arguments =
-{
-(* just passed unchanged from 'params': *)
-maxvars   : int,
-(* whether to use 'make_equality' or 'make_def_equality': *)
-def_eq    : bool,
-(* the following may change during the translation: *)
-next_idx  : int,
-bounds    : interpretation list,
-wellformed: prop_formula
-};
-structure Data = Theory_Data
-(
-type T =
-{interpreters: (string * (Proof.context -> model -> arguments -> term ->
-(interpretation * model * arguments) option)) list,
-printers: (string * (Proof.context -> model -> typ -> interpretation ->
-(int -> bool) -> term option)) list,
-parameters: string Symtab.table};
-val empty = {interpreters = [], printers = [], parameters = Symtab.empty};
-val extend = I;
-fun merge
-({interpreters = in1, printers = pr1, parameters = pa1},
-{interpreters = in2, printers = pr2, parameters = pa2}) : T =
-{interpreters = AList.merge (op =) (K true) (in1, in2),
-printers = AList.merge (op =) (K true) (pr1, pr2),
-parameters = Symtab.merge (op =) (pa1, pa2)};
-);
-val get_data = Data.get o Proof_Context.theory_of;
-(* ------------------------------------------------------------------------- *)
-(* interpret: interprets the term 't' using a suitable interpreter; returns  *)
-(*            the interpretation and a (possibly extended) model that keeps  *)
-(*            track of the interpretation of subterms                        *)
-(* ------------------------------------------------------------------------- *)
-fun interpret ctxt model args t =
-case get_first (fn (_, f) => f ctxt model args t)
-(#interpreters (get_data ctxt)) of
-NONE => raise REFUTE ("interpret",
-"no interpreter for term " ^ quote (Syntax.string_of_term ctxt t))
-| SOME x => x;
-(* ------------------------------------------------------------------------- *)
-(* print: converts the interpretation 'intr', which must denote a term of    *)
-(*        type 'T', into a term using a suitable printer                     *)
-(* ------------------------------------------------------------------------- *)
-fun print ctxt model T intr assignment =
-case get_first (fn (_, f) => f ctxt model T intr assignment)
-(#printers (get_data ctxt)) of
-NONE => raise REFUTE ("print",
-"no printer for type " ^ quote (Syntax.string_of_typ ctxt T))
-| SOME x => x;
-(* ------------------------------------------------------------------------- *)
-(* print_model: turns the model into a string, using a fixed interpretation  *)
-(*              (given by an assignment for Boolean variables) and suitable  *)
-(*              printers                                                     *)
-(* ------------------------------------------------------------------------- *)
-fun print_model ctxt model assignment =
-let
-val (typs, terms) = model
-val typs_msg =
-if null typs then
-"empty universe (no type variables in term)\n"
-else
-"Size of types: " ^ commas (map (fn (T, i) =>
-Syntax.string_of_typ ctxt T ^ ": " ^ string_of_int i) typs) ^ "\n"
-val show_consts_msg =
-if not (Config.get ctxt show_consts) andalso Library.exists (is_Const o fst) terms then
-"enable \"show_consts\" to show the interpretation of constants\n"
-else
-""
-val terms_msg =
-if null terms then
-"empty interpretation (no free variables in term)\n"
-else
-cat_lines (map_filter (fn (t, intr) =>
-(* print constants only if 'show_consts' is true *)
-if Config.get ctxt show_consts orelse not (is_Const t) then
-SOME (Syntax.string_of_term ctxt t ^ ": " ^
-Syntax.string_of_term ctxt
-(print ctxt model (Term.type_of t) intr assignment))
-else
-NONE) terms) ^ "\n"
-in
-typs_msg ^ show_consts_msg ^ terms_msg
-end;
-(* ------------------------------------------------------------------------- *)
-(* PARAMETER MANAGEMENT                                                      *)
-(* ------------------------------------------------------------------------- *)
-fun add_interpreter name f = Data.map (fn {interpreters, printers, parameters} =>
-case AList.lookup (op =) interpreters name of
-NONE => {interpreters = (name, f) :: interpreters,
-printers = printers, parameters = parameters}
-| SOME _ => error ("Interpreter " ^ name ^ " already declared"));
-fun add_printer name f = Data.map (fn {interpreters, printers, parameters} =>
-case AList.lookup (op =) printers name of
-NONE => {interpreters = interpreters,
-printers = (name, f) :: printers, parameters = parameters}
-| SOME _ => error ("Printer " ^ name ^ " already declared"));
-(* ------------------------------------------------------------------------- *)
-(* set_default_param: stores the '(name, value)' pair in Data's              *)
-(*                    parameter table                                        *)
-(* ------------------------------------------------------------------------- *)
-fun set_default_param (name, value) = Data.map
-(fn {interpreters, printers, parameters} =>
-{interpreters = interpreters, printers = printers,
-parameters = Symtab.update (name, value) parameters});
-(* ------------------------------------------------------------------------- *)
-(* get_default_param: retrieves the value associated with 'name' from        *)
-(*                    Data's parameter table                                 *)
-(* ------------------------------------------------------------------------- *)
-val get_default_param = Symtab.lookup o #parameters o get_data;
-(* ------------------------------------------------------------------------- *)
-(* get_default_params: returns a list of all '(name, value)' pairs that are  *)
-(*                     stored in Data's parameter table                      *)
-(* ------------------------------------------------------------------------- *)
-val get_default_params = Symtab.dest o #parameters o get_data;
-(* ------------------------------------------------------------------------- *)
-(* actual_params: takes a (possibly empty) list 'params' of parameters that  *)
-(*      override the default parameters currently specified, and             *)
-(*      returns a record that can be passed to 'find_model'.                 *)
-(* ------------------------------------------------------------------------- *)
-fun actual_params ctxt override =
-let
-(* (string * string) list * string -> bool *)
-fun read_bool (parms, name) =
-case AList.lookup (op =) parms name of
-SOME "true" => true
-| SOME "false" => false
-| SOME s => error ("parameter " ^ quote name ^
-" (value is " ^ quote s ^ ") must be \"true\" or \"false\"")
-| NONE   => error ("parameter " ^ quote name ^
-" must be assigned a value")
-(* (string * string) list * string -> int *)
-fun read_int (parms, name) =
-case AList.lookup (op =) parms name of
-SOME s =>
-(case Int.fromString s of
-SOME i => i
-| NONE   => error ("parameter " ^ quote name ^
-" (value is " ^ quote s ^ ") must be an integer value"))
-| NONE => error ("parameter " ^ quote name ^
-" must be assigned a value")
-(* (string * string) list * string -> string *)
-fun read_string (parms, name) =
-case AList.lookup (op =) parms name of
-SOME s => s
-| NONE => error ("parameter " ^ quote name ^
-" must be assigned a value")
-(* 'override' first, defaults last: *)
-(* (string * string) list *)
-val allparams = override @ get_default_params ctxt
-(* int *)
-val minsize = read_int (allparams, "minsize")
-val maxsize = read_int (allparams, "maxsize")
-val maxvars = read_int (allparams, "maxvars")
-val maxtime = read_int (allparams, "maxtime")
-(* string *)
-val satsolver = read_string (allparams, "satsolver")
-val no_assms = read_bool (allparams, "no_assms")
-val expect = the_default "" (AList.lookup (op =) allparams "expect")
-(* all remaining parameters of the form "string=int" are collected in *)
-(* 'sizes'                                                            *)
-(* TODO: it is currently not possible to specify a size for a type    *)
-(*       whose name is one of the other parameters (e.g. 'maxvars')   *)
-(* (string * int) list *)
-val sizes = map_filter
-(fn (name, value) => Option.map (pair name) (Int.fromString value))
-(filter (fn (name, _) => name<>"minsize" andalso name<>"maxsize"
-andalso name<>"maxvars" andalso name<>"maxtime"
-andalso name<>"satsolver" andalso name<>"no_assms") allparams)
-in
-{sizes=sizes, minsize=minsize, maxsize=maxsize, maxvars=maxvars,
-maxtime=maxtime, satsolver=satsolver, no_assms=no_assms, expect=expect}
-end;
-(* ------------------------------------------------------------------------- *)
-(* TRANSLATION HOL -> PROPOSITIONAL LOGIC, BOOLEAN ASSIGNMENT -> MODEL       *)
-(* ------------------------------------------------------------------------- *)
-val typ_of_dtyp = ATP_Util.typ_of_dtyp
-(* ------------------------------------------------------------------------- *)
-(* close_form: universal closure over schematic variables in 't'             *)
-(* ------------------------------------------------------------------------- *)
-(* Term.term -> Term.term *)
-fun close_form t =
-let
-val vars = sort_wrt (fst o fst) (Term.add_vars t [])
-in
-fold (fn ((x, i), T) => fn t' =>
-Logic.all_const T $ Abs (x, T, abstract_over (Var ((x, i), T), t'))) vars t
-end;
-val monomorphic_term = ATP_Util.monomorphic_term
-val specialize_type = ATP_Util.specialize_type
-(* ------------------------------------------------------------------------- *)
-(* is_const_of_class: returns 'true' iff 'Const (s, T)' is a constant that   *)
-(*                    denotes membership to an axiomatic type class          *)
-(* ------------------------------------------------------------------------- *)
-fun is_const_of_class thy (s, _) =
-let
-val class_const_names = map Logic.const_of_class (Sign.all_classes thy)
-in
-(* I'm not quite sure if checking the name 's' is sufficient, *)
-(* or if we should also check the type 'T'.                   *)
-member (op =) class_const_names s
-end;
-(* ------------------------------------------------------------------------- *)
-(* is_IDT_constructor: returns 'true' iff 'Const (s, T)' is the constructor  *)
-(*                     of an inductive datatype in 'thy'                     *)
-(* ------------------------------------------------------------------------- *)
-fun is_IDT_constructor thy (s, T) =
-(case body_type T of
-Type (s', _) =>
-(case Datatype.get_constrs thy s' of
-SOME constrs =>
-List.exists (fn (cname, cty) =>
-cname = s andalso Sign.typ_instance thy (T, cty)) constrs
-| NONE => false)
-| _  => false);
-(* ------------------------------------------------------------------------- *)
-(* is_IDT_recursor: returns 'true' iff 'Const (s, T)' is the recursion       *)
-(*                  operator of an inductive datatype in 'thy'               *)
-(* ------------------------------------------------------------------------- *)
-fun is_IDT_recursor thy (s, _) =
-let
-val rec_names = Symtab.fold (append o #rec_names o snd)
-(Datatype.get_all thy) []
-in
-(* I'm not quite sure if checking the name 's' is sufficient, *)
-(* or if we should also check the type 'T'.                   *)
-member (op =) rec_names s
-end;
-(* ------------------------------------------------------------------------- *)
-(* norm_rhs: maps  f ?t1 ... ?tn == rhs  to  %t1...tn. rhs                   *)
-(* ------------------------------------------------------------------------- *)
-fun norm_rhs eqn =
-let
-fun lambda (v as Var ((x, _), T)) t = Abs (x, T, abstract_over (v, t))
-| lambda v t = raise TERM ("lambda", [v, t])
-val (lhs, rhs) = Logic.dest_equals eqn
-val (_, args) = Term.strip_comb lhs
-in
-fold lambda (rev args) rhs
-end
-(* ------------------------------------------------------------------------- *)
-(* get_def: looks up the definition of a constant                            *)
-(* ------------------------------------------------------------------------- *)
-fun get_def thy (s, T) =
-let
-(* (string * Term.term) list -> (string * Term.term) option *)
-fun get_def_ax [] = NONE
-| get_def_ax ((axname, ax) :: axioms) =
-(let
-val (lhs, _) = Logic.dest_equals ax  (* equations only *)
-val c        = Term.head_of lhs
-val (s', T') = Term.dest_Const c
-in
-if s=s' then
-let
-val typeSubs = Sign.typ_match thy (T', T) Vartab.empty
-val ax'      = monomorphic_term typeSubs ax
-val rhs      = norm_rhs ax'
-in
-SOME (axname, rhs)
-end
-else
-get_def_ax axioms
-end handle ERROR _         => get_def_ax axioms
-| TERM _          => get_def_ax axioms
-| Type.TYPE_MATCH => get_def_ax axioms)
-in
-get_def_ax (Theory.all_axioms_of thy)
-end;
-(* ------------------------------------------------------------------------- *)
-(* get_typedef: looks up the definition of a type, as created by "typedef"   *)
-(* ------------------------------------------------------------------------- *)
-fun get_typedef thy T =
-let
-(* (string * Term.term) list -> (string * Term.term) option *)
-fun get_typedef_ax [] = NONE
-| get_typedef_ax ((axname, ax) :: axioms) =
-(let
-(* Term.term -> Term.typ option *)
-fun type_of_type_definition (Const (s', T')) =
-if s'= @{const_name type_definition} then
-SOME T'
-else
-NONE
-| type_of_type_definition (Free _) = NONE
-| type_of_type_definition (Var _) = NONE
-| type_of_type_definition (Bound _) = NONE
-| type_of_type_definition (Abs (_, _, body)) =
-type_of_type_definition body
-| type_of_type_definition (t1 $ t2) =
-(case type_of_type_definition t1 of
-SOME x => SOME x
-| NONE => type_of_type_definition t2)
-in
-case type_of_type_definition ax of
-SOME T' =>
-let
-val T'' = domain_type (domain_type T')
-val typeSubs = Sign.typ_match thy (T'', T) Vartab.empty
-in
-SOME (axname, monomorphic_term typeSubs ax)
-end
-| NONE => get_typedef_ax axioms
-end handle ERROR _         => get_typedef_ax axioms
-| TERM _          => get_typedef_ax axioms
-| Type.TYPE_MATCH => get_typedef_ax axioms)
-in
-get_typedef_ax (Theory.all_axioms_of thy)
-end;
-(* ------------------------------------------------------------------------- *)
-(* get_classdef: looks up the defining axiom for an axiomatic type class, as *)
-(*               created by the "axclass" command                            *)
-(* ------------------------------------------------------------------------- *)
-fun get_classdef thy class =
-let
-val axname = class ^ "_class_def"
-in
-Option.map (pair axname)
-(AList.lookup (op =) (Theory.all_axioms_of thy) axname)
-end;
-(* ------------------------------------------------------------------------- *)
-(* unfold_defs: unfolds all defined constants in a term 't', beta-eta        *)
-(*              normalizes the result term; certain constants are not        *)
-(*              unfolded (cf. 'collect_axioms' and the various interpreters  *)
-(*              below): if the interpretation respects a definition anyway,  *)
-(*              that definition does not need to be unfolded                 *)
-(* ------------------------------------------------------------------------- *)
-(* Note: we could intertwine unfolding of constants and beta-(eta-)       *)
-(*       normalization; this would save some unfolding for terms where    *)
-(*       constants are eliminated by beta-reduction (e.g. 'K c1 c2').  On *)
-(*       the other hand, this would cause additional work for terms where *)
-(*       constants are duplicated by beta-reduction (e.g. 'S c1 c2 c3').  *)
-fun unfold_defs thy t =
-let
-(* Term.term -> Term.term *)
-fun unfold_loop t =
-case t of
-(* Pure *)
-Const (@{const_name all}, _) => t
-| Const (@{const_name "=="}, _) => t
-| Const (@{const_name "==>"}, _) => t
-| Const (@{const_name TYPE}, _) => t  (* axiomatic type classes *)
-(* HOL *)
-| Const (@{const_name Trueprop}, _) => t
-| Const (@{const_name Not}, _) => t
-| (* redundant, since 'True' is also an IDT constructor *)
-Const (@{const_name True}, _) => t
-| (* redundant, since 'False' is also an IDT constructor *)
-Const (@{const_name False}, _) => t
-| Const (@{const_name undefined}, _) => t
-| Const (@{const_name The}, _) => t
-| Const (@{const_name Hilbert_Choice.Eps}, _) => t
-| Const (@{const_name All}, _) => t
-| Const (@{const_name Ex}, _) => t
-| Const (@{const_name HOL.eq}, _) => t
-| Const (@{const_name HOL.conj}, _) => t
-| Const (@{const_name HOL.disj}, _) => t
-| Const (@{const_name HOL.implies}, _) => t
-(* sets *)
-| Const (@{const_name Collect}, _) => t
-| Const (@{const_name Set.member}, _) => t
-(* other optimizations *)
-| Const (@{const_name Finite_Set.card}, _) => t
-| Const (@{const_name Finite_Set.finite}, _) => t
-| Const (@{const_name Orderings.less}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ bool}])])) => t
-| Const (@{const_name Groups.plus}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) => t
-| Const (@{const_name Groups.minus}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) => t
-| Const (@{const_name Groups.times}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) => t
-| Const (@{const_name List.append}, _) => t
-(* UNSOUND
-| Const (@{const_name lfp}, _) => t
-| Const (@{const_name gfp}, _) => t
-*)
-| Const (@{const_name fst}, _) => t
-| Const (@{const_name snd}, _) => t
-(* simply-typed lambda calculus *)
-| Const (s, T) =>
-(if is_IDT_constructor thy (s, T)
-orelse is_IDT_recursor thy (s, T) then
-t  (* do not unfold IDT constructors/recursors *)
-(* unfold the constant if there is a defining equation *)
-else
-case get_def thy (s, T) of
-SOME ((*axname*) _, rhs) =>
-(* Note: if the term to be unfolded (i.e. 'Const (s, T)')  *)
-(* occurs on the right-hand side of the equation, i.e. in  *)
-(* 'rhs', we must not use this equation to unfold, because *)
-(* that would loop.  Here would be the right place to      *)
-(* check this.  However, getting this really right seems   *)
-(* difficult because the user may state arbitrary axioms,  *)
-(* which could interact with overloading to create loops.  *)
-((*tracing (" unfolding: " ^ axname);*)
-unfold_loop rhs)
-| NONE => t)
-| Free _ => t
-| Var _ => t
-| Bound _ => t
-| Abs (s, T, body) => Abs (s, T, unfold_loop body)
-| t1 $ t2 => (unfold_loop t1) $ (unfold_loop t2)
-val result = Envir.beta_eta_contract (unfold_loop t)
-in
-result
-end;
-(* ------------------------------------------------------------------------- *)
-(* collect_axioms: collects (monomorphic, universally quantified, unfolded   *)
-(*                 versions of) all HOL axioms that are relevant w.r.t 't'   *)
-(* ------------------------------------------------------------------------- *)
-(* Note: to make the collection of axioms more easily extensible, this    *)
-(*       function could be based on user-supplied "axiom collectors",     *)
-(*       similar to 'interpret'/interpreters or 'print'/printers          *)
-(* Note: currently we use "inverse" functions to the definitional         *)
-(*       mechanisms provided by Isabelle/HOL, e.g. for "axclass",         *)
-(*       "typedef", "definition".  A more general approach could consider *)
-(*       *every* axiom of the theory and collect it if it has a constant/ *)
-(*       type/typeclass in common with the term 't'.                      *)
-(* Which axioms are "relevant" for a particular term/type goes hand in    *)
-(* hand with the interpretation of that term/type by its interpreter (see *)
-(* way below): if the interpretation respects an axiom anyway, the axiom  *)
-(* does not need to be added as a constraint here.                        *)
-(* To avoid collecting the same axiom multiple times, we use an           *)
-(* accumulator 'axs' which contains all axioms collected so far.          *)
-fun collect_axioms ctxt t =
-let
-val thy = Proof_Context.theory_of ctxt
-val _ = tracing "Adding axioms..."
-val axioms = Theory.all_axioms_of thy
-fun collect_this_axiom (axname, ax) axs =
-let
-val ax' = unfold_defs thy ax
-in
-if member (op aconv) axs ax' then axs
-else (tracing axname; collect_term_axioms ax' (ax' :: axs))
-end
-and collect_sort_axioms T axs =
-let
-val sort =
-(case T of
-TFree (_, sort) => sort
-| TVar (_, sort)  => sort
-| _ => raise REFUTE ("collect_axioms",
-"type " ^ Syntax.string_of_typ ctxt T ^ " is not a variable"))
-(* obtain axioms for all superclasses *)
-val superclasses = sort @ maps (Sign.super_classes thy) sort
-(* merely an optimization, because 'collect_this_axiom' disallows *)
-(* duplicate axioms anyway:                                       *)
-val superclasses = distinct (op =) superclasses
-val class_axioms = maps (fn class => map (fn ax =>
-("<" ^ class ^ ">", Thm.prop_of ax))
-(#axioms (AxClass.get_info thy class) handle ERROR _ => []))
-superclasses
-(* replace the (at most one) schematic type variable in each axiom *)
-(* by the actual type 'T'                                          *)
-val monomorphic_class_axioms = map (fn (axname, ax) =>
-(case Term.add_tvars ax [] of
-[] => (axname, ax)
-| [(idx, S)] => (axname, monomorphic_term (Vartab.make [(idx, (S, T))]) ax)
-| _ =>
-raise REFUTE ("collect_axioms", "class axiom " ^ axname ^ " (" ^
-Syntax.string_of_term ctxt ax ^
-") contains more than one type variable")))
-class_axioms
-in
-fold collect_this_axiom monomorphic_class_axioms axs
-end
-and collect_type_axioms T axs =
-case T of
-(* simple types *)
-Type ("prop", []) => axs
-| Type ("fun", [T1, T2]) => collect_type_axioms T2 (collect_type_axioms T1 axs)
-| Type (@{type_name set}, [T1]) => collect_type_axioms T1 axs
-(* axiomatic type classes *)
-| Type ("itself", [T1]) => collect_type_axioms T1 axs
-| Type (s, Ts) =>
-(case Datatype.get_info thy s of
-SOME _ =>  (* inductive datatype *)
-(* only collect relevant type axioms for the argument types *)
-fold collect_type_axioms Ts axs
-| NONE =>
-(case get_typedef thy T of
-SOME (axname, ax) =>
-collect_this_axiom (axname, ax) axs
-| NONE =>
-(* unspecified type, perhaps introduced with "typedecl" *)
-(* at least collect relevant type axioms for the argument types *)
-fold collect_type_axioms Ts axs))
-(* axiomatic type classes *)
-| TFree _ => collect_sort_axioms T axs
-(* axiomatic type classes *)
-| TVar _ => collect_sort_axioms T axs
-and collect_term_axioms t axs =
-case t of
-(* Pure *)
-Const (@{const_name all}, _) => axs
-| Const (@{const_name "=="}, _) => axs
-| Const (@{const_name "==>"}, _) => axs
-(* axiomatic type classes *)
-| Const (@{const_name TYPE}, T) => collect_type_axioms T axs
-(* HOL *)
-| Const (@{const_name Trueprop}, _) => axs
-| Const (@{const_name Not}, _) => axs
-(* redundant, since 'True' is also an IDT constructor *)
-| Const (@{const_name True}, _) => axs
-(* redundant, since 'False' is also an IDT constructor *)
-| Const (@{const_name False}, _) => axs
-| Const (@{const_name undefined}, T) => collect_type_axioms T axs
-| Const (@{const_name The}, T) =>
-let
-val ax = specialize_type thy (@{const_name The}, T)
-(the (AList.lookup (op =) axioms "HOL.the_eq_trivial"))
-in
-collect_this_axiom ("HOL.the_eq_trivial", ax) axs
-end
-| Const (@{const_name Hilbert_Choice.Eps}, T) =>
-let
-val ax = specialize_type thy (@{const_name Hilbert_Choice.Eps}, T)
-(the (AList.lookup (op =) axioms "Hilbert_Choice.someI"))
-in
-collect_this_axiom ("Hilbert_Choice.someI", ax) axs
-end
-| Const (@{const_name All}, T) => collect_type_axioms T axs
-| Const (@{const_name Ex}, T) => collect_type_axioms T axs
-| Const (@{const_name HOL.eq}, T) => collect_type_axioms T axs
-| Const (@{const_name HOL.conj}, _) => axs
-| Const (@{const_name HOL.disj}, _) => axs
-| Const (@{const_name HOL.implies}, _) => axs
-(* sets *)
-| Const (@{const_name Collect}, T) => collect_type_axioms T axs
-| Const (@{const_name Set.member}, T) => collect_type_axioms T axs
-(* other optimizations *)
-| Const (@{const_name Finite_Set.card}, T) => collect_type_axioms T axs
-| Const (@{const_name Finite_Set.finite}, T) =>
-collect_type_axioms T axs
-| Const (@{const_name Orderings.less}, T as Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ bool}])])) =>
-collect_type_axioms T axs
-| Const (@{const_name Groups.plus}, T as Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) =>
-collect_type_axioms T axs
-| Const (@{const_name Groups.minus}, T as Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) =>
-collect_type_axioms T axs
-| Const (@{const_name Groups.times}, T as Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) =>
-collect_type_axioms T axs
-| Const (@{const_name List.append}, T) => collect_type_axioms T axs
-(* UNSOUND
-| Const (@{const_name lfp}, T) => collect_type_axioms T axs
-| Const (@{const_name gfp}, T) => collect_type_axioms T axs
-*)
-| Const (@{const_name fst}, T) => collect_type_axioms T axs
-| Const (@{const_name snd}, T) => collect_type_axioms T axs
-(* simply-typed lambda calculus *)
-| Const (s, T) =>
-if is_const_of_class thy (s, T) then
-(* axiomatic type classes: add "OFCLASS(?'a::c, c_class)" *)
-(* and the class definition                               *)
-let
-val class = Logic.class_of_const s
-val of_class = Logic.mk_of_class (TVar (("'a", 0), [class]), class)
-val ax_in = SOME (specialize_type thy (s, T) of_class)
-(* type match may fail due to sort constraints *)
-handle Type.TYPE_MATCH => NONE
-val ax_1 = Option.map (fn ax => (Syntax.string_of_term ctxt ax, ax)) ax_in
-val ax_2 = Option.map (apsnd (specialize_type thy (s, T))) (get_classdef thy class)
-in
-collect_type_axioms T (fold collect_this_axiom (map_filter I [ax_1, ax_2]) axs)
-end
-else if is_IDT_constructor thy (s, T)
-orelse is_IDT_recursor thy (s, T)
-then
-(* only collect relevant type axioms *)
-collect_type_axioms T axs
-else
-(* other constants should have been unfolded, with some *)
-(* exceptions: e.g. Abs_xxx/Rep_xxx functions for       *)
-(* typedefs, or type-class related constants            *)
-(* only collect relevant type axioms *)
-collect_type_axioms T axs
-| Free (_, T) => collect_type_axioms T axs
-| Var (_, T) => collect_type_axioms T axs
-| Bound _ => axs
-| Abs (_, T, body) => collect_term_axioms body (collect_type_axioms T axs)
-| t1 $ t2 => collect_term_axioms t2 (collect_term_axioms t1 axs)
-val result = map close_form (collect_term_axioms t [])
-val _ = tracing " ...done."
-in
-result
-end;
-(* ------------------------------------------------------------------------- *)
-(* ground_types: collects all ground types in a term (including argument     *)
-(*               types of other types), suppressing duplicates.  Does not    *)
-(*               return function types, set types, non-recursive IDTs, or    *)
-(*               'propT'.  For IDTs, also the argument types of constructors *)
-(*               and all mutually recursive IDTs are considered.             *)
-(* ------------------------------------------------------------------------- *)
-fun ground_types ctxt t =
-let
-val thy = Proof_Context.theory_of ctxt
-fun collect_types T acc =
-(case T of
-Type ("fun", [T1, T2]) => collect_types T1 (collect_types T2 acc)
-| Type ("prop", []) => acc
-| Type (@{type_name set}, [T1]) => collect_types T1 acc
-| Type (s, Ts) =>
-(case Datatype.get_info thy s of
-SOME info =>  (* inductive datatype *)
-let
-val index = #index info
-val descr = #descr info
-val (_, typs, _) = the (AList.lookup (op =) descr index)
-val typ_assoc = typs ~~ Ts
-(* sanity check: every element in 'dtyps' must be a *)
-(* 'DtTFree'                                        *)
-val _ = if Library.exists (fn d =>
-case d of Datatype.DtTFree _ => false | _ => true) typs then
-raise REFUTE ("ground_types", "datatype argument (for type "
-^ Syntax.string_of_typ ctxt T ^ ") is not a variable")
-else ()
-(* required for mutually recursive datatypes; those need to   *)
-(* be added even if they are an instance of an otherwise non- *)
-(* recursive datatype                                         *)
-fun collect_dtyp d acc =
-let
-val dT = typ_of_dtyp descr typ_assoc d
-in
-case d of
-Datatype.DtTFree _ =>
-collect_types dT acc
-| Datatype.DtType (_, ds) =>
-collect_types dT (fold_rev collect_dtyp ds acc)
-| Datatype.DtRec i =>
-if member (op =) acc dT then
-acc  (* prevent infinite recursion *)
-else
-let
-val (_, dtyps, dconstrs) = the (AList.lookup (op =) descr i)
-(* if the current type is a recursive IDT (i.e. a depth *)
-(* is required), add it to 'acc'                        *)
-val acc_dT = if Library.exists (fn (_, ds) =>
-Library.exists Datatype_Aux.is_rec_type ds) dconstrs then
-insert (op =) dT acc
-else acc
-(* collect argument types *)
-val acc_dtyps = fold_rev collect_dtyp dtyps acc_dT
-(* collect constructor types *)
-val acc_dconstrs = fold_rev collect_dtyp (maps snd dconstrs) acc_dtyps
-in
-acc_dconstrs
-end
-end
-in
-(* argument types 'Ts' could be added here, but they are also *)
-(* added by 'collect_dtyp' automatically                      *)
-collect_dtyp (Datatype.DtRec index) acc
-end
-| NONE =>
-(* not an inductive datatype, e.g. defined via "typedef" or *)
-(* "typedecl"                                               *)
-insert (op =) T (fold collect_types Ts acc))
-| TFree _ => insert (op =) T acc
-| TVar _ => insert (op =) T acc)
-in
-fold_types collect_types t []
-end;
-(* ------------------------------------------------------------------------- *)
-(* string_of_typ: (rather naive) conversion from types to strings, used to   *)
-(*                look up the size of a type in 'sizes'.  Parameterized      *)
-(*                types with different parameters (e.g. "'a list" vs. "bool  *)
-(*                list") are identified.                                     *)
-(* ------------------------------------------------------------------------- *)
-(* Term.typ -> string *)
-fun string_of_typ (Type (s, _))     = s
-| string_of_typ (TFree (s, _))    = s
-| string_of_typ (TVar ((s,_), _)) = s;
-(* ------------------------------------------------------------------------- *)
-(* first_universe: returns the "first" (i.e. smallest) universe by assigning *)
-(*                 'minsize' to every type for which no size is specified in *)
-(*                 'sizes'                                                   *)
-(* ------------------------------------------------------------------------- *)
-(* Term.typ list -> (string * int) list -> int -> (Term.typ * int) list *)
-fun first_universe xs sizes minsize =
-let
-fun size_of_typ T =
-case AList.lookup (op =) sizes (string_of_typ T) of
-SOME n => n
-| NONE => minsize
-in
-map (fn T => (T, size_of_typ T)) xs
-end;
-(* ------------------------------------------------------------------------- *)
-(* next_universe: enumerates all universes (i.e. assignments of sizes to     *)
-(*                types), where the minimal size of a type is given by       *)
-(*                'minsize', the maximal size is given by 'maxsize', and a   *)
-(*                type may have a fixed size given in 'sizes'                *)
-(* ------------------------------------------------------------------------- *)
-(* (Term.typ * int) list -> (string * int) list -> int -> int ->
-(Term.typ * int) list option *)
-fun next_universe xs sizes minsize maxsize =
-let
-(* creates the "first" list of length 'len', where the sum of all list *)
-(* elements is 'sum', and the length of the list is 'len'              *)
-(* int -> int -> int -> int list option *)
-fun make_first _ 0 sum =
-if sum = 0 then
-SOME []
-else
-NONE
-| make_first max len sum =
-if sum <= max orelse max < 0 then
-Option.map (fn xs' => sum :: xs') (make_first max (len-1) 0)
-else
-Option.map (fn xs' => max :: xs') (make_first max (len-1) (sum-max))
-(* enumerates all int lists with a fixed length, where 0<=x<='max' for *)
-(* all list elements x (unless 'max'<0)                                *)
-(* int -> int -> int -> int list -> int list option *)
-fun next _ _ _ [] =
-NONE
-| next max len sum [x] =
-(* we've reached the last list element, so there's no shift possible *)
-make_first max (len+1) (sum+x+1)  (* increment 'sum' by 1 *)
-| next max len sum (x1::x2::xs) =
-if x1>0 andalso (x2<max orelse max<0) then
-(* we can shift *)
-SOME (the (make_first max (len+1) (sum+x1-1)) @ (x2+1) :: xs)
-else
-(* continue search *)
-next max (len+1) (sum+x1) (x2::xs)
-(* only consider those types for which the size is not fixed *)
-val mutables = filter_out (AList.defined (op =) sizes o string_of_typ o fst) xs
-(* subtract 'minsize' from every size (will be added again at the end) *)
-val diffs = map (fn (_, n) => n-minsize) mutables
-in
-case next (maxsize-minsize) 0 0 diffs of
-SOME diffs' =>
-(* merge with those types for which the size is fixed *)
-SOME (fst (fold_map (fn (T, _) => fn ds =>
-case AList.lookup (op =) sizes (string_of_typ T) of
-(* return the fixed size *)
-SOME n => ((T, n), ds)
-(* consume the head of 'ds', add 'minsize' *)
-| NONE   => ((T, minsize + hd ds), tl ds))
-xs diffs'))
-| NONE => NONE
-end;
-(* ------------------------------------------------------------------------- *)
-(* toTrue: converts the interpretation of a Boolean value to a propositional *)
-(*         formula that is true iff the interpretation denotes "true"        *)
-(* ------------------------------------------------------------------------- *)
-(* interpretation -> prop_formula *)
-fun toTrue (Leaf [fm, _]) = fm
-| toTrue _ = raise REFUTE ("toTrue", "interpretation does not denote a Boolean value");
-(* ------------------------------------------------------------------------- *)
-(* toFalse: converts the interpretation of a Boolean value to a              *)
-(*          propositional formula that is true iff the interpretation        *)
-(*          denotes "false"                                                  *)
-(* ------------------------------------------------------------------------- *)
-(* interpretation -> prop_formula *)
-fun toFalse (Leaf [_, fm]) = fm
-| toFalse _ = raise REFUTE ("toFalse", "interpretation does not denote a Boolean value");
-(* ------------------------------------------------------------------------- *)
-(* find_model: repeatedly calls 'interpret' with appropriate parameters,     *)
-(*             applies a SAT solver, and (in case a model is found) displays *)
-(*             the model to the user by calling 'print_model'                *)
-(* {...}     : parameters that control the translation/model generation      *)
-(* assm_ts   : assumptions to be considered unless "no_assms" is specified   *)
-(* t         : term to be translated into a propositional formula            *)
-(* negate    : if true, find a model that makes 't' false (rather than true) *)
-(* ------------------------------------------------------------------------- *)
-fun find_model ctxt
-{sizes, minsize, maxsize, maxvars, maxtime, satsolver, no_assms, expect}
-assm_ts t negate =
-let
-val thy = Proof_Context.theory_of ctxt
-(* string -> string *)
-fun check_expect outcome_code =
-if expect = "" orelse outcome_code = expect then outcome_code
-else error ("Unexpected outcome: " ^ quote outcome_code ^ ".")
-(* unit -> string *)
-fun wrapper () =
-let
-val timer = Timer.startRealTimer ()
-val t =
-if no_assms then t
-else if negate then Logic.list_implies (assm_ts, t)
-else Logic.mk_conjunction_list (t :: assm_ts)
-val u = unfold_defs thy t
-val _ = tracing ("Unfolded term: " ^ Syntax.string_of_term ctxt u)
-val axioms = collect_axioms ctxt u
-(* Term.typ list *)
-val types = fold (union (op =) o ground_types ctxt) (u :: axioms) []
-val _ = tracing ("Ground types: "
-^ (if null types then "none."
-else commas (map (Syntax.string_of_typ ctxt) types)))
-(* we can only consider fragments of recursive IDTs, so we issue a  *)
-(* warning if the formula contains a recursive IDT                  *)
-(* TODO: no warning needed for /positive/ occurrences of IDTs       *)
-val maybe_spurious = Library.exists (fn
-Type (s, _) =>
-(case Datatype.get_info thy s of
-SOME info =>  (* inductive datatype *)
-let
-val index           = #index info
-val descr           = #descr info
-val (_, _, constrs) = the (AList.lookup (op =) descr index)
-in
-(* recursive datatype? *)
-Library.exists (fn (_, ds) =>
-Library.exists Datatype_Aux.is_rec_type ds) constrs
-end
-| NONE => false)
-| _ => false) types
-val _ =
-if maybe_spurious then
-warning ("Term contains a recursive datatype; "
-^ "countermodel(s) may be spurious!")
-else
-()
-(* (Term.typ * int) list -> string *)
-fun find_model_loop universe =
-let
-val msecs_spent = Time.toMilliseconds (Timer.checkRealTimer timer)
-val _ = maxtime = 0 orelse msecs_spent < 1000 * maxtime
-orelse raise TimeLimit.TimeOut
-val init_model = (universe, [])
-val init_args  = {maxvars = maxvars, def_eq = false, next_idx = 1,
-bounds = [], wellformed = True}
-val _ = tracing ("Translating term (sizes: "
-^ commas (map (fn (_, n) => string_of_int n) universe) ^ ") ...")
-(* translate 'u' and all axioms *)
-val (intrs, (model, args)) = fold_map (fn t' => fn (m, a) =>
-let
-val (i, m', a') = interpret ctxt m a t'
-in
-(* set 'def_eq' to 'true' *)
-(i, (m', {maxvars = #maxvars a', def_eq = true,
-next_idx = #next_idx a', bounds = #bounds a',
-wellformed = #wellformed a'}))
-end) (u :: axioms) (init_model, init_args)
-(* make 'u' either true or false, and make all axioms true, and *)
-(* add the well-formedness side condition                       *)
-val fm_u = (if negate then toFalse else toTrue) (hd intrs)
-val fm_ax = Prop_Logic.all (map toTrue (tl intrs))
-val fm = Prop_Logic.all [#wellformed args, fm_ax, fm_u]
-val _ =
-(if satsolver = "dpll" orelse satsolver = "enumerate" then
-warning ("Using SAT solver " ^ quote satsolver ^
-"; for better performance, consider installing an \
-\external solver.")
-else ());
-val solver =
-SatSolver.invoke_solver satsolver
-handle Option.Option =>
-error ("Unknown SAT solver: " ^ quote satsolver ^
-". Available solvers: " ^
-commas (map (quote o fst) (!SatSolver.solvers)) ^ ".")
-in
-Output.urgent_message "Invoking SAT solver...";
-(case solver fm of
-SatSolver.SATISFIABLE assignment =>
-(Output.urgent_message ("Model found:\n" ^ print_model ctxt model
-(fn i => case assignment i of SOME b => b | NONE => true));
-if maybe_spurious then "potential" else "genuine")
-| SatSolver.UNSATISFIABLE _ =>
-(Output.urgent_message "No model exists.";
-case next_universe universe sizes minsize maxsize of
-SOME universe' => find_model_loop universe'
-| NONE => (Output.urgent_message
-"Search terminated, no larger universe within the given limits.";
-"none"))
-| SatSolver.UNKNOWN =>
-(Output.urgent_message "No model found.";
-case next_universe universe sizes minsize maxsize of
-SOME universe' => find_model_loop universe'
-| NONE => (Output.urgent_message
-"Search terminated, no larger universe within the given limits.";
-"unknown"))) handle SatSolver.NOT_CONFIGURED =>
-(error ("SAT solver " ^ quote satsolver ^ " is not configured.");
-"unknown")
-end
-handle MAXVARS_EXCEEDED =>
-(Output.urgent_message ("Search terminated, number of Boolean variables ("
-^ string_of_int maxvars ^ " allowed) exceeded.");
-"unknown")
-val outcome_code = find_model_loop (first_universe types sizes minsize)
-in
-check_expect outcome_code
-end
-in
-(* some parameter sanity checks *)
-minsize>=1 orelse
-error ("\"minsize\" is " ^ string_of_int minsize ^ ", must be at least 1");
-maxsize>=1 orelse
-error ("\"maxsize\" is " ^ string_of_int maxsize ^ ", must be at least 1");
-maxsize>=minsize orelse
-error ("\"maxsize\" (=" ^ string_of_int maxsize ^
-") is less than \"minsize\" (=" ^ string_of_int minsize ^ ").");
-maxvars>=0 orelse
-error ("\"maxvars\" is " ^ string_of_int maxvars ^ ", must be at least 0");
-maxtime>=0 orelse
-error ("\"maxtime\" is " ^ string_of_int maxtime ^ ", must be at least 0");
-(* enter loop with or without time limit *)
-Output.urgent_message ("Trying to find a model that "
-^ (if negate then "refutes" else "satisfies") ^ ": "
-^ Syntax.string_of_term ctxt t);
-if maxtime > 0 then (
-TimeLimit.timeLimit (Time.fromSeconds maxtime)
-wrapper ()
-handle TimeLimit.TimeOut =>
-(Output.urgent_message ("Search terminated, time limit (" ^
-string_of_int maxtime
-^ (if maxtime=1 then " second" else " seconds") ^ ") exceeded.");
-check_expect "unknown")
-) else wrapper ()
-end;
-(* ------------------------------------------------------------------------- *)
-(* INTERFACE, PART 2: FINDING A MODEL                                        *)
-(* ------------------------------------------------------------------------- *)
-(* ------------------------------------------------------------------------- *)
-(* satisfy_term: calls 'find_model' to find a model that satisfies 't'       *)
-(* params      : list of '(name, value)' pairs used to override default      *)
-(*               parameters                                                  *)
-(* ------------------------------------------------------------------------- *)
-fun satisfy_term ctxt params assm_ts t =
-find_model ctxt (actual_params ctxt params) assm_ts t false;
-(* ------------------------------------------------------------------------- *)
-(* refute_term: calls 'find_model' to find a model that refutes 't'          *)
-(* params     : list of '(name, value)' pairs used to override default       *)
-(*              parameters                                                   *)
-(* ------------------------------------------------------------------------- *)
-fun refute_term ctxt params assm_ts t =
-let
-(* disallow schematic type variables, since we cannot properly negate  *)
-(* terms containing them (their logical meaning is that there EXISTS a *)
-(* type s.t. ...; to refute such a formula, we would have to show that *)
-(* for ALL types, not ...)                                             *)
-val _ = null (Term.add_tvars t []) orelse
-error "Term to be refuted contains schematic type variables"
-(* existential closure over schematic variables *)
-val vars = sort_wrt (fst o fst) (Term.add_vars t [])
-(* Term.term *)
-val ex_closure = fold (fn ((x, i), T) => fn t' =>
-HOLogic.exists_const T $
-Abs (x, T, abstract_over (Var ((x, i), T), t'))) vars t
-(* Note: If 't' is of type 'propT' (rather than 'boolT'), applying   *)
-(* 'HOLogic.exists_const' is not type-correct.  However, this is not *)
-(* really a problem as long as 'find_model' still interprets the     *)
-(* resulting term correctly, without checking its type.              *)
-(* replace outermost universally quantified variables by Free's:     *)
-(* refuting a term with Free's is generally faster than refuting a   *)
-(* term with (nested) quantifiers, because quantifiers are expanded, *)
-(* while the SAT solver searches for an interpretation for Free's.   *)
-(* Also we get more information back that way, namely an             *)
-(* interpretation which includes values for the (formerly)           *)
-(* quantified variables.                                             *)
-(* maps  !!x1...xn. !xk...xm. t   to   t  *)
-fun strip_all_body (Const (@{const_name all}, _) $ Abs (_, _, t)) =
-strip_all_body t
-| strip_all_body (Const (@{const_name Trueprop}, _) $ t) =
-strip_all_body t
-| strip_all_body (Const (@{const_name All}, _) $ Abs (_, _, t)) =
-strip_all_body t
-| strip_all_body t = t
-(* maps  !!x1...xn. !xk...xm. t   to   [x1, ..., xn, xk, ..., xm]  *)
-fun strip_all_vars (Const (@{const_name all}, _) $ Abs (a, T, t)) =
-(a, T) :: strip_all_vars t
-| strip_all_vars (Const (@{const_name Trueprop}, _) $ t) =
-strip_all_vars t
-| strip_all_vars (Const (@{const_name All}, _) $ Abs (a, T, t)) =
-(a, T) :: strip_all_vars t
-| strip_all_vars _ = [] : (string * typ) list
-val strip_t = strip_all_body ex_closure
-val frees = Term.rename_wrt_term strip_t (strip_all_vars ex_closure)
-val subst_t = Term.subst_bounds (map Free frees, strip_t)
-in
-find_model ctxt (actual_params ctxt params) assm_ts subst_t true
-end;
-(* ------------------------------------------------------------------------- *)
-(* refute_goal                                                               *)
-(* ------------------------------------------------------------------------- *)
-fun refute_goal ctxt params th i =
-let
-val t = th |> prop_of
-in
-if Logic.count_prems t = 0 then
-(Output.urgent_message "No subgoal!"; "none")
-else
-let
-val assms = map term_of (Assumption.all_assms_of ctxt)
-val (t, frees) = Logic.goal_params t i
-in
-refute_term ctxt params assms (subst_bounds (frees, t))
-end
-end
-(* ------------------------------------------------------------------------- *)
-(* INTERPRETERS: Auxiliary Functions                                         *)
-(* ------------------------------------------------------------------------- *)
-(* ------------------------------------------------------------------------- *)
-(* make_constants: returns all interpretations for type 'T' that consist of  *)
-(*                 unit vectors with 'True'/'False' only (no Boolean         *)
-(*                 variables)                                                *)
-(* ------------------------------------------------------------------------- *)
-fun make_constants ctxt model T =
-let
-(* returns a list with all unit vectors of length n *)
-(* int -> interpretation list *)
-fun unit_vectors n =
-let
-(* returns the k-th unit vector of length n *)
-(* int * int -> interpretation *)
-fun unit_vector (k, n) =
-Leaf ((replicate (k-1) False) @ (True :: (replicate (n-k) False)))
-(* int -> interpretation list *)
-fun unit_vectors_loop k =
-if k>n then [] else unit_vector (k,n) :: unit_vectors_loop (k+1)
-in
-unit_vectors_loop 1
-end
-(* returns a list of lists, each one consisting of n (possibly *)
-(* identical) elements from 'xs'                               *)
-(* int -> 'a list -> 'a list list *)
-fun pick_all 1 xs = map single xs
-| pick_all n xs =
-let val rec_pick = pick_all (n - 1) xs in
-maps (fn x => map (cons x) rec_pick) xs
-end
-(* returns all constant interpretations that have the same tree *)
-(* structure as the interpretation argument                     *)
-(* interpretation -> interpretation list *)
-fun make_constants_intr (Leaf xs) = unit_vectors (length xs)
-| make_constants_intr (Node xs) = map Node (pick_all (length xs)
-(make_constants_intr (hd xs)))
-(* obtain the interpretation for a variable of type 'T' *)
-val (i, _, _) = interpret ctxt model {maxvars=0, def_eq=false, next_idx=1,
-bounds=[], wellformed=True} (Free ("dummy", T))
-in
-make_constants_intr i
-end;
-(* ------------------------------------------------------------------------- *)
-(* size_of_type: returns the number of elements in a type 'T' (i.e. 'length  *)
-(*               (make_constants T)', but implemented more efficiently)      *)
-(* ------------------------------------------------------------------------- *)
-(* returns 0 for an empty ground type or a function type with empty      *)
-(* codomain, but fails for a function type with empty domain --          *)
-(* admissibility of datatype constructor argument types (see "Inductive  *)
-(* datatypes in HOL - lessons learned ...", S. Berghofer, M. Wenzel,     *)
-(* TPHOLs 99) ensures that recursive, possibly empty, datatype fragments *)
-(* never occur as the domain of a function type that is the type of a    *)
-(* constructor argument                                                  *)
-fun size_of_type ctxt model T =
-let
-(* returns the number of elements that have the same tree structure as a *)
-(* given interpretation                                                  *)
-fun size_of_intr (Leaf xs) = length xs
-| size_of_intr (Node xs) = Integer.pow (length xs) (size_of_intr (hd xs))
-(* obtain the interpretation for a variable of type 'T' *)
-val (i, _, _) = interpret ctxt model {maxvars=0, def_eq=false, next_idx=1,
-bounds=[], wellformed=True} (Free ("dummy", T))
-in
-size_of_intr i
-end;
-(* ------------------------------------------------------------------------- *)
-(* TT/FF: interpretations that denote "true" or "false", respectively        *)
-(* ------------------------------------------------------------------------- *)
-(* interpretation *)
-val TT = Leaf [True, False];
-val FF = Leaf [False, True];
-(* ------------------------------------------------------------------------- *)
-(* make_equality: returns an interpretation that denotes (extensional)       *)
-(*                equality of two interpretations                            *)
-(* - two interpretations are 'equal' iff they are both defined and denote    *)
-(*   the same value                                                          *)
-(* - two interpretations are 'not_equal' iff they are both defined at least  *)
-(*   partially, and a defined part denotes different values                  *)
-(* - a completely undefined interpretation is neither 'equal' nor            *)
-(*   'not_equal' to another interpretation                                   *)
-(* ------------------------------------------------------------------------- *)
-(* We could in principle represent '=' on a type T by a particular        *)
-(* interpretation.  However, the size of that interpretation is quadratic *)
-(* in the size of T.  Therefore comparing the interpretations 'i1' and    *)
-(* 'i2' directly is more efficient than constructing the interpretation   *)
-(* for equality on T first, and "applying" this interpretation to 'i1'    *)
-(* and 'i2' in the usual way (cf. 'interpretation_apply') then.           *)
-(* interpretation * interpretation -> interpretation *)
-fun make_equality (i1, i2) =
-let
-(* interpretation * interpretation -> prop_formula *)
-fun equal (i1, i2) =
-(case i1 of
-Leaf xs =>
-(case i2 of
-Leaf ys => Prop_Logic.dot_product (xs, ys)  (* defined and equal *)
-| Node _  => raise REFUTE ("make_equality",
-"second interpretation is higher"))
-| Node xs =>
-(case i2 of
-Leaf _  => raise REFUTE ("make_equality",
-"first interpretation is higher")
-| Node ys => Prop_Logic.all (map equal (xs ~~ ys))))
-(* interpretation * interpretation -> prop_formula *)
-fun not_equal (i1, i2) =
-(case i1 of
-Leaf xs =>
-(case i2 of
-(* defined and not equal *)
-Leaf ys => Prop_Logic.all ((Prop_Logic.exists xs)
-:: (Prop_Logic.exists ys)
-:: (map (fn (x,y) => SOr (SNot x, SNot y)) (xs ~~ ys)))
-| Node _  => raise REFUTE ("make_equality",
-"second interpretation is higher"))
-| Node xs =>
-(case i2 of
-Leaf _  => raise REFUTE ("make_equality",
-"first interpretation is higher")
-| Node ys => Prop_Logic.exists (map not_equal (xs ~~ ys))))
-in
-(* a value may be undefined; therefore 'not_equal' is not just the *)
-(* negation of 'equal'                                             *)
-Leaf [equal (i1, i2), not_equal (i1, i2)]
-end;
-(* ------------------------------------------------------------------------- *)
-(* make_def_equality: returns an interpretation that denotes (extensional)   *)
-(*                    equality of two interpretations                        *)
-(* This function treats undefined/partially defined interpretations          *)
-(* different from 'make_equality': two undefined interpretations are         *)
-(* considered equal, while a defined interpretation is considered not equal  *)
-(* to an undefined interpretation.                                           *)
-(* ------------------------------------------------------------------------- *)
-(* interpretation * interpretation -> interpretation *)
-fun make_def_equality (i1, i2) =
-let
-(* interpretation * interpretation -> prop_formula *)
-fun equal (i1, i2) =
-(case i1 of
-Leaf xs =>
-(case i2 of
-(* defined and equal, or both undefined *)
-Leaf ys => SOr (Prop_Logic.dot_product (xs, ys),
-SAnd (Prop_Logic.all (map SNot xs), Prop_Logic.all (map SNot ys)))
-| Node _  => raise REFUTE ("make_def_equality",
-"second interpretation is higher"))
-| Node xs =>
-(case i2 of
-Leaf _  => raise REFUTE ("make_def_equality",
-"first interpretation is higher")
-| Node ys => Prop_Logic.all (map equal (xs ~~ ys))))
-(* interpretation *)
-val eq = equal (i1, i2)
-in
-Leaf [eq, SNot eq]
-end;
-(* ------------------------------------------------------------------------- *)
-(* interpretation_apply: returns an interpretation that denotes the result   *)
-(*                       of applying the function denoted by 'i1' to the     *)
-(*                       argument denoted by 'i2'                            *)
-(* ------------------------------------------------------------------------- *)
-(* interpretation * interpretation -> interpretation *)
-fun interpretation_apply (i1, i2) =
-let
-(* interpretation * interpretation -> interpretation *)
-fun interpretation_disjunction (tr1,tr2) =
-tree_map (fn (xs,ys) => map (fn (x,y) => SOr(x,y)) (xs ~~ ys))
-(tree_pair (tr1,tr2))
-(* prop_formula * interpretation -> interpretation *)
-fun prop_formula_times_interpretation (fm,tr) =
-tree_map (map (fn x => SAnd (fm,x))) tr
-(* prop_formula list * interpretation list -> interpretation *)
-fun prop_formula_list_dot_product_interpretation_list ([fm],[tr]) =
-prop_formula_times_interpretation (fm,tr)
-| prop_formula_list_dot_product_interpretation_list (fm::fms,tr::trees) =
-interpretation_disjunction (prop_formula_times_interpretation (fm,tr),
-prop_formula_list_dot_product_interpretation_list (fms,trees))
-| prop_formula_list_dot_product_interpretation_list (_,_) =
-raise REFUTE ("interpretation_apply", "empty list (in dot product)")
-(* returns a list of lists, each one consisting of one element from each *)
-(* element of 'xss'                                                      *)
-(* 'a list list -> 'a list list *)
-fun pick_all [xs] = map single xs
-| pick_all (xs::xss) =
-let val rec_pick = pick_all xss in
-maps (fn x => map (cons x) rec_pick) xs
-end
-| pick_all _ = raise REFUTE ("interpretation_apply", "empty list (in pick_all)")
-(* interpretation -> prop_formula list *)
-fun interpretation_to_prop_formula_list (Leaf xs) = xs
-| interpretation_to_prop_formula_list (Node trees) =
-map Prop_Logic.all (pick_all
-(map interpretation_to_prop_formula_list trees))
-in
-case i1 of
-Leaf _ =>
-raise REFUTE ("interpretation_apply", "first interpretation is a leaf")
-| Node xs =>
-prop_formula_list_dot_product_interpretation_list
-(interpretation_to_prop_formula_list i2, xs)
-end;
-(* ------------------------------------------------------------------------- *)
-(* eta_expand: eta-expands a term 't' by adding 'i' lambda abstractions      *)
-(* ------------------------------------------------------------------------- *)
-(* Term.term -> int -> Term.term *)
-fun eta_expand t i =
-let
-val Ts = Term.binder_types (Term.fastype_of t)
-val t' = Term.incr_boundvars i t
-in
-fold_rev (fn T => fn term => Abs ("<eta_expand>", T, term))
-(List.take (Ts, i))
-(Term.list_comb (t', map Bound (i-1 downto 0)))
-end;
-(* ------------------------------------------------------------------------- *)
-(* size_of_dtyp: the size of (an initial fragment of) an inductive data type *)
-(*               is the sum (over its constructors) of the product (over     *)
-(*               their arguments) of the size of the argument types          *)
-(* ------------------------------------------------------------------------- *)
-fun size_of_dtyp ctxt typ_sizes descr typ_assoc constructors =
-Integer.sum (map (fn (_, dtyps) =>
-Integer.prod (map (size_of_type ctxt (typ_sizes, []) o
-(typ_of_dtyp descr typ_assoc)) dtyps))
-constructors);
-(* ------------------------------------------------------------------------- *)
-(* INTERPRETERS: Actual Interpreters                                         *)
-(* ------------------------------------------------------------------------- *)
-(* simply typed lambda calculus: Isabelle's basic term syntax, with type *)
-(* variables, function types, and propT                                  *)
-fun stlc_interpreter ctxt model args t =
-let
-val (typs, terms) = model
-val {maxvars, def_eq, next_idx, bounds, wellformed} = args
-(* Term.typ -> (interpretation * model * arguments) option *)
-fun interpret_groundterm T =
-let
-(* unit -> (interpretation * model * arguments) option *)
-fun interpret_groundtype () =
-let
-(* the model must specify a size for ground types *)
-val size =
-if T = Term.propT then 2
-else the (AList.lookup (op =) typs T)
-val next = next_idx + size
-(* check if 'maxvars' is large enough *)
-val _ = (if next - 1 > maxvars andalso maxvars > 0 then
-raise MAXVARS_EXCEEDED else ())
-(* prop_formula list *)
-val fms  = map BoolVar (next_idx upto (next_idx + size - 1))
-(* interpretation *)
-val intr = Leaf fms
-(* prop_formula list -> prop_formula *)
-fun one_of_two_false [] = True
-| one_of_two_false (x::xs) = SAnd (Prop_Logic.all (map (fn x' =>
-SOr (SNot x, SNot x')) xs), one_of_two_false xs)
-(* prop_formula *)
-val wf = one_of_two_false fms
-in
-(* extend the model, increase 'next_idx', add well-formedness *)
-(* condition                                                  *)
-SOME (intr, (typs, (t, intr)::terms), {maxvars = maxvars,
-def_eq = def_eq, next_idx = next, bounds = bounds,
-wellformed = SAnd (wellformed, wf)})
-end
-in
-case T of
-Type ("fun", [T1, T2]) =>
-let
-(* we create 'size_of_type ... T1' different copies of the        *)
-(* interpretation for 'T2', which are then combined into a single *)
-(* new interpretation                                             *)
-(* make fresh copies, with different variable indices *)
-(* 'idx': next variable index                         *)
-(* 'n'  : number of copies                            *)
-(* int -> int -> (int * interpretation list * prop_formula *)
-fun make_copies idx 0 = (idx, [], True)
-| make_copies idx n =
-let
-val (copy, _, new_args) = interpret ctxt (typs, [])
-{maxvars = maxvars, def_eq = false, next_idx = idx,
-bounds = [], wellformed = True} (Free ("dummy", T2))
-val (idx', copies, wf') = make_copies (#next_idx new_args) (n-1)
-in
-(idx', copy :: copies, SAnd (#wellformed new_args, wf'))
-end
-val (next, copies, wf) = make_copies next_idx
-(size_of_type ctxt model T1)
-(* combine copies into a single interpretation *)
-val intr = Node copies
-in
-(* extend the model, increase 'next_idx', add well-formedness *)
-(* condition                                                  *)
-SOME (intr, (typs, (t, intr)::terms), {maxvars = maxvars,
-def_eq = def_eq, next_idx = next, bounds = bounds,
-wellformed = SAnd (wellformed, wf)})
-end
-| Type _  => interpret_groundtype ()
-| TFree _ => interpret_groundtype ()
-| TVar  _ => interpret_groundtype ()
-end
-in
-case AList.lookup (op =) terms t of
-SOME intr =>
-(* return an existing interpretation *)
-SOME (intr, model, args)
-| NONE =>
-(case t of
-Const (_, T) => interpret_groundterm T
-| Free (_, T) => interpret_groundterm T
-| Var (_, T) => interpret_groundterm T
-| Bound i => SOME (nth (#bounds args) i, model, args)
-| Abs (_, T, body) =>
-let
-(* create all constants of type 'T' *)
-val constants = make_constants ctxt model T
-(* interpret the 'body' separately for each constant *)
-val (bodies, (model', args')) = fold_map
-(fn c => fn (m, a) =>
-let
-(* add 'c' to 'bounds' *)
-val (i', m', a') = interpret ctxt m {maxvars = #maxvars a,
-def_eq = #def_eq a, next_idx = #next_idx a,
-bounds = (c :: #bounds a), wellformed = #wellformed a} body
-in
-(* keep the new model m' and 'next_idx' and 'wellformed', *)
-(* but use old 'bounds'                                   *)
-(i', (m', {maxvars = maxvars, def_eq = def_eq,
-next_idx = #next_idx a', bounds = bounds,
-wellformed = #wellformed a'}))
-end)
-constants (model, args)
-in
-SOME (Node bodies, model', args')
-end
-| t1 $ t2 =>
-let
-(* interpret 't1' and 't2' separately *)
-val (intr1, model1, args1) = interpret ctxt model args t1
-val (intr2, model2, args2) = interpret ctxt model1 args1 t2
-in
-SOME (interpretation_apply (intr1, intr2), model2, args2)
-end)
-end;
-fun Pure_interpreter ctxt model args t =
-case t of
-Const (@{const_name all}, _) $ t1 =>
-let
-val (i, m, a) = interpret ctxt model args t1
-in
-case i of
-Node xs =>
-(* 3-valued logic *)
-let
-val fmTrue  = Prop_Logic.all (map toTrue xs)
-val fmFalse = Prop_Logic.exists (map toFalse xs)
-in
-SOME (Leaf [fmTrue, fmFalse], m, a)
-end
-| _ =>
-raise REFUTE ("Pure_interpreter",
-"\"all\" is followed by a non-function")
-end
-| Const (@{const_name all}, _) =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name "=="}, _) $ t1 $ t2 =>
-let
-val (i1, m1, a1) = interpret ctxt model args t1
-val (i2, m2, a2) = interpret ctxt m1 a1 t2
-in
-(* we use either 'make_def_equality' or 'make_equality' *)
-SOME ((if #def_eq args then make_def_equality else make_equality)
-(i1, i2), m2, a2)
-end
-| Const (@{const_name "=="}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name "=="}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-| Const (@{const_name "==>"}, _) $ t1 $ t2 =>
-(* 3-valued logic *)
-let
-val (i1, m1, a1) = interpret ctxt model args t1
-val (i2, m2, a2) = interpret ctxt m1 a1 t2
-val fmTrue = Prop_Logic.SOr (toFalse i1, toTrue i2)
-val fmFalse = Prop_Logic.SAnd (toTrue i1, toFalse i2)
-in
-SOME (Leaf [fmTrue, fmFalse], m2, a2)
-end
-| Const (@{const_name "==>"}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name "==>"}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-| _ => NONE;
-fun HOLogic_interpreter ctxt model args t =
-(* Providing interpretations directly is more efficient than unfolding the *)
-(* logical constants.  In HOL however, logical constants can themselves be *)
-(* arguments.  They are then translated using eta-expansion.               *)
-case t of
-Const (@{const_name Trueprop}, _) =>
-SOME (Node [TT, FF], model, args)
-| Const (@{const_name Not}, _) =>
-SOME (Node [FF, TT], model, args)
-(* redundant, since 'True' is also an IDT constructor *)
-| Const (@{const_name True}, _) =>
-SOME (TT, model, args)
-(* redundant, since 'False' is also an IDT constructor *)
-| Const (@{const_name False}, _) =>
-SOME (FF, model, args)
-| Const (@{const_name All}, _) $ t1 =>  (* similar to "all" (Pure) *)
-let
-val (i, m, a) = interpret ctxt model args t1
-in
-case i of
-Node xs =>
-(* 3-valued logic *)
-let
-val fmTrue = Prop_Logic.all (map toTrue xs)
-val fmFalse = Prop_Logic.exists (map toFalse xs)
-in
-SOME (Leaf [fmTrue, fmFalse], m, a)
-end
-| _ =>
-raise REFUTE ("HOLogic_interpreter",
-"\"All\" is followed by a non-function")
-end
-| Const (@{const_name All}, _) =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name Ex}, _) $ t1 =>
-let
-val (i, m, a) = interpret ctxt model args t1
-in
-case i of
-Node xs =>
-(* 3-valued logic *)
-let
-val fmTrue = Prop_Logic.exists (map toTrue xs)
-val fmFalse = Prop_Logic.all (map toFalse xs)
-in
-SOME (Leaf [fmTrue, fmFalse], m, a)
-end
-| _ =>
-raise REFUTE ("HOLogic_interpreter",
-"\"Ex\" is followed by a non-function")
-end
-| Const (@{const_name Ex}, _) =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name HOL.eq}, _) $ t1 $ t2 =>  (* similar to "==" (Pure) *)
-let
-val (i1, m1, a1) = interpret ctxt model args t1
-val (i2, m2, a2) = interpret ctxt m1 a1 t2
-in
-SOME (make_equality (i1, i2), m2, a2)
-end
-| Const (@{const_name HOL.eq}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name HOL.eq}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-| Const (@{const_name HOL.conj}, _) $ t1 $ t2 =>
-(* 3-valued logic *)
-let
-val (i1, m1, a1) = interpret ctxt model args t1
-val (i2, m2, a2) = interpret ctxt m1 a1 t2
-val fmTrue = Prop_Logic.SAnd (toTrue i1, toTrue i2)
-val fmFalse = Prop_Logic.SOr (toFalse i1, toFalse i2)
-in
-SOME (Leaf [fmTrue, fmFalse], m2, a2)
-end
-| Const (@{const_name HOL.conj}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name HOL.conj}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-(* this would make "undef" propagate, even for formulae like *)
-(* "False & undef":                                          *)
-(* SOME (Node [Node [TT, FF], Node [FF, FF]], model, args) *)
-| Const (@{const_name HOL.disj}, _) $ t1 $ t2 =>
-(* 3-valued logic *)
-let
-val (i1, m1, a1) = interpret ctxt model args t1
-val (i2, m2, a2) = interpret ctxt m1 a1 t2
-val fmTrue = Prop_Logic.SOr (toTrue i1, toTrue i2)
-val fmFalse = Prop_Logic.SAnd (toFalse i1, toFalse i2)
-in
-SOME (Leaf [fmTrue, fmFalse], m2, a2)
-end
-| Const (@{const_name HOL.disj}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name HOL.disj}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-(* this would make "undef" propagate, even for formulae like *)
-(* "True | undef":                                           *)
-(* SOME (Node [Node [TT, TT], Node [TT, FF]], model, args) *)
-| Const (@{const_name HOL.implies}, _) $ t1 $ t2 =>  (* similar to "==>" (Pure) *)
-(* 3-valued logic *)
-let
-val (i1, m1, a1) = interpret ctxt model args t1
-val (i2, m2, a2) = interpret ctxt m1 a1 t2
-val fmTrue = Prop_Logic.SOr (toFalse i1, toTrue i2)
-val fmFalse = Prop_Logic.SAnd (toTrue i1, toFalse i2)
-in
-SOME (Leaf [fmTrue, fmFalse], m2, a2)
-end
-| Const (@{const_name HOL.implies}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name HOL.implies}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-(* this would make "undef" propagate, even for formulae like *)
-(* "False --> undef":                                        *)
-(* SOME (Node [Node [TT, FF], Node [TT, TT]], model, args) *)
-| _ => NONE;
-(* interprets variables and constants whose type is an IDT (this is        *)
-(* relatively easy and merely requires us to compute the size of the IDT); *)
-(* constructors of IDTs however are properly interpreted by                *)
-(* 'IDT_constructor_interpreter'                                           *)
-fun IDT_interpreter ctxt model args t =
-let
-val thy = Proof_Context.theory_of ctxt
-val (typs, terms) = model
-(* Term.typ -> (interpretation * model * arguments) option *)
-fun interpret_term (Type (s, Ts)) =
-(case Datatype.get_info thy s of
-SOME info =>  (* inductive datatype *)
-let
-(* int option -- only recursive IDTs have an associated depth *)
-val depth = AList.lookup (op =) typs (Type (s, Ts))
-(* sanity check: depth must be at least 0 *)
-val _ =
-(case depth of SOME n =>
-if n < 0 then
-raise REFUTE ("IDT_interpreter", "negative depth")
-else ()
-| _ => ())
-in
-(* termination condition to avoid infinite recursion *)
-if depth = (SOME 0) then
-(* return a leaf of size 0 *)
-SOME (Leaf [], model, args)
-else
-let
-val index               = #index info
-val descr               = #descr info
-val (_, dtyps, constrs) = the (AList.lookup (op =) descr index)
-val typ_assoc           = dtyps ~~ Ts
-(* sanity check: every element in 'dtyps' must be a 'DtTFree' *)
-val _ =
-if Library.exists (fn d =>
-case d of Datatype.DtTFree _ => false | _ => true) dtyps
-then
-raise REFUTE ("IDT_interpreter",
-"datatype argument (for type "
-^ Syntax.string_of_typ ctxt (Type (s, Ts))
-^ ") is not a variable")
-else ()
-(* if the model specifies a depth for the current type, *)
-(* decrement it to avoid infinite recursion             *)
-val typs' = case depth of NONE => typs | SOME n =>
-AList.update (op =) (Type (s, Ts), n-1) typs
-(* recursively compute the size of the datatype *)
-val size     = size_of_dtyp ctxt typs' descr typ_assoc constrs
-val next_idx = #next_idx args
-val next     = next_idx+size
-(* check if 'maxvars' is large enough *)
-val _        = (if next-1 > #maxvars args andalso
-#maxvars args > 0 then raise MAXVARS_EXCEEDED else ())
-(* prop_formula list *)
-val fms      = map BoolVar (next_idx upto (next_idx+size-1))
-(* interpretation *)
-val intr     = Leaf fms
-(* prop_formula list -> prop_formula *)
-fun one_of_two_false [] = True
-| one_of_two_false (x::xs) = SAnd (Prop_Logic.all (map (fn x' =>
-SOr (SNot x, SNot x')) xs), one_of_two_false xs)
-(* prop_formula *)
-val wf = one_of_two_false fms
-in
-(* extend the model, increase 'next_idx', add well-formedness *)
-(* condition                                                  *)
-SOME (intr, (typs, (t, intr)::terms), {maxvars = #maxvars args,
-def_eq = #def_eq args, next_idx = next, bounds = #bounds args,
-wellformed = SAnd (#wellformed args, wf)})
-end
-end
-| NONE =>  (* not an inductive datatype *)
-NONE)
-| interpret_term _ =  (* a (free or schematic) type variable *)
-NONE
-in
-case AList.lookup (op =) terms t of
-SOME intr =>
-(* return an existing interpretation *)
-SOME (intr, model, args)
-| NONE =>
-(case t of
-Free (_, T) => interpret_term T
-| Var (_, T) => interpret_term T
-| Const (_, T) => interpret_term T
-| _ => NONE)
-end;
-(* This function imposes an order on the elements of a datatype fragment  *)
-(* as follows: C_i x_1 ... x_n < C_j y_1 ... y_m iff i < j or             *)
-(* (x_1, ..., x_n) < (y_1, ..., y_m).  With this order, a constructor is  *)
-(* a function C_i that maps some argument indices x_1, ..., x_n to the    *)
-(* datatype element given by index C_i x_1 ... x_n.  The idea remains the *)
-(* same for recursive datatypes, although the computation of indices gets *)
-(* a little tricky.                                                       *)
-fun IDT_constructor_interpreter ctxt model args t =
-let
-val thy = Proof_Context.theory_of ctxt
-(* returns a list of canonical representations for terms of the type 'T' *)
-(* It would be nice if we could just use 'print' for this, but 'print'   *)
-(* for IDTs calls 'IDT_constructor_interpreter' again, and this could    *)
-(* lead to infinite recursion when we have (mutually) recursive IDTs.    *)
-(* (Term.typ * int) list -> Term.typ -> Term.term list *)
-fun canonical_terms typs T =
-(case T of
-Type ("fun", [T1, T2]) =>
-(* 'T2' might contain a recursive IDT, so we cannot use 'print' (at *)
-(* least not for 'T2'                                               *)
-let
-(* returns a list of lists, each one consisting of n (possibly *)
-(* identical) elements from 'xs'                               *)
-(* int -> 'a list -> 'a list list *)
-fun pick_all 1 xs = map single xs
-| pick_all n xs =
-let val rec_pick = pick_all (n-1) xs in
-maps (fn x => map (cons x) rec_pick) xs
-end
-(* ["x1", ..., "xn"] *)
-val terms1 = canonical_terms typs T1
-(* ["y1", ..., "ym"] *)
-val terms2 = canonical_terms typs T2
-(* [[("x1", "y1"), ..., ("xn", "y1")], ..., *)
-(*   [("x1", "ym"), ..., ("xn", "ym")]]     *)
-val functions = map (curry (op ~~) terms1)
-(pick_all (length terms1) terms2)
-(* [["(x1, y1)", ..., "(xn, y1)"], ..., *)
-(*   ["(x1, ym)", ..., "(xn, ym)"]]     *)
-val pairss = map (map HOLogic.mk_prod) functions
-(* Term.typ *)
-val HOLogic_prodT = HOLogic.mk_prodT (T1, T2)
-val HOLogic_setT  = HOLogic.mk_setT HOLogic_prodT
-(* Term.term *)
-val HOLogic_empty_set = Const (@{const_abbrev Set.empty}, HOLogic_setT)
-val HOLogic_insert    =
-Const (@{const_name insert}, HOLogic_prodT --> HOLogic_setT --> HOLogic_setT)
-in
-(* functions as graphs, i.e. as a (HOL) set of pairs "(x, y)" *)
-map (fn ps => fold_rev (fn pair => fn acc => HOLogic_insert $ pair $ acc) ps
-HOLogic_empty_set) pairss
-end
-| Type (s, Ts) =>
-(case Datatype.get_info thy s of
-SOME info =>
-(case AList.lookup (op =) typs T of
-SOME 0 =>
-(* termination condition to avoid infinite recursion *)
-[]  (* at depth 0, every IDT is empty *)
-| _ =>
-let
-val index = #index info
-val descr = #descr info
-val (_, dtyps, constrs) = the (AList.lookup (op =) descr index)
-val typ_assoc = dtyps ~~ Ts
-(* sanity check: every element in 'dtyps' must be a 'DtTFree' *)
-val _ =
-if Library.exists (fn d =>
-case d of Datatype.DtTFree _ => false | _ => true) dtyps
-then
-raise REFUTE ("IDT_constructor_interpreter",
-"datatype argument (for type "
-^ Syntax.string_of_typ ctxt T
-^ ") is not a variable")
-else ()
-(* decrement depth for the IDT 'T' *)
-val typs' =
-(case AList.lookup (op =) typs T of NONE => typs
-| SOME n => AList.update (op =) (T, n-1) typs)
-fun constructor_terms terms [] = terms
-| constructor_terms terms (d::ds) =
-let
-val dT = typ_of_dtyp descr typ_assoc d
-val d_terms = canonical_terms typs' dT
-in
-(* C_i x_1 ... x_n < C_i y_1 ... y_n if *)
-(* (x_1, ..., x_n) < (y_1, ..., y_n)    *)
-constructor_terms
-(map_product (curry op $) terms d_terms) ds
-end
-in
-(* C_i ... < C_j ... if i < j *)
-maps (fn (cname, ctyps) =>
-let
-val cTerm = Const (cname,
-map (typ_of_dtyp descr typ_assoc) ctyps ---> T)
-in
-constructor_terms [cTerm] ctyps
-end) constrs
-end)
-| NONE =>
-(* not an inductive datatype; in this case the argument types in *)
-(* 'Ts' may not be IDTs either, so 'print' should be safe        *)
-map (fn intr => print ctxt (typs, []) T intr (K false))
-(make_constants ctxt (typs, []) T))
-| _ =>  (* TFree ..., TVar ... *)
-map (fn intr => print ctxt (typs, []) T intr (K false))
-(make_constants ctxt (typs, []) T))
-val (typs, terms) = model
-in
-case AList.lookup (op =) terms t of
-SOME intr =>
-(* return an existing interpretation *)
-SOME (intr, model, args)
-| NONE =>
-(case t of
-Const (s, T) =>
-(case body_type T of
-Type (s', Ts') =>
-(case Datatype.get_info thy s' of
-SOME info =>  (* body type is an inductive datatype *)
-let
-val index               = #index info
-val descr               = #descr info
-val (_, dtyps, constrs) = the (AList.lookup (op =) descr index)
-val typ_assoc           = dtyps ~~ Ts'
-(* sanity check: every element in 'dtyps' must be a 'DtTFree' *)
-val _ = if Library.exists (fn d =>
-case d of Datatype.DtTFree _ => false | _ => true) dtyps
-then
-raise REFUTE ("IDT_constructor_interpreter",
-"datatype argument (for type "
-^ Syntax.string_of_typ ctxt (Type (s', Ts'))
-^ ") is not a variable")
-else ()
-(* split the constructors into those occuring before/after *)
-(* 'Const (s, T)'                                          *)
-val (constrs1, constrs2) = take_prefix (fn (cname, ctypes) =>
-not (cname = s andalso Sign.typ_instance thy (T,
-map (typ_of_dtyp descr typ_assoc) ctypes
----> Type (s', Ts')))) constrs
-in
-case constrs2 of
-[] =>
-(* 'Const (s, T)' is not a constructor of this datatype *)
-NONE
-| (_, ctypes)::_ =>
-let
-(* int option -- only /recursive/ IDTs have an associated *)
-(*               depth                                    *)
-val depth = AList.lookup (op =) typs (Type (s', Ts'))
-(* this should never happen: at depth 0, this IDT fragment *)
-(* is definitely empty, and in this case we don't need to  *)
-(* interpret its constructors                              *)
-val _ = (case depth of SOME 0 =>
-raise REFUTE ("IDT_constructor_interpreter",
-"depth is 0")
-| _ => ())
-val typs' = (case depth of NONE => typs | SOME n =>
-AList.update (op =) (Type (s', Ts'), n-1) typs)
-(* elements of the datatype come before elements generated *)
-(* by 'Const (s, T)' iff they are generated by a           *)
-(* constructor in constrs1                                 *)
-val offset = size_of_dtyp ctxt typs' descr typ_assoc constrs1
-(* compute the total (current) size of the datatype *)
-val total = offset +
-size_of_dtyp ctxt typs' descr typ_assoc constrs2
-(* sanity check *)
-val _ = if total <> size_of_type ctxt (typs, [])
-(Type (s', Ts')) then
-raise REFUTE ("IDT_constructor_interpreter",
-"total is not equal to current size")
-else ()
-(* returns an interpretation where everything is mapped to *)
-(* an "undefined" element of the datatype                  *)
-fun make_undef [] = Leaf (replicate total False)
-| make_undef (d::ds) =
-let
-(* compute the current size of the type 'd' *)
-val dT   = typ_of_dtyp descr typ_assoc d
-val size = size_of_type ctxt (typs, []) dT
-in
-Node (replicate size (make_undef ds))
-end
-(* returns the interpretation for a constructor *)
-fun make_constr [] offset =
-if offset < total then
-(Leaf (replicate offset False @ True ::
-(replicate (total - offset - 1) False)), offset + 1)
-else
-raise REFUTE ("IDT_constructor_interpreter",
-"offset >= total")
-| make_constr (d::ds) offset =
-let
-(* Term.typ *)
-val dT = typ_of_dtyp descr typ_assoc d
-(* compute canonical term representations for all   *)
-(* elements of the type 'd' (with the reduced depth *)
-(* for the IDT)                                     *)
-val terms' = canonical_terms typs' dT
-(* sanity check *)
-val _ =
-if length terms' <> size_of_type ctxt (typs', []) dT
-then
-raise REFUTE ("IDT_constructor_interpreter",
-"length of terms' is not equal to old size")
-else ()
-(* compute canonical term representations for all   *)
-(* elements of the type 'd' (with the current depth *)
-(* for the IDT)                                     *)
-val terms = canonical_terms typs dT
-(* sanity check *)
-val _ =
-if length terms <> size_of_type ctxt (typs, []) dT
-then
-raise REFUTE ("IDT_constructor_interpreter",
-"length of terms is not equal to current size")
-else ()
-(* sanity check *)
-val _ =
-if length terms < length terms' then
-raise REFUTE ("IDT_constructor_interpreter",
-"current size is less than old size")
-else ()
-(* sanity check: every element of terms' must also be *)
-(*               present in terms                     *)
-val _ =
-if forall (member (op =) terms) terms' then ()
-else
-raise REFUTE ("IDT_constructor_interpreter",
-"element has disappeared")
-(* sanity check: the order on elements of terms' is    *)
-(*               the same in terms, for those elements *)
-val _ =
-let
-fun search (x::xs) (y::ys) =
-if x = y then search xs ys else search (x::xs) ys
-| search (_::_) [] =
-raise REFUTE ("IDT_constructor_interpreter",
-"element order not preserved")
-| search [] _ = ()
-in search terms' terms end
-(* int * interpretation list *)
-val (intrs, new_offset) =
-fold_map (fn t_elem => fn off =>
-(* if 't_elem' existed at the previous depth,    *)
-(* proceed recursively, otherwise map the entire *)
-(* subtree to "undefined"                        *)
-if member (op =) terms' t_elem then
-make_constr ds off
-else
-(make_undef ds, off))
-terms offset
-in
-(Node intrs, new_offset)
-end
-in
-SOME (fst (make_constr ctypes offset), model, args)
-end
-end
-| NONE =>  (* body type is not an inductive datatype *)
-NONE)
-| _ =>  (* body type is a (free or schematic) type variable *)
-NONE)
-| _ =>  (* term is not a constant *)
-NONE)
-end;
-(* Difficult code ahead.  Make sure you understand the                *)
-(* 'IDT_constructor_interpreter' and the order in which it enumerates *)
-(* elements of an IDT before you try to understand this function.     *)
-fun IDT_recursion_interpreter ctxt model args t =
-let
-val thy = Proof_Context.theory_of ctxt
-in
-(* careful: here we descend arbitrarily deep into 't', possibly before *)
-(* any other interpreter for atomic terms has had a chance to look at  *)
-(* 't'                                                                 *)
-case strip_comb t of
-(Const (s, T), params) =>
-(* iterate over all datatypes in 'thy' *)
-Symtab.fold (fn (_, info) => fn result =>
-case result of
-SOME _ =>
-result  (* just keep 'result' *)
-| NONE =>
-if member (op =) (#rec_names info) s then
-(* we do have a recursion operator of one of the (mutually *)
-(* recursive) datatypes given by 'info'                    *)
-let
-(* number of all constructors, including those of different  *)
-(* (mutually recursive) datatypes within the same descriptor *)
-val mconstrs_count =
-Integer.sum (map (fn (_, (_, _, cs)) => length cs) (#descr info))
-in
-if mconstrs_count < length params then
-(* too many actual parameters; for now we'll use the *)
-(* 'stlc_interpreter' to strip off one application   *)
-NONE
-else if mconstrs_count > length params then
-(* too few actual parameters; we use eta expansion          *)
-(* Note that the resulting expansion of lambda abstractions *)
-(* by the 'stlc_interpreter' may be rather slow (depending  *)
-(* on the argument types and the size of the IDT, of        *)
-(* course).                                                 *)
-SOME (interpret ctxt model args (eta_expand t
-(mconstrs_count - length params)))
-else  (* mconstrs_count = length params *)
-let
-(* interpret each parameter separately *)
-val (p_intrs, (model', args')) = fold_map (fn p => fn (m, a) =>
-let
-val (i, m', a') = interpret ctxt m a p
-in
-(i, (m', a'))
-end) params (model, args)
-val (typs, _) = model'
-(* 'index' is /not/ necessarily the index of the IDT that *)
-(* the recursion operator is associated with, but merely  *)
-(* the index of some mutually recursive IDT               *)
-val index         = #index info
-val descr         = #descr info
-val (_, dtyps, _) = the (AList.lookup (op =) descr index)
-(* sanity check: we assume that the order of constructors *)
-(*               in 'descr' is the same as the order of   *)
-(*               corresponding parameters, otherwise the  *)
-(*               association code below won't match the   *)
-(*               right constructors/parameters; we also   *)
-(*               assume that the order of recursion       *)
-(*               operators in '#rec_names info' is the    *)
-(*               same as the order of corresponding       *)
-(*               datatypes in 'descr'                     *)
-val _ = if map fst descr <> (0 upto (length descr - 1)) then
-raise REFUTE ("IDT_recursion_interpreter",
-"order of constructors and corresponding parameters/" ^
-"recursion operators and corresponding datatypes " ^
-"different?")
-else ()
-(* sanity check: every element in 'dtyps' must be a *)
-(*               'DtTFree'                          *)
-val _ =
-if Library.exists (fn d =>
-case d of Datatype.DtTFree _ => false
-| _ => true) dtyps
-then
-raise REFUTE ("IDT_recursion_interpreter",
-"datatype argument is not a variable")
-else ()
-(* the type of a recursion operator is *)
-(* [T1, ..., Tn, IDT] ---> Tresult     *)
-val IDT = nth (binder_types T) mconstrs_count
-(* by our assumption on the order of recursion operators *)
-(* and datatypes, this is the index of the datatype      *)
-(* corresponding to the given recursion operator         *)
-val idt_index = find_index (fn s' => s' = s) (#rec_names info)
-(* mutually recursive types must have the same type   *)
-(* parameters, unless the mutual recursion comes from *)
-(* indirect recursion                                 *)
-fun rec_typ_assoc acc [] = acc
-| rec_typ_assoc acc ((d, T)::xs) =
-(case AList.lookup op= acc d of
-NONE =>
-(case d of
-Datatype.DtTFree _ =>
-(* add the association, proceed *)
-rec_typ_assoc ((d, T)::acc) xs
-| Datatype.DtType (s, ds) =>
-let
-val (s', Ts) = dest_Type T
-in
-if s=s' then
-rec_typ_assoc ((d, T)::acc) ((ds ~~ Ts) @ xs)
-else
-raise REFUTE ("IDT_recursion_interpreter",
-"DtType/Type mismatch")
-end
-| Datatype.DtRec i =>
-let
-val (_, ds, _) = the (AList.lookup (op =) descr i)
-val (_, Ts)    = dest_Type T
-in
-rec_typ_assoc ((d, T)::acc) ((ds ~~ Ts) @ xs)
-end)
-| SOME T' =>
-if T=T' then
-(* ignore the association since it's already *)
-(* present, proceed                          *)
-rec_typ_assoc acc xs
-else
-raise REFUTE ("IDT_recursion_interpreter",
-"different type associations for the same dtyp"))
-val typ_assoc = filter
-(fn (Datatype.DtTFree _, _) => true | (_, _) => false)
-(rec_typ_assoc []
-(#2 (the (AList.lookup (op =) descr idt_index)) ~~ (snd o dest_Type) IDT))
-(* sanity check: typ_assoc must associate types to the   *)
-(*               elements of 'dtyps' (and only to those) *)
-val _ =
-if not (eq_set (op =) (dtyps, map fst typ_assoc))
-then
-raise REFUTE ("IDT_recursion_interpreter",
-"type association has extra/missing elements")
-else ()
-(* interpret each constructor in the descriptor (including *)
-(* those of mutually recursive datatypes)                  *)
-(* (int * interpretation list) list *)
-val mc_intrs = map (fn (idx, (_, _, cs)) =>
-let
-val c_return_typ = typ_of_dtyp descr typ_assoc
-(Datatype.DtRec idx)
-in
-(idx, map (fn (cname, cargs) =>
-(#1 o interpret ctxt (typs, []) {maxvars=0,
-def_eq=false, next_idx=1, bounds=[],
-wellformed=True}) (Const (cname, map (typ_of_dtyp
-descr typ_assoc) cargs ---> c_return_typ))) cs)
-end) descr
-(* associate constructors with corresponding parameters *)
-(* (int * (interpretation * interpretation) list) list *)
-val (mc_p_intrs, p_intrs') = fold_map
-(fn (idx, c_intrs) => fn p_intrs' =>
-let
-val len = length c_intrs
-in
-((idx, c_intrs ~~ List.take (p_intrs', len)),
-List.drop (p_intrs', len))
-end) mc_intrs p_intrs
-(* sanity check: no 'p_intr' may be left afterwards *)
-val _ =
-if p_intrs' <> [] then
-raise REFUTE ("IDT_recursion_interpreter",
-"more parameter than constructor interpretations")
-else ()
-(* The recursion operator, applied to 'mconstrs_count'     *)
-(* arguments, is a function that maps every element of the *)
-(* inductive datatype to an element of some result type.   *)
-(* Recursion operators for mutually recursive IDTs are     *)
-(* translated simultaneously.                              *)
-(* Since the order on datatype elements is given by an     *)
-(* order on constructors (and then by the order on         *)
-(* argument tuples), we can simply copy corresponding      *)
-(* subtrees from 'p_intrs', in the order in which they are *)
-(* given.                                                  *)
-(* interpretation * interpretation -> interpretation list *)
-fun ci_pi (Leaf xs, pi) =
-(* if the constructor does not match the arguments to a *)
-(* defined element of the IDT, the corresponding value  *)
-(* of the parameter must be ignored                     *)
-if List.exists (equal True) xs then [pi] else []
-| ci_pi (Node xs, Node ys) = maps ci_pi (xs ~~ ys)
-| ci_pi (Node _, Leaf _) =
-raise REFUTE ("IDT_recursion_interpreter",
-"constructor takes more arguments than the " ^
-"associated parameter")
-(* (int * interpretation list) list *)
-val rec_operators = map (fn (idx, c_p_intrs) =>
-(idx, maps ci_pi c_p_intrs)) mc_p_intrs
-(* sanity check: every recursion operator must provide as  *)
-(*               many values as the corresponding datatype *)
-(*               has elements                              *)
-val _ = map (fn (idx, intrs) =>
-let
-val T = typ_of_dtyp descr typ_assoc
-(Datatype.DtRec idx)
-in
-if length intrs <> size_of_type ctxt (typs, []) T then
-raise REFUTE ("IDT_recursion_interpreter",
-"wrong number of interpretations for rec. operator")
-else ()
-end) rec_operators
-(* For non-recursive datatypes, we are pretty much done at *)
-(* this point.  For recursive datatypes however, we still  *)
-(* need to apply the interpretations in 'rec_operators' to *)
-(* (recursively obtained) interpretations for recursive    *)
-(* constructor arguments.  To do so more efficiently, we   *)
-(* copy 'rec_operators' into arrays first.  Each Boolean   *)
-(* indicates whether the recursive arguments have been     *)
-(* considered already.                                     *)
-(* (int * (bool * interpretation) Array.array) list *)
-val REC_OPERATORS = map (fn (idx, intrs) =>
-(idx, Array.fromList (map (pair false) intrs)))
-rec_operators
-(* takes an interpretation, and if some leaf of this     *)
-(* interpretation is the 'elem'-th element of the type,  *)
-(* the indices of the arguments leading to this leaf are *)
-(* returned                                              *)
-(* interpretation -> int -> int list option *)
-fun get_args (Leaf xs) elem =
-if find_index (fn x => x = True) xs = elem then
-SOME []
-else
-NONE
-| get_args (Node xs) elem =
-let
-(* interpretation list * int -> int list option *)
-fun search ([], _) =
-NONE
-| search (x::xs, n) =
-(case get_args x elem of
-SOME result => SOME (n::result)
-| NONE        => search (xs, n+1))
-in
-search (xs, 0)
-end
-(* returns the index of the constructor and indices for *)
-(* its arguments that generate the 'elem'-th element of *)
-(* the datatype given by 'idx'                          *)
-(* int -> int -> int * int list *)
-fun get_cargs idx elem =
-let
-(* int * interpretation list -> int * int list *)
-fun get_cargs_rec (_, []) =
-raise REFUTE ("IDT_recursion_interpreter",
-"no matching constructor found for datatype element")
-| get_cargs_rec (n, x::xs) =
-(case get_args x elem of
-SOME args => (n, args)
-| NONE => get_cargs_rec (n+1, xs))
-in
-get_cargs_rec (0, the (AList.lookup (op =) mc_intrs idx))
-end
-(* computes one entry in 'REC_OPERATORS', and recursively *)
-(* all entries needed for it, where 'idx' gives the       *)
-(* datatype and 'elem' the element of it                  *)
-(* int -> int -> interpretation *)
-fun compute_array_entry idx elem =
-let
-val arr = the (AList.lookup (op =) REC_OPERATORS idx)
-val (flag, intr) = Array.sub (arr, elem)
-in
-if flag then
-(* simply return the previously computed result *)
-intr
-else
-(* we have to apply 'intr' to interpretations for all *)
-(* recursive arguments                                *)
-let
-(* int * int list *)
-val (c, args) = get_cargs idx elem
-(* find the indices of the constructor's /recursive/ *)
-(* arguments                                         *)
-val (_, _, constrs) = the (AList.lookup (op =) descr idx)
-val (_, dtyps) = nth constrs c
-val rec_dtyps_args = filter
-(Datatype_Aux.is_rec_type o fst) (dtyps ~~ args)
-(* map those indices to interpretations *)
-val rec_dtyps_intrs = map (fn (dtyp, arg) =>
-let
-val dT = typ_of_dtyp descr typ_assoc dtyp
-val consts = make_constants ctxt (typs, []) dT
-val arg_i = nth consts arg
-in
-(dtyp, arg_i)
-end) rec_dtyps_args
-(* takes the dtyp and interpretation of an element, *)
-(* and computes the interpretation for the          *)
-(* corresponding recursive argument                 *)
-fun rec_intr (Datatype.DtRec i) (Leaf xs) =
-(* recursive argument is "rec_i params elem" *)
-compute_array_entry i (find_index (fn x => x = True) xs)
-| rec_intr (Datatype.DtRec _) (Node _) =
-raise REFUTE ("IDT_recursion_interpreter",
-"interpretation for IDT is a node")
-| rec_intr (Datatype.DtType ("fun", [_, dt2])) (Node xs) =
-(* recursive argument is something like     *)
-(* "\<lambda>x::dt1. rec_? params (elem x)" *)
-Node (map (rec_intr dt2) xs)
-| rec_intr (Datatype.DtType ("fun", [_, _])) (Leaf _) =
-raise REFUTE ("IDT_recursion_interpreter",
-"interpretation for function dtyp is a leaf")
-| rec_intr _ _ =
-(* admissibility ensures that every recursive type *)
-(* is of the form 'Dt_1 -> ... -> Dt_k ->          *)
-(* (DtRec i)'                                      *)
-raise REFUTE ("IDT_recursion_interpreter",
-"non-recursive codomain in recursive dtyp")
-(* obtain interpretations for recursive arguments *)
-(* interpretation list *)
-val arg_intrs = map (uncurry rec_intr) rec_dtyps_intrs
-(* apply 'intr' to all recursive arguments *)
-val result = fold (fn arg_i => fn i =>
-interpretation_apply (i, arg_i)) arg_intrs intr
-(* update 'REC_OPERATORS' *)
-val _ = Array.update (arr, elem, (true, result))
-in
-result
-end
-end
-val idt_size = Array.length (the (AList.lookup (op =) REC_OPERATORS idt_index))
-(* sanity check: the size of 'IDT' should be 'idt_size' *)
-val _ =
-if idt_size <> size_of_type ctxt (typs, []) IDT then
-raise REFUTE ("IDT_recursion_interpreter",
-"unexpected size of IDT (wrong type associated?)")
-else ()
-(* interpretation *)
-val rec_op = Node (map_range (compute_array_entry idt_index) idt_size)
-in
-SOME (rec_op, model', args')
-end
-end
-else
-NONE  (* not a recursion operator of this datatype *)
-) (Datatype.get_all thy) NONE
-| _ =>  (* head of term is not a constant *)
-NONE
-end;
-fun set_interpreter ctxt model args t =
-let
-val (typs, terms) = model
-in
-case AList.lookup (op =) terms t of
-SOME intr =>
-(* return an existing interpretation *)
-SOME (intr, model, args)
-| NONE =>
-(case t of
-Free (x, Type (@{type_name set}, [T])) =>
-let
-val (intr, _, args') =
-interpret ctxt (typs, []) args (Free (x, T --> HOLogic.boolT))
-in
-SOME (intr, (typs, (t, intr)::terms), args')
-end
-| Var ((x, i), Type (@{type_name set}, [T])) =>
-let
-val (intr, _, args') =
-interpret ctxt (typs, []) args (Var ((x,i), T --> HOLogic.boolT))
-in
-SOME (intr, (typs, (t, intr)::terms), args')
-end
-| Const (s, Type (@{type_name set}, [T])) =>
-let
-val (intr, _, args') =
-interpret ctxt (typs, []) args (Const (s, T --> HOLogic.boolT))
-in
-SOME (intr, (typs, (t, intr)::terms), args')
-end
-(* 'Collect' == identity *)
-| Const (@{const_name Collect}, _) $ t1 =>
-SOME (interpret ctxt model args t1)
-| Const (@{const_name Collect}, _) =>
-SOME (interpret ctxt model args (eta_expand t 1))
-(* 'op :' == application *)
-| Const (@{const_name Set.member}, _) $ t1 $ t2 =>
-SOME (interpret ctxt model args (t2 $ t1))
-| Const (@{const_name Set.member}, _) $ _ =>
-SOME (interpret ctxt model args (eta_expand t 1))
-| Const (@{const_name Set.member}, _) =>
-SOME (interpret ctxt model args (eta_expand t 2))
-| _ => NONE)
-end;
-(* only an optimization: 'card' could in principle be interpreted with *)
-(* interpreters available already (using its definition), but the code *)
-(* below is more efficient                                             *)
-fun Finite_Set_card_interpreter ctxt model args t =
-case t of
-Const (@{const_name Finite_Set.card},
-Type ("fun", [Type (@{type_name set}, [T]), @{typ nat}])) =>
-let
-(* interpretation -> int *)
-fun number_of_elements (Node xs) =
-fold (fn x => fn n =>
-if x = TT then
-n + 1
-else if x = FF then
-n
-else
-raise REFUTE ("Finite_Set_card_interpreter",
-"interpretation for set type does not yield a Boolean"))
-xs 0
-| number_of_elements (Leaf _) =
-raise REFUTE ("Finite_Set_card_interpreter",
-"interpretation for set type is a leaf")
-val size_of_nat = size_of_type ctxt model (@{typ nat})
-(* takes an interpretation for a set and returns an interpretation *)
-(* for a 'nat' denoting the set's cardinality                      *)
-(* interpretation -> interpretation *)
-fun card i =
-let
-val n = number_of_elements i
-in
-if n < size_of_nat then
-Leaf ((replicate n False) @ True ::
-(replicate (size_of_nat-n-1) False))
-else
-Leaf (replicate size_of_nat False)
-end
-val set_constants = make_constants ctxt model (HOLogic.mk_setT T)
-in
-SOME (Node (map card set_constants), model, args)
-end
-| _ => NONE;
-(* only an optimization: 'finite' could in principle be interpreted with  *)
-(* interpreters available already (using its definition), but the code    *)
-(* below is more efficient                                                *)
-fun Finite_Set_finite_interpreter ctxt model args t =
-case t of
-Const (@{const_name Finite_Set.finite},
-Type ("fun", [_, @{typ bool}])) $ _ =>
-(* we only consider finite models anyway, hence EVERY set is *)
-(* "finite"                                                  *)
-SOME (TT, model, args)
-| Const (@{const_name Finite_Set.finite},
-Type ("fun", [set_T, @{typ bool}])) =>
-let
-val size_of_set = size_of_type ctxt model set_T
-in
-(* we only consider finite models anyway, hence EVERY set is *)
-(* "finite"                                                  *)
-SOME (Node (replicate size_of_set TT), model, args)
-end
-| _ => NONE;
-(* only an optimization: 'less' could in principle be interpreted with *)
-(* interpreters available already (using its definition), but the code     *)
-(* below is more efficient                                                 *)
-fun Nat_less_interpreter ctxt model args t =
-case t of
-Const (@{const_name Orderings.less}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ bool}])])) =>
-let
-val size_of_nat = size_of_type ctxt model (@{typ nat})
-(* the 'n'-th nat is not less than the first 'n' nats, while it *)
-(* is less than the remaining 'size_of_nat - n' nats            *)
-(* int -> interpretation *)
-fun less n = Node ((replicate n FF) @ (replicate (size_of_nat - n) TT))
-in
-SOME (Node (map less (1 upto size_of_nat)), model, args)
-end
-| _ => NONE;
-(* only an optimization: 'plus' could in principle be interpreted with *)
-(* interpreters available already (using its definition), but the code     *)
-(* below is more efficient                                                 *)
-fun Nat_plus_interpreter ctxt model args t =
-case t of
-Const (@{const_name Groups.plus}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) =>
-let
-val size_of_nat = size_of_type ctxt model (@{typ nat})
-(* int -> int -> interpretation *)
-fun plus m n =
-let
-val element = m + n
-in
-if element > size_of_nat - 1 then
-Leaf (replicate size_of_nat False)
-else
-Leaf ((replicate element False) @ True ::
-(replicate (size_of_nat - element - 1) False))
-end
-in
-SOME (Node (map_range (fn m => Node (map_range (plus m) size_of_nat)) size_of_nat),
-model, args)
-end
-| _ => NONE;
-(* only an optimization: 'minus' could in principle be interpreted *)
-(* with interpreters available already (using its definition), but the *)
-(* code below is more efficient                                        *)
-fun Nat_minus_interpreter ctxt model args t =
-case t of
-Const (@{const_name Groups.minus}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) =>
-let
-val size_of_nat = size_of_type ctxt model (@{typ nat})
-(* int -> int -> interpretation *)
-fun minus m n =
-let
-val element = Int.max (m-n, 0)
-in
-Leaf ((replicate element False) @ True ::
-(replicate (size_of_nat - element - 1) False))
-end
-in
-SOME (Node (map_range (fn m => Node (map_range (minus m) size_of_nat)) size_of_nat),
-model, args)
-end
-| _ => NONE;
-(* only an optimization: 'times' could in principle be interpreted *)
-(* with interpreters available already (using its definition), but the *)
-(* code below is more efficient                                        *)
-fun Nat_times_interpreter ctxt model args t =
-case t of
-Const (@{const_name Groups.times}, Type ("fun", [@{typ nat},
-Type ("fun", [@{typ nat}, @{typ nat}])])) =>
-let
-val size_of_nat = size_of_type ctxt model (@{typ nat})
-(* nat -> nat -> interpretation *)
-fun mult m n =
-let
-val element = m * n
-in
-if element > size_of_nat - 1 then
-Leaf (replicate size_of_nat False)
-else
-Leaf ((replicate element False) @ True ::
-(replicate (size_of_nat - element - 1) False))
-end
-in
-SOME (Node (map_range (fn m => Node (map_range (mult m) size_of_nat)) size_of_nat),
-model, args)
-end
-| _ => NONE;
-(* only an optimization: 'append' could in principle be interpreted with *)
-(* interpreters available already (using its definition), but the code   *)
-(* below is more efficient                                               *)
-fun List_append_interpreter ctxt model args t =
-case t of
-Const (@{const_name List.append}, Type ("fun", [Type ("List.list", [T]), Type ("fun",
-[Type ("List.list", [_]), Type ("List.list", [_])])])) =>
-let
-val size_elem = size_of_type ctxt model T
-val size_list = size_of_type ctxt model (Type ("List.list", [T]))
-(* maximal length of lists; 0 if we only consider the empty list *)
-val list_length =
-let
-(* int -> int -> int -> int *)
-fun list_length_acc len lists total =
-if lists = total then
-len
-else if lists < total then
-list_length_acc (len+1) (lists*size_elem) (total-lists)
-else
-raise REFUTE ("List_append_interpreter",
-"size_list not equal to 1 + size_elem + ... + " ^
-"size_elem^len, for some len")
-in
-list_length_acc 0 1 size_list
-end
-val elements = 0 upto (size_list-1)
-(* FIXME: there should be a nice formula, which computes the same as *)
-(*        the following, but without all this intermediate tree      *)
-(*        length/offset stuff                                        *)
-(* associate each list with its length and offset in a complete tree *)
-(* of width 'size_elem' and depth 'length_list' (with 'size_list'    *)
-(* nodes total)                                                      *)
-(* (int * (int * int)) list *)
-val (lenoff_lists, _) = fold_map (fn elem => fn (offsets, off) =>
-(* corresponds to a pre-order traversal of the tree *)
-let
-val len = length offsets
-(* associate the given element with len/off *)
-val assoc = (elem, (len, off))
-in
-if len < list_length then
-(* go to first child node *)
-(assoc, (off :: offsets, off * size_elem))
-else if off mod size_elem < size_elem - 1 then
-(* go to next sibling node *)
-(assoc, (offsets, off + 1))
-else
-(* go back up the stack until we find a level where we can go *)
-(* to the next sibling node                                   *)
-let
-val offsets' = snd (take_prefix
-(fn off' => off' mod size_elem = size_elem - 1) offsets)
-in
-case offsets' of
-[] =>
-(* we're at the last node in the tree; the next value *)
-(* won't be used anyway                               *)
-(assoc, ([], 0))
-| off'::offs' =>
-(* go to next sibling node *)
-(assoc, (offs', off' + 1))
-end
-end) elements ([], 0)
-(* we also need the reverse association (from length/offset to *)
-(* index)                                                      *)
-val lenoff'_lists = map Library.swap lenoff_lists
-(* returns the interpretation for "(list no. m) @ (list no. n)" *)
-(* nat -> nat -> interpretation *)
-fun append m n =
-let
-val (len_m, off_m) = the (AList.lookup (op =) lenoff_lists m)
-val (len_n, off_n) = the (AList.lookup (op =) lenoff_lists n)
-val len_elem = len_m + len_n
-val off_elem = off_m * Integer.pow len_n size_elem + off_n
-in
-case AList.lookup op= lenoff'_lists (len_elem, off_elem) of
-NONE =>
-(* undefined *)
-Leaf (replicate size_list False)
-| SOME element =>
-Leaf ((replicate element False) @ True ::
-(replicate (size_list - element - 1) False))
-end
-in
-SOME (Node (map (fn m => Node (map (append m) elements)) elements),
-model, args)
-end
-| _ => NONE;
-(* only an optimization: 'lfp' could in principle be interpreted with  *)
-(* interpreters available already (using its definition), but the code *)
-(* below is more efficient                                             *)
-fun lfp_interpreter ctxt model args t =
-case t of
-Const (@{const_name lfp}, Type ("fun", [Type ("fun",
-[Type (@{type_name set}, [T]),
-Type (@{type_name set}, [_])]),
-Type (@{type_name set}, [_])])) =>
-let
-val size_elem = size_of_type ctxt model T
-(* the universe (i.e. the set that contains every element) *)
-val i_univ = Node (replicate size_elem TT)
-(* all sets with elements from type 'T' *)
-val i_sets = make_constants ctxt model (HOLogic.mk_setT T)
-(* all functions that map sets to sets *)
-val i_funs = make_constants ctxt model (Type ("fun",
-[HOLogic.mk_setT T, HOLogic.mk_setT T]))
-(* "lfp(f) == Inter({u. f(u) <= u})" *)
-(* interpretation * interpretation -> bool *)
-fun is_subset (Node subs, Node sups) =
-forall (fn (sub, sup) => (sub = FF) orelse (sup = TT)) (subs ~~ sups)
-| is_subset (_, _) =
-raise REFUTE ("lfp_interpreter",
-"is_subset: interpretation for set is not a node")
-(* interpretation * interpretation -> interpretation *)
-fun intersection (Node xs, Node ys) =
-Node (map (fn (x, y) => if x=TT andalso y=TT then TT else FF)
-(xs ~~ ys))
-| intersection (_, _) =
-raise REFUTE ("lfp_interpreter",
-"intersection: interpretation for set is not a node")
-(* interpretation -> interpretaion *)
-fun lfp (Node resultsets) =
-fold (fn (set, resultset) => fn acc =>
-if is_subset (resultset, set) then
-intersection (acc, set)
-else
-acc) (i_sets ~~ resultsets) i_univ
-| lfp _ =
-raise REFUTE ("lfp_interpreter",
-"lfp: interpretation for function is not a node")
-in
-SOME (Node (map lfp i_funs), model, args)
-end
-| _ => NONE;
-(* only an optimization: 'gfp' could in principle be interpreted with  *)
-(* interpreters available already (using its definition), but the code *)
-(* below is more efficient                                             *)
-fun gfp_interpreter ctxt model args t =
-case t of
-Const (@{const_name gfp}, Type ("fun", [Type ("fun",
-[Type (@{type_name set}, [T]),
-Type (@{type_name set}, [_])]),
-Type (@{type_name set}, [_])])) =>
-let
-val size_elem = size_of_type ctxt model T
-(* the universe (i.e. the set that contains every element) *)
-val i_univ = Node (replicate size_elem TT)
-(* all sets with elements from type 'T' *)
-val i_sets = make_constants ctxt model (HOLogic.mk_setT T)
-(* all functions that map sets to sets *)
-val i_funs = make_constants ctxt model (Type ("fun",
-[HOLogic.mk_setT T, HOLogic.mk_setT T]))
-(* "gfp(f) == Union({u. u <= f(u)})" *)
-(* interpretation * interpretation -> bool *)
-fun is_subset (Node subs, Node sups) =
-forall (fn (sub, sup) => (sub = FF) orelse (sup = TT))
-(subs ~~ sups)
-| is_subset (_, _) =
-raise REFUTE ("gfp_interpreter",
-"is_subset: interpretation for set is not a node")
-(* interpretation * interpretation -> interpretation *)
-fun union (Node xs, Node ys) =
-Node (map (fn (x,y) => if x=TT orelse y=TT then TT else FF)
-(xs ~~ ys))
-| union (_, _) =
-raise REFUTE ("gfp_interpreter",
-"union: interpretation for set is not a node")
-(* interpretation -> interpretaion *)
-fun gfp (Node resultsets) =
-fold (fn (set, resultset) => fn acc =>
-if is_subset (set, resultset) then
-union (acc, set)
-else
-acc) (i_sets ~~ resultsets) i_univ
-| gfp _ =
-raise REFUTE ("gfp_interpreter",
-"gfp: interpretation for function is not a node")
-in
-SOME (Node (map gfp i_funs), model, args)
-end
-| _ => NONE;
-(* only an optimization: 'fst' could in principle be interpreted with  *)
-(* interpreters available already (using its definition), but the code *)
-(* below is more efficient                                             *)
-fun Product_Type_fst_interpreter ctxt model args t =
-case t of
-Const (@{const_name fst}, Type ("fun", [Type (@{type_name Product_Type.prod}, [T, U]), _])) =>
-let
-val constants_T = make_constants ctxt model T
-val size_U = size_of_type ctxt model U
-in
-SOME (Node (maps (replicate size_U) constants_T), model, args)
-end
-| _ => NONE;
-(* only an optimization: 'snd' could in principle be interpreted with  *)
-(* interpreters available already (using its definition), but the code *)
-(* below is more efficient                                             *)
-fun Product_Type_snd_interpreter ctxt model args t =
-case t of
-Const (@{const_name snd}, Type ("fun", [Type (@{type_name Product_Type.prod}, [T, U]), _])) =>
-let
-val size_T = size_of_type ctxt model T
-val constants_U = make_constants ctxt model U
-in
-SOME (Node (flat (replicate size_T constants_U)), model, args)
-end
-| _ => NONE;
-(* ------------------------------------------------------------------------- *)
-(* PRINTERS                                                                  *)
-(* ------------------------------------------------------------------------- *)
-fun stlc_printer ctxt model T intr assignment =
-let
-(* string -> string *)
-val strip_leading_quote = perhaps (try (unprefix "'"))
-(* Term.typ -> string *)
-fun string_of_typ (Type (s, _)) = s
-| string_of_typ (TFree (x, _)) = strip_leading_quote x
-| string_of_typ (TVar ((x,i), _)) =
-strip_leading_quote x ^ string_of_int i
-(* interpretation -> int *)
-fun index_from_interpretation (Leaf xs) =
-find_index (Prop_Logic.eval assignment) xs
-| index_from_interpretation _ =
-raise REFUTE ("stlc_printer",
-"interpretation for ground type is not a leaf")
-in
-case T of
-Type ("fun", [T1, T2]) =>
-let
-(* create all constants of type 'T1' *)
-val constants = make_constants ctxt model T1
-(* interpretation list *)
-val results =
-(case intr of
-Node xs => xs
-| _ => raise REFUTE ("stlc_printer",
-"interpretation for function type is a leaf"))
-(* Term.term list *)
-val pairs = map (fn (arg, result) =>
-HOLogic.mk_prod
-(print ctxt model T1 arg assignment,
-print ctxt model T2 result assignment))
-(constants ~~ results)
-(* Term.typ *)
-val HOLogic_prodT = HOLogic.mk_prodT (T1, T2)
-val HOLogic_setT  = HOLogic.mk_setT HOLogic_prodT
-(* Term.term *)
-val HOLogic_empty_set = Const (@{const_abbrev Set.empty}, HOLogic_setT)
-val HOLogic_insert    =
-Const (@{const_name insert}, HOLogic_prodT --> HOLogic_setT --> HOLogic_setT)
-in
-SOME (fold_rev (fn pair => fn acc => HOLogic_insert $ pair $ acc) pairs HOLogic_empty_set)
-end
-| Type ("prop", []) =>
-(case index_from_interpretation intr of
-~1 => SOME (HOLogic.mk_Trueprop (Const (@{const_name undefined}, HOLogic.boolT)))
-| 0  => SOME (HOLogic.mk_Trueprop @{term True})
-| 1  => SOME (HOLogic.mk_Trueprop @{term False})
-| _  => raise REFUTE ("stlc_interpreter",
-"illegal interpretation for a propositional value"))
-| Type _  =>
-if index_from_interpretation intr = (~1) then
-SOME (Const (@{const_name undefined}, T))
-else
-SOME (Const (string_of_typ T ^
-string_of_int (index_from_interpretation intr), T))
-| TFree _ =>
-if index_from_interpretation intr = (~1) then
-SOME (Const (@{const_name undefined}, T))
-else
-SOME (Const (string_of_typ T ^
-string_of_int (index_from_interpretation intr), T))
-| TVar _  =>
-if index_from_interpretation intr = (~1) then
-SOME (Const (@{const_name undefined}, T))
-else
-SOME (Const (string_of_typ T ^
-string_of_int (index_from_interpretation intr), T))
-end;
-fun set_printer ctxt model T intr assignment =
-(case T of
-Type (@{type_name set}, [T1]) =>
-let
-(* create all constants of type 'T1' *)
-val constants = make_constants ctxt model T1
-(* interpretation list *)
-val results = (case intr of
-Node xs => xs
-| _       => raise REFUTE ("set_printer",
-"interpretation for set type is a leaf"))
-(* Term.term list *)
-val elements = List.mapPartial (fn (arg, result) =>
-case result of
-Leaf [fmTrue, (* fmFalse *) _] =>
-if Prop_Logic.eval assignment fmTrue then
-SOME (print ctxt model T1 arg assignment)
-else (* if Prop_Logic.eval assignment fmFalse then *)
-NONE
-| _ =>
-raise REFUTE ("set_printer",
-"illegal interpretation for a Boolean value"))
-(constants ~~ results)
-(* Term.typ *)
-val HOLogic_setT1     = HOLogic.mk_setT T1
-(* Term.term *)
-val HOLogic_empty_set = Const (@{const_abbrev Set.empty}, HOLogic_setT1)
-val HOLogic_insert    =
-Const (@{const_name insert}, T1 --> HOLogic_setT1 --> HOLogic_setT1)
-in
-SOME (Library.foldl (fn (acc, elem) => HOLogic_insert $ elem $ acc)
-(HOLogic_empty_set, elements))
-end
-| _ =>
-NONE);
-fun IDT_printer ctxt model T intr assignment =
-let
-val thy = Proof_Context.theory_of ctxt
-in
-(case T of
-Type (s, Ts) =>
-(case Datatype.get_info thy s of
-SOME info =>  (* inductive datatype *)
-let
-val (typs, _)           = model
-val index               = #index info
-val descr               = #descr info
-val (_, dtyps, constrs) = the (AList.lookup (op =) descr index)
-val typ_assoc           = dtyps ~~ Ts
-(* sanity check: every element in 'dtyps' must be a 'DtTFree' *)
-val _ =
-if Library.exists (fn d =>
-case d of Datatype.DtTFree _ => false | _ => true) dtyps
-then
-raise REFUTE ("IDT_printer", "datatype argument (for type " ^
-Syntax.string_of_typ ctxt (Type (s, Ts)) ^ ") is not a variable")
-else ()
-(* the index of the element in the datatype *)
-val element =
-(case intr of
-Leaf xs => find_index (Prop_Logic.eval assignment) xs
-| Node _  => raise REFUTE ("IDT_printer",
-"interpretation is not a leaf"))
-in
-if element < 0 then
-SOME (Const (@{const_name undefined}, Type (s, Ts)))
-else
-let
-(* takes a datatype constructor, and if for some arguments this  *)
-(* constructor generates the datatype's element that is given by *)
-(* 'element', returns the constructor (as a term) as well as the *)
-(* indices of the arguments                                      *)
-fun get_constr_args (cname, cargs) =
-let
-val cTerm      = Const (cname,
-map (typ_of_dtyp descr typ_assoc) cargs ---> Type (s, Ts))
-val (iC, _, _) = interpret ctxt (typs, []) {maxvars=0,
-def_eq=false, next_idx=1, bounds=[], wellformed=True} cTerm
-(* interpretation -> int list option *)
-fun get_args (Leaf xs) =
-if find_index (fn x => x = True) xs = element then
-SOME []
-else
-NONE
-| get_args (Node xs) =
-let
-(* interpretation * int -> int list option *)
-fun search ([], _) =
-NONE
-| search (x::xs, n) =
-(case get_args x of
-SOME result => SOME (n::result)
-| NONE        => search (xs, n+1))
-in
-search (xs, 0)
-end
-in
-Option.map (fn args => (cTerm, cargs, args)) (get_args iC)
-end
-val (cTerm, cargs, args) =
-(* we could speed things up by computing the correct          *)
-(* constructor directly (rather than testing all              *)
-(* constructors), based on the order in which constructors    *)
-(* generate elements of datatypes; the current implementation *)
-(* of 'IDT_printer' however is independent of the internals   *)
-(* of 'IDT_constructor_interpreter'                           *)
-(case get_first get_constr_args constrs of
-SOME x => x
-| NONE   => raise REFUTE ("IDT_printer",
-"no matching constructor found for element " ^
-string_of_int element))
-val argsTerms = map (fn (d, n) =>
-let
-val dT = typ_of_dtyp descr typ_assoc d
-(* we only need the n-th element of this list, so there   *)
-(* might be a more efficient implementation that does not *)
-(* generate all constants                                 *)
-val consts = make_constants ctxt (typs, []) dT
-in
-print ctxt (typs, []) dT (nth consts n) assignment
-end) (cargs ~~ args)
-in
-SOME (list_comb (cTerm, argsTerms))
-end
-end
-| NONE =>  (* not an inductive datatype *)
-NONE)
-| _ =>  (* a (free or schematic) type variable *)
-NONE)
-end;
-(* ------------------------------------------------------------------------- *)
-(* use 'setup Refute.setup' in an Isabelle theory to initialize the 'Refute' *)
-(* structure                                                                 *)
-(* ------------------------------------------------------------------------- *)
-(* ------------------------------------------------------------------------- *)
-(* Note: the interpreters and printers are used in reverse order; however,   *)
-(*       an interpreter that can handle non-atomic terms ends up being       *)
-(*       applied before the 'stlc_interpreter' breaks the term apart into    *)
-(*       subterms that are then passed to other interpreters!                *)
-(* ------------------------------------------------------------------------- *)
-val setup =
-add_interpreter "stlc"    stlc_interpreter #>
-add_interpreter "Pure"    Pure_interpreter #>
-add_interpreter "HOLogic" HOLogic_interpreter #>
-add_interpreter "set"     set_interpreter #>
-add_interpreter "IDT"             IDT_interpreter #>
-add_interpreter "IDT_constructor" IDT_constructor_interpreter #>
-add_interpreter "IDT_recursion"   IDT_recursion_interpreter #>
-add_interpreter "Finite_Set.card"    Finite_Set_card_interpreter #>
-add_interpreter "Finite_Set.finite"  Finite_Set_finite_interpreter #>
-add_interpreter "Nat_Orderings.less" Nat_less_interpreter #>
-add_interpreter "Nat_HOL.plus"       Nat_plus_interpreter #>
-add_interpreter "Nat_HOL.minus"      Nat_minus_interpreter #>
-add_interpreter "Nat_HOL.times"      Nat_times_interpreter #>
-add_interpreter "List.append" List_append_interpreter #>
-(* UNSOUND
-add_interpreter "lfp" lfp_interpreter #>
-add_interpreter "gfp" gfp_interpreter #>
-*)
-add_interpreter "Product_Type.fst" Product_Type_fst_interpreter #>
-add_interpreter "Product_Type.snd" Product_Type_snd_interpreter #>
-add_printer "stlc" stlc_printer #>
-add_printer "set" set_printer #>
-add_printer "IDT"  IDT_printer;
-(** outer syntax commands 'refute' and 'refute_params' **)
-(* argument parsing *)
-(*optional list of arguments of the form [name1=value1, name2=value2, ...]*)
-val scan_parm = Parse.name -- (Scan.optional (@{keyword "="} |-- Parse.name) "true")
-val scan_parms = Scan.optional (@{keyword "["} |-- Parse.list scan_parm --| @{keyword "]"}) [];
-(* 'refute' command *)
-val _ =
-Outer_Syntax.improper_command @{command_spec "refute"}
-"try to find a model that refutes a given subgoal"
-(scan_parms -- Scan.optional Parse.nat 1 >>
-(fn (parms, i) =>
-Toplevel.keep (fn state =>
-let
-val ctxt = Toplevel.context_of state;
-val {goal = st, ...} = Proof.raw_goal (Toplevel.proof_of state);
-in refute_goal ctxt parms st i; () end)));
-(* 'refute_params' command *)
-val _ =
-Outer_Syntax.command @{command_spec "refute_params"}
-"show/store default parameters for the 'refute' command"
-(scan_parms >> (fn parms =>
-Toplevel.theory (fn thy =>
-let
-val thy' = fold set_default_param parms thy;
-val output =
-(case get_default_params (Proof_Context.init_global thy') of
-[] => "none"
-| new_defaults => cat_lines (map (fn (x, y) => x ^ "=" ^ y) new_defaults));
-val _ = writeln ("Default parameters for 'refute':\n" ^ output);
-in thy' end)));
-end;

changeset 49985	5b4b0e4e5205
parent 49984	9f655a6bffd8
child 49986	90e7be285b49