--- a/src/HOL/Tools/refute.ML Tue Apr 03 19:24:10 2007 +0200
+++ b/src/HOL/Tools/refute.ML Tue Apr 03 19:24:11 2007 +0200
@@ -14,67 +14,67 @@
signature REFUTE =
sig
- exception REFUTE of string * string
+ exception REFUTE of string * string
(* ------------------------------------------------------------------------- *)
(* Model/interpretation related code (translation HOL -> propositional logic *)
(* ------------------------------------------------------------------------- *)
- type params
- type interpretation
- type model
- type arguments
+ type params
+ type interpretation
+ type model
+ type arguments
- exception MAXVARS_EXCEEDED
+ exception MAXVARS_EXCEEDED
- val add_interpreter : string -> (theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option) -> theory -> theory
- val add_printer : string -> (theory -> model -> Term.term ->
- interpretation -> (int -> bool) -> Term.term option) -> theory -> theory
+ val add_interpreter : string -> (theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option) -> theory -> theory
+ val add_printer : string -> (theory -> model -> Term.term ->
+ interpretation -> (int -> bool) -> Term.term option) -> theory -> theory
- val interpret : theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments)
+ val interpret : theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments)
- val print : theory -> model -> Term.term -> interpretation ->
- (int -> bool) -> Term.term
- val print_model : theory -> model -> (int -> bool) -> string
+ val print : theory -> model -> Term.term -> interpretation ->
+ (int -> bool) -> Term.term
+ val print_model : theory -> model -> (int -> bool) -> string
(* ------------------------------------------------------------------------- *)
(* Interface *)
(* ------------------------------------------------------------------------- *)
- val set_default_param : (string * string) -> theory -> theory
- val get_default_param : theory -> string -> string option
- val get_default_params : theory -> (string * string) list
- val actual_params : theory -> (string * string) list -> params
+ val set_default_param : (string * string) -> theory -> theory
+ val get_default_param : theory -> string -> string option
+ val get_default_params : theory -> (string * string) list
+ val actual_params : theory -> (string * string) list -> params
- val find_model : theory -> params -> Term.term -> bool -> unit
+ val find_model : theory -> params -> Term.term -> bool -> unit
- (* tries to find a model for a formula: *)
- val satisfy_term : theory -> (string * string) list -> Term.term -> unit
- (* tries to find a model that refutes a formula: *)
- val refute_term : theory -> (string * string) list -> Term.term -> unit
- val refute_subgoal :
- theory -> (string * string) list -> Thm.thm -> int -> unit
+ (* tries to find a model for a formula: *)
+ val satisfy_term : theory -> (string * string) list -> Term.term -> unit
+ (* tries to find a model that refutes a formula: *)
+ val refute_term : theory -> (string * string) list -> Term.term -> unit
+ val refute_subgoal :
+ theory -> (string * string) list -> Thm.thm -> int -> unit
- val setup : theory -> theory
+ val setup : theory -> theory
end; (* signature REFUTE *)
structure Refute : REFUTE =
struct
- open PropLogic;
+ open PropLogic;
- (* 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") *)
+ (* 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;
+ (* should be raised by an interpreter when more variables would be *)
+ (* required than allowed by 'maxvars' *)
+ exception MAXVARS_EXCEEDED;
(* ------------------------------------------------------------------------- *)
(* TREES *)
@@ -85,43 +85,43 @@
(* of (lists of ...) elements *)
(* ------------------------------------------------------------------------- *)
- datatype 'a tree =
- Leaf of 'a
- | Node of ('a tree) list;
+ datatype 'a tree =
+ Leaf of 'a
+ | Node of ('a tree) list;
- (* ('a -> 'b) -> 'a tree -> 'b tree *)
+ (* ('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);
+ 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 *)
+ (* ('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;
+ 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 *)
+ (* '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)"));
+ 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 *)
@@ -143,76 +143,76 @@
(* "satsolver" string SAT solver to be used. *)
(* ------------------------------------------------------------------------- *)
- type params =
- {
- sizes : (string * int) list,
- minsize : int,
- maxsize : int,
- maxvars : int,
- maxtime : int,
- satsolver: string
- };
+ type params =
+ {
+ sizes : (string * int) list,
+ minsize : int,
+ maxsize : int,
+ maxvars : int,
+ maxtime : int,
+ satsolver: string
+ };
(* ------------------------------------------------------------------------- *)
(* interpretation: a term's interpretation is given by a variable of type *)
(* 'interpretation' *)
(* ------------------------------------------------------------------------- *)
- type interpretation =
- prop_formula list tree;
+ type interpretation =
+ prop_formula list tree;
(* ------------------------------------------------------------------------- *)
(* model: a model specifies the size of types and the interpretation of *)
(* terms *)
(* ------------------------------------------------------------------------- *)
- type model =
- (Term.typ * int) list * (Term.term * interpretation) list;
+ type model =
+ (Term.typ * int) list * (Term.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
- };
+ 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 RefuteDataArgs =
- struct
- val name = "HOL/refute";
- type T =
- {interpreters: (string * (theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option)) list,
- printers: (string * (theory -> model -> Term.term -> interpretation ->
- (int -> bool) -> Term.term option)) list,
- parameters: string Symtab.table};
- val empty = {interpreters = [], printers = [], parameters = Symtab.empty};
- val copy = I;
- val extend = I;
- fun merge _
- ({interpreters = in1, printers = pr1, parameters = pa1},
- {interpreters = in2, printers = pr2, parameters = pa2}) =
- {interpreters = AList.merge (op =) (K true) (in1, in2),
- printers = AList.merge (op =) (K true) (pr1, pr2),
- parameters = Symtab.merge (op=) (pa1, pa2)};
- fun print sg {interpreters, printers, parameters} =
- Pretty.writeln (Pretty.chunks
- [Pretty.strs ("default parameters:" :: List.concat (map
- (fn (name, value) => [name, "=", value]) (Symtab.dest parameters))),
- Pretty.strs ("interpreters:" :: map fst interpreters),
- Pretty.strs ("printers:" :: map fst printers)]);
- end;
+ structure RefuteDataArgs =
+ struct
+ val name = "HOL/refute";
+ type T =
+ {interpreters: (string * (theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option)) list,
+ printers: (string * (theory -> model -> Term.term -> interpretation ->
+ (int -> bool) -> Term.term option)) list,
+ parameters: string Symtab.table};
+ val empty = {interpreters = [], printers = [], parameters = Symtab.empty};
+ val copy = I;
+ val extend = I;
+ fun merge _
+ ({interpreters = in1, printers = pr1, parameters = pa1},
+ {interpreters = in2, printers = pr2, parameters = pa2}) =
+ {interpreters = AList.merge (op =) (K true) (in1, in2),
+ printers = AList.merge (op =) (K true) (pr1, pr2),
+ parameters = Symtab.merge (op=) (pa1, pa2)};
+ fun print sg {interpreters, printers, parameters} =
+ Pretty.writeln (Pretty.chunks
+ [Pretty.strs ("default parameters:" :: List.concat (map
+ (fn (name, value) => [name, "=", value]) (Symtab.dest parameters))),
+ Pretty.strs ("interpreters:" :: map fst interpreters),
+ Pretty.strs ("printers:" :: map fst printers)]);
+ end;
- structure RefuteData = TheoryDataFun(RefuteDataArgs);
+ structure RefuteData = TheoryDataFun(RefuteDataArgs);
(* ------------------------------------------------------------------------- *)
@@ -221,30 +221,30 @@
(* track of the interpretation of subterms *)
(* ------------------------------------------------------------------------- *)
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) *)
- fun interpret thy model args t =
- case get_first (fn (_, f) => f thy model args t)
- (#interpreters (RefuteData.get thy)) of
- NONE => raise REFUTE ("interpret",
- "no interpreter for term " ^ quote (Sign.string_of_term thy t))
- | SOME x => x;
+ fun interpret thy model args t =
+ case get_first (fn (_, f) => f thy model args t)
+ (#interpreters (RefuteData.get thy)) of
+ NONE => raise REFUTE ("interpret",
+ "no interpreter for term " ^ quote (Sign.string_of_term thy t))
+ | SOME x => x;
(* ------------------------------------------------------------------------- *)
(* print: converts the constant denoted by the term 't' into a term using a *)
(* suitable printer *)
(* ------------------------------------------------------------------------- *)
- (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
- Term.term *)
+ (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
+ Term.term *)
- fun print thy model t intr assignment =
- case get_first (fn (_, f) => f thy model t intr assignment)
- (#printers (RefuteData.get thy)) of
- NONE => raise REFUTE ("print",
- "no printer for term " ^ quote (Sign.string_of_term thy t))
- | SOME x => x;
+ fun print thy model t intr assignment =
+ case get_first (fn (_, f) => f thy model t intr assignment)
+ (#printers (RefuteData.get thy)) of
+ NONE => raise REFUTE ("print",
+ "no printer for term " ^ quote (Sign.string_of_term thy t))
+ | SOME x => x;
(* ------------------------------------------------------------------------- *)
(* print_model: turns the model into a string, using a fixed interpretation *)
@@ -252,105 +252,105 @@
(* printers *)
(* ------------------------------------------------------------------------- *)
- (* theory -> model -> (int -> bool) -> string *)
+ (* theory -> model -> (int -> bool) -> string *)
- fun print_model thy 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) =>
- Sign.string_of_typ thy T ^ ": " ^ string_of_int i) typs) ^ "\n"
- val show_consts_msg =
- if not (!show_consts) andalso Library.exists (is_Const o fst) terms then
- "set \"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
- space_implode "\n" (List.mapPartial (fn (t, intr) =>
- (* print constants only if 'show_consts' is true *)
- if (!show_consts) orelse not (is_Const t) then
- SOME (Sign.string_of_term thy t ^ ": " ^
- Sign.string_of_term thy (print thy model t intr assignment))
- else
- NONE) terms) ^ "\n"
- in
- typs_msg ^ show_consts_msg ^ terms_msg
- end;
+ fun print_model thy 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) =>
+ Sign.string_of_typ thy T ^ ": " ^ string_of_int i) typs) ^ "\n"
+ val show_consts_msg =
+ if not (!show_consts) andalso Library.exists (is_Const o fst) terms then
+ "set \"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
+ space_implode "\n" (List.mapPartial (fn (t, intr) =>
+ (* print constants only if 'show_consts' is true *)
+ if (!show_consts) orelse not (is_Const t) then
+ SOME (Sign.string_of_term thy t ^ ": " ^
+ Sign.string_of_term thy (print thy model t intr assignment))
+ else
+ NONE) terms) ^ "\n"
+ in
+ typs_msg ^ show_consts_msg ^ terms_msg
+ end;
(* ------------------------------------------------------------------------- *)
(* PARAMETER MANAGEMENT *)
(* ------------------------------------------------------------------------- *)
- (* string -> (theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option) -> theory -> theory *)
+ (* string -> (theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option) -> theory -> theory *)
- fun add_interpreter name f thy =
- let
- val {interpreters, printers, parameters} = RefuteData.get thy
- in
- case AList.lookup (op =) interpreters name of
- NONE => RefuteData.put {interpreters = (name, f) :: interpreters,
- printers = printers, parameters = parameters} thy
- | SOME _ => error ("Interpreter " ^ name ^ " already declared")
- end;
+ fun add_interpreter name f thy =
+ let
+ val {interpreters, printers, parameters} = RefuteData.get thy
+ in
+ case AList.lookup (op =) interpreters name of
+ NONE => RefuteData.put {interpreters = (name, f) :: interpreters,
+ printers = printers, parameters = parameters} thy
+ | SOME _ => error ("Interpreter " ^ name ^ " already declared")
+ end;
- (* string -> (theory -> model -> Term.term -> interpretation ->
- (int -> bool) -> Term.term option) -> theory -> theory *)
+ (* string -> (theory -> model -> Term.term -> interpretation ->
+ (int -> bool) -> Term.term option) -> theory -> theory *)
- fun add_printer name f thy =
- let
- val {interpreters, printers, parameters} = RefuteData.get thy
- in
- case AList.lookup (op =) printers name of
- NONE => RefuteData.put {interpreters = interpreters,
- printers = (name, f) :: printers, parameters = parameters} thy
- | SOME _ => error ("Printer " ^ name ^ " already declared")
- end;
+ fun add_printer name f thy =
+ let
+ val {interpreters, printers, parameters} = RefuteData.get thy
+ in
+ case AList.lookup (op =) printers name of
+ NONE => RefuteData.put {interpreters = interpreters,
+ printers = (name, f) :: printers, parameters = parameters} thy
+ | SOME _ => error ("Printer " ^ name ^ " already declared")
+ end;
(* ------------------------------------------------------------------------- *)
(* set_default_param: stores the '(name, value)' pair in RefuteData's *)
(* parameter table *)
(* ------------------------------------------------------------------------- *)
- (* (string * string) -> theory -> theory *)
+ (* (string * string) -> theory -> theory *)
- fun set_default_param (name, value) thy =
- let
- val {interpreters, printers, parameters} = RefuteData.get thy
- in
- RefuteData.put (case Symtab.lookup parameters name of
- NONE =>
- {interpreters = interpreters, printers = printers,
- parameters = Symtab.extend (parameters, [(name, value)])}
- | SOME _ =>
- {interpreters = interpreters, printers = printers,
- parameters = Symtab.update (name, value) parameters}) thy
- end;
+ fun set_default_param (name, value) thy =
+ let
+ val {interpreters, printers, parameters} = RefuteData.get thy
+ in
+ RefuteData.put (case Symtab.lookup parameters name of
+ NONE =>
+ {interpreters = interpreters, printers = printers,
+ parameters = Symtab.extend (parameters, [(name, value)])}
+ | SOME _ =>
+ {interpreters = interpreters, printers = printers,
+ parameters = Symtab.update (name, value) parameters}) thy
+ end;
(* ------------------------------------------------------------------------- *)
(* get_default_param: retrieves the value associated with 'name' from *)
(* RefuteData's parameter table *)
(* ------------------------------------------------------------------------- *)
- (* theory -> string -> string option *)
+ (* theory -> string -> string option *)
- val get_default_param = Symtab.lookup o #parameters o RefuteData.get;
+ val get_default_param = Symtab.lookup o #parameters o RefuteData.get;
(* ------------------------------------------------------------------------- *)
(* get_default_params: returns a list of all '(name, value)' pairs that are *)
(* stored in RefuteData's parameter table *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * string) list *)
+ (* theory -> (string * string) list *)
- val get_default_params = Symtab.dest o #parameters o RefuteData.get;
+ val get_default_params = Symtab.dest o #parameters o RefuteData.get;
(* ------------------------------------------------------------------------- *)
(* actual_params: takes a (possibly empty) list 'params' of parameters that *)
@@ -358,59 +358,59 @@
(* returns a record that can be passed to 'find_model'. *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * string) list -> params *)
+ (* theory -> (string * string) list -> params *)
- fun actual_params thy override =
- let
- (* (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 thy)
- (* 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")
- (* 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 = List.mapPartial
- (fn (name, value) => Option.map (pair name) (Int.fromString value))
- (List.filter (fn (name, _) => name<>"minsize" andalso name<>"maxsize"
- andalso name<>"maxvars" andalso name<>"maxtime"
- andalso name<>"satsolver") allparams)
- in
- {sizes=sizes, minsize=minsize, maxsize=maxsize, maxvars=maxvars,
- maxtime=maxtime, satsolver=satsolver}
- end;
+ fun actual_params thy override =
+ let
+ (* (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 thy)
+ (* 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")
+ (* 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 = List.mapPartial
+ (fn (name, value) => Option.map (pair name) (Int.fromString value))
+ (List.filter (fn (name, _) => name<>"minsize" andalso name<>"maxsize"
+ andalso name<>"maxvars" andalso name<>"maxtime"
+ andalso name<>"satsolver") allparams)
+ in
+ {sizes=sizes, minsize=minsize, maxsize=maxsize, maxvars=maxvars,
+ maxtime=maxtime, satsolver=satsolver}
+ end;
(* ------------------------------------------------------------------------- *)
(* TRANSLATION HOL -> PROPOSITIONAL LOGIC, BOOLEAN ASSIGNMENT -> MODEL *)
(* ------------------------------------------------------------------------- *)
- (* (''a * 'b) list -> ''a -> 'b *)
+ (* (''a * 'b) list -> ''a -> 'b *)
- fun lookup xs key =
- Option.valOf (AList.lookup (op =) xs key);
+ fun lookup xs key =
+ Option.valOf (AList.lookup (op =) xs key);
(* ------------------------------------------------------------------------- *)
(* typ_of_dtyp: converts a data type ('DatatypeAux.dtyp') into a type *)
@@ -418,55 +418,55 @@
(* arguments *)
(* ------------------------------------------------------------------------- *)
- (* DatatypeAux.descr -> (DatatypeAux.dtyp * Term.typ) list ->
- DatatypeAux.dtyp -> Term.typ *)
+ (* DatatypeAux.descr -> (DatatypeAux.dtyp * Term.typ) list ->
+ DatatypeAux.dtyp -> Term.typ *)
- fun typ_of_dtyp descr typ_assoc (DatatypeAux.DtTFree a) =
- (* replace a 'DtTFree' variable by the associated type *)
- lookup typ_assoc (DatatypeAux.DtTFree a)
- | typ_of_dtyp descr typ_assoc (DatatypeAux.DtType (s, ds)) =
- Type (s, map (typ_of_dtyp descr typ_assoc) ds)
- | typ_of_dtyp descr typ_assoc (DatatypeAux.DtRec i) =
- let
- val (s, ds, _) = lookup descr i
- in
- Type (s, map (typ_of_dtyp descr typ_assoc) ds)
- end;
+ fun typ_of_dtyp descr typ_assoc (DatatypeAux.DtTFree a) =
+ (* replace a 'DtTFree' variable by the associated type *)
+ lookup typ_assoc (DatatypeAux.DtTFree a)
+ | typ_of_dtyp descr typ_assoc (DatatypeAux.DtType (s, ds)) =
+ Type (s, map (typ_of_dtyp descr typ_assoc) ds)
+ | typ_of_dtyp descr typ_assoc (DatatypeAux.DtRec i) =
+ let
+ val (s, ds, _) = lookup descr i
+ in
+ Type (s, map (typ_of_dtyp descr typ_assoc) ds)
+ end;
(* ------------------------------------------------------------------------- *)
(* close_form: universal closure over schematic variables in 't' *)
(* ------------------------------------------------------------------------- *)
- (* Term.term -> Term.term *)
+ (* Term.term -> Term.term *)
- fun close_form t =
- let
- (* (Term.indexname * Term.typ) list *)
- val vars = sort_wrt (fst o fst) (map dest_Var (term_vars t))
- in
- Library.foldl (fn (t', ((x, i), T)) =>
- (Term.all T) $ Abs (x, T, abstract_over (Var ((x, i), T), t')))
- (t, vars)
- end;
+ fun close_form t =
+ let
+ (* (Term.indexname * Term.typ) list *)
+ val vars = sort_wrt (fst o fst) (map dest_Var (term_vars t))
+ in
+ Library.foldl (fn (t', ((x, i), T)) =>
+ (Term.all T) $ Abs (x, T, abstract_over (Var ((x, i), T), t')))
+ (t, vars)
+ end;
(* ------------------------------------------------------------------------- *)
(* monomorphic_term: applies a type substitution 'typeSubs' for all type *)
(* variables in a term 't' *)
(* ------------------------------------------------------------------------- *)
- (* Type.tyenv -> Term.term -> Term.term *)
+ (* Type.tyenv -> Term.term -> Term.term *)
- fun monomorphic_term typeSubs t =
- map_types (map_type_tvar
- (fn v =>
- case Type.lookup (typeSubs, v) of
- NONE =>
- (* schematic type variable not instantiated *)
- raise REFUTE ("monomorphic_term",
- "no substitution for type variable " ^ fst (fst v) ^
- " in term " ^ Display.raw_string_of_term t)
- | SOME typ =>
- typ)) t;
+ fun monomorphic_term typeSubs t =
+ map_types (map_type_tvar
+ (fn v =>
+ case Type.lookup (typeSubs, v) of
+ NONE =>
+ (* schematic type variable not instantiated *)
+ raise REFUTE ("monomorphic_term",
+ "no substitution for type variable " ^ fst (fst v) ^
+ " in term " ^ Display.raw_string_of_term t)
+ | SOME typ =>
+ typ)) t;
(* ------------------------------------------------------------------------- *)
(* specialize_type: given a constant 's' of type 'T', which is a subterm of *)
@@ -475,186 +475,186 @@
(* match the type 'T' (may raise Type.TYPE_MATCH) *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * Term.typ) -> Term.term -> Term.term *)
+ (* theory -> (string * Term.typ) -> Term.term -> Term.term *)
- fun specialize_type thy (s, T) t =
- let
- fun find_typeSubs (Const (s', T')) =
- if s=s' then
- SOME (Sign.typ_match thy (T', T) Vartab.empty)
- handle Type.TYPE_MATCH => NONE
- else
- NONE
- | find_typeSubs (Free _) = NONE
- | find_typeSubs (Var _) = NONE
- | find_typeSubs (Bound _) = NONE
- | find_typeSubs (Abs (_, _, body)) = find_typeSubs body
- | find_typeSubs (t1 $ t2) =
- (case find_typeSubs t1 of SOME x => SOME x
- | NONE => find_typeSubs t2)
- in
- case find_typeSubs t of
- SOME typeSubs =>
- monomorphic_term typeSubs t
- | NONE =>
- (* no match found - perhaps due to sort constraints *)
- raise Type.TYPE_MATCH
- end;
+ fun specialize_type thy (s, T) t =
+ let
+ fun find_typeSubs (Const (s', T')) =
+ if s=s' then
+ SOME (Sign.typ_match thy (T', T) Vartab.empty)
+ handle Type.TYPE_MATCH => NONE
+ else
+ NONE
+ | find_typeSubs (Free _) = NONE
+ | find_typeSubs (Var _) = NONE
+ | find_typeSubs (Bound _) = NONE
+ | find_typeSubs (Abs (_, _, body)) = find_typeSubs body
+ | find_typeSubs (t1 $ t2) =
+ (case find_typeSubs t1 of SOME x => SOME x
+ | NONE => find_typeSubs t2)
+ in
+ case find_typeSubs t of
+ SOME typeSubs =>
+ monomorphic_term typeSubs t
+ | NONE =>
+ (* no match found - perhaps due to sort constraints *)
+ raise Type.TYPE_MATCH
+ end;
(* ------------------------------------------------------------------------- *)
(* is_const_of_class: returns 'true' iff 'Const (s, T)' is a constant that *)
(* denotes membership to an axiomatic type class *)
(* ------------------------------------------------------------------------- *)
- (* theory -> string * Term.typ -> bool *)
+ (* theory -> string * Term.typ -> bool *)
- fun is_const_of_class thy (s, T) =
- 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'. *)
- s mem_string class_const_names
- end;
+ fun is_const_of_class thy (s, T) =
+ 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'. *)
+ s mem_string class_const_names
+ end;
(* ------------------------------------------------------------------------- *)
(* is_IDT_constructor: returns 'true' iff 'Const (s, T)' is the constructor *)
(* of an inductive datatype in 'thy' *)
(* ------------------------------------------------------------------------- *)
- (* theory -> string * Term.typ -> bool *)
+ (* theory -> string * Term.typ -> bool *)
- fun is_IDT_constructor thy (s, T) =
- (case body_type T of
- Type (s', _) =>
- (case DatatypePackage.get_datatype_constrs thy s' of
- SOME constrs =>
- List.exists (fn (cname, cty) =>
- cname = s andalso Sign.typ_instance thy (T, cty)) constrs
- | NONE =>
- false)
- | _ =>
- false);
+ fun is_IDT_constructor thy (s, T) =
+ (case body_type T of
+ Type (s', _) =>
+ (case DatatypePackage.get_datatype_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' *)
(* ------------------------------------------------------------------------- *)
- (* theory -> string * Term.typ -> bool *)
+ (* theory -> string * Term.typ -> bool *)
- fun is_IDT_recursor thy (s, T) =
- let
- val rec_names = Symtab.fold (append o #rec_names o snd)
- (DatatypePackage.get_datatypes thy) []
- in
- (* I'm not quite sure if checking the name 's' is sufficient, *)
- (* or if we should also check the type 'T'. *)
- s mem_string rec_names
- end;
+ fun is_IDT_recursor thy (s, T) =
+ let
+ val rec_names = Symtab.fold (append o #rec_names o snd)
+ (DatatypePackage.get_datatypes thy) []
+ in
+ (* I'm not quite sure if checking the name 's' is sufficient, *)
+ (* or if we should also check the type 'T'. *)
+ s mem_string rec_names
+ end;
(* ------------------------------------------------------------------------- *)
(* get_def: looks up the definition of a constant, as created by "constdefs" *)
(* ------------------------------------------------------------------------- *)
- (* theory -> string * Term.typ -> (string * Term.term) option *)
+ (* theory -> string * Term.typ -> (string * Term.term) option *)
- fun get_def thy (s, T) =
- let
- (* 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
- (* (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;
+ fun get_def thy (s, T) =
+ let
+ (* 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
+ (* (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" *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * Term.typ) -> (string * Term.term) option *)
+ (* theory -> (string * Term.typ) -> (string * Term.term) option *)
- 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'="Typedef.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 o 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
- | MATCH => get_typedef_ax axioms
- | Type.TYPE_MATCH => get_typedef_ax axioms)
- in
- get_typedef_ax (Theory.all_axioms_of thy)
- end;
+ 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'="Typedef.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 o 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
+ | MATCH => 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 *)
(* ------------------------------------------------------------------------- *)
- (* theory -> string -> (string * Term.term) option *)
+ (* theory -> string -> (string * Term.term) option *)
- 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;
+ 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 *)
@@ -664,293 +664,293 @@
(* that definition does not need to be unfolded *)
(* ------------------------------------------------------------------------- *)
- (* theory -> Term.term -> Term.term *)
+ (* theory -> Term.term -> Term.term *)
- (* 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'). *)
+ (* 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 ("all", _) => t
- | Const ("==", _) => t
- | Const ("==>", _) => t
- | Const ("TYPE", _) => t (* axiomatic type classes *)
- (* HOL *)
- | Const ("Trueprop", _) => t
- | Const ("Not", _) => t
- | (* redundant, since 'True' is also an IDT constructor *)
- Const ("True", _) => t
- | (* redundant, since 'False' is also an IDT constructor *)
- Const ("False", _) => t
- | Const ("arbitrary", _) => t
- | Const ("The", _) => t
- | Const ("Hilbert_Choice.Eps", _) => t
- | Const ("All", _) => t
- | Const ("Ex", _) => t
- | Const ("op =", _) => t
- | Const ("op &", _) => t
- | Const ("op |", _) => t
- | Const ("op -->", _) => t
- (* sets *)
- | Const ("Collect", _) => t
- | Const ("op :", _) => t
- (* other optimizations *)
- | Const ("Finite_Set.card", _) => t
- | Const ("Finite_Set.Finites", _) => t
- | Const ("Finite_Set.finite", _) => t
- | Const ("Orderings.less", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("bool", [])])])) => t
- | Const ("HOL.plus", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
- | Const ("HOL.minus", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
- | Const ("HOL.times", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
- | Const ("List.op @", _) => t
- | Const ("Lfp.lfp", _) => t
- | Const ("Gfp.gfp", _) => t
- | Const ("fst", _) => t
- | Const ("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. *)
- ((*immediate_output (" 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;
+ fun unfold_defs thy t =
+ let
+ (* Term.term -> Term.term *)
+ fun unfold_loop t =
+ case t of
+ (* Pure *)
+ Const ("all", _) => t
+ | Const ("==", _) => t
+ | Const ("==>", _) => t
+ | Const ("TYPE", _) => t (* axiomatic type classes *)
+ (* HOL *)
+ | Const ("Trueprop", _) => t
+ | Const ("Not", _) => t
+ | (* redundant, since 'True' is also an IDT constructor *)
+ Const ("True", _) => t
+ | (* redundant, since 'False' is also an IDT constructor *)
+ Const ("False", _) => t
+ | Const ("arbitrary", _) => t
+ | Const ("The", _) => t
+ | Const ("Hilbert_Choice.Eps", _) => t
+ | Const ("All", _) => t
+ | Const ("Ex", _) => t
+ | Const ("op =", _) => t
+ | Const ("op &", _) => t
+ | Const ("op |", _) => t
+ | Const ("op -->", _) => t
+ (* sets *)
+ | Const ("Collect", _) => t
+ | Const ("op :", _) => t
+ (* other optimizations *)
+ | Const ("Finite_Set.card", _) => t
+ | Const ("Finite_Set.Finites", _) => t
+ | Const ("Finite_Set.finite", _) => t
+ | Const ("Orderings.less", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("bool", [])])])) => t
+ | Const ("HOL.plus", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
+ | Const ("HOL.minus", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
+ | Const ("HOL.times", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) => t
+ | Const ("List.op @", _) => t
+ | Const ("Lfp.lfp", _) => t
+ | Const ("Gfp.gfp", _) => t
+ | Const ("fst", _) => t
+ | Const ("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. *)
+ ((*immediate_output (" 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: 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", "constdefs". 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'. *)
+ (* Note: currently we use "inverse" functions to the definitional *)
+ (* mechanisms provided by Isabelle/HOL, e.g. for "axclass", *)
+ (* "typedef", "constdefs". 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'. *)
- (* theory -> Term.term -> Term.term list *)
+ (* theory -> Term.term -> Term.term list *)
- (* 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. *)
+ (* 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. *)
+ (* To avoid collecting the same axiom multiple times, we use an *)
+ (* accumulator 'axs' which contains all axioms collected so far. *)
- fun collect_axioms thy t =
- let
- val _ = immediate_output "Adding axioms..."
- (* (string * Term.term) list *)
- val axioms = Theory.all_axioms_of thy
- (* string * Term.term -> Term.term list -> Term.term list *)
- fun collect_this_axiom (axname, ax) axs =
- let
- val ax' = unfold_defs thy ax
- in
- if member (op aconv) axs ax' then
- axs
- else (
- immediate_output (" " ^ axname);
- collect_term_axioms (ax' :: axs, ax')
- )
- end
- (* Term.term list * Term.typ -> Term.term list *)
- and collect_sort_axioms (axs, T) =
- let
- (* string list *)
- val sort = (case T of
- TFree (_, sort) => sort
- | TVar (_, sort) => sort
- | _ => raise REFUTE ("collect_axioms", "type " ^
- Sign.string_of_typ thy 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_definition 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.term_tvars ax of
- [] =>
- (axname, ax)
- | [(idx, S)] =>
- (axname, monomorphic_term (Vartab.make [(idx, (S, T))]) ax)
- | _ =>
- raise REFUTE ("collect_axioms", "class axiom " ^ axname ^ " (" ^
- Sign.string_of_term thy ax ^
- ") contains more than one type variable")))
- class_axioms
- in
- fold collect_this_axiom monomorphic_class_axioms axs
- end
- (* Term.term list * Term.typ -> Term.term list *)
- and collect_type_axioms (axs, T) =
- case T of
- (* simple types *)
- Type ("prop", []) => axs
- | Type ("fun", [T1, T2]) => collect_type_axioms
- (collect_type_axioms (axs, T1), T2)
- | Type ("set", [T1]) => collect_type_axioms (axs, T1)
- (* axiomatic type classes *)
- | Type ("itself", [T1]) => collect_type_axioms (axs, T1)
- | Type (s, Ts) =>
- (case DatatypePackage.get_datatype thy s of
- SOME info => (* inductive datatype *)
- (* only collect relevant type axioms for the argument types *)
- Library.foldl collect_type_axioms (axs, Ts)
- | 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 *)
- Library.foldl collect_type_axioms (axs, Ts)))
- (* axiomatic type classes *)
- | TFree _ => collect_sort_axioms (axs, T)
- (* axiomatic type classes *)
- | TVar _ => collect_sort_axioms (axs, T)
- (* Term.term list * Term.term -> Term.term list *)
- and collect_term_axioms (axs, t) =
- case t of
- (* Pure *)
- Const ("all", _) => axs
- | Const ("==", _) => axs
- | Const ("==>", _) => axs
- (* axiomatic type classes *)
- | Const ("TYPE", T) => collect_type_axioms (axs, T)
- (* HOL *)
- | Const ("Trueprop", _) => axs
- | Const ("Not", _) => axs
- (* redundant, since 'True' is also an IDT constructor *)
- | Const ("True", _) => axs
- (* redundant, since 'False' is also an IDT constructor *)
- | Const ("False", _) => axs
- | Const ("arbitrary", T) => collect_type_axioms (axs, T)
- | Const ("The", T) =>
- let
- val ax = specialize_type thy ("The", T)
- (lookup axioms "HOL.the_eq_trivial")
- in
- collect_this_axiom ("HOL.the_eq_trivial", ax) axs
- end
- | Const ("Hilbert_Choice.Eps", T) =>
- let
- val ax = specialize_type thy ("Hilbert_Choice.Eps", T)
- (lookup axioms "Hilbert_Choice.someI")
- in
- collect_this_axiom ("Hilbert_Choice.someI", ax) axs
- end
- | Const ("All", T) => collect_type_axioms (axs, T)
- | Const ("Ex", T) => collect_type_axioms (axs, T)
- | Const ("op =", T) => collect_type_axioms (axs, T)
- | Const ("op &", _) => axs
- | Const ("op |", _) => axs
- | Const ("op -->", _) => axs
- (* sets *)
- | Const ("Collect", T) => collect_type_axioms (axs, T)
- | Const ("op :", T) => collect_type_axioms (axs, T)
- (* other optimizations *)
- | Const ("Finite_Set.card", T) => collect_type_axioms (axs, T)
- | Const ("Finite_Set.Finites", T) => collect_type_axioms (axs, T)
- | Const ("Finite_Set.finite", T) => collect_type_axioms (axs, T)
- | Const ("Orderings.less", T as Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("bool", [])])])) =>
- collect_type_axioms (axs, T)
- | Const ("HOL.plus", T as Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
- collect_type_axioms (axs, T)
- | Const ("HOL.minus", T as Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
- collect_type_axioms (axs, T)
- | Const ("HOL.times", T as Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
- collect_type_axioms (axs, T)
- | Const ("List.op @", T) => collect_type_axioms (axs, T)
- | Const ("Lfp.lfp", T) => collect_type_axioms (axs, T)
- | Const ("Gfp.gfp", T) => collect_type_axioms (axs, T)
- | Const ("fst", T) => collect_type_axioms (axs, T)
- | Const ("snd", T) => collect_type_axioms (axs, T)
- (* 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 inclass = Logic.mk_inclass (TVar (("'a", 0), [class]), class)
- val ax_in = SOME (specialize_type thy (s, T) inclass)
- (* type match may fail due to sort constraints *)
- handle Type.TYPE_MATCH => NONE
- val ax_1 = Option.map (fn ax => (Sign.string_of_term thy ax, ax))
- ax_in
- val ax_2 = Option.map (apsnd (specialize_type thy (s, T)))
- (get_classdef thy class)
- in
- collect_type_axioms (fold collect_this_axiom
- (map_filter I [ax_1, ax_2]) axs, T)
- 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 (axs, T)
- 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 (axs, T)
- | Free (_, T) => collect_type_axioms (axs, T)
- | Var (_, T) => collect_type_axioms (axs, T)
- | Bound i => axs
- | Abs (_, T, body) => collect_term_axioms
- (collect_type_axioms (axs, T), body)
- | t1 $ t2 => collect_term_axioms
- (collect_term_axioms (axs, t1), t2)
- (* Term.term list *)
- val result = map close_form (collect_term_axioms ([], t))
- val _ = writeln " ...done."
- in
- result
- end;
+ fun collect_axioms thy t =
+ let
+ val _ = immediate_output "Adding axioms..."
+ (* (string * Term.term) list *)
+ val axioms = Theory.all_axioms_of thy
+ (* string * Term.term -> Term.term list -> Term.term list *)
+ fun collect_this_axiom (axname, ax) axs =
+ let
+ val ax' = unfold_defs thy ax
+ in
+ if member (op aconv) axs ax' then
+ axs
+ else (
+ immediate_output (" " ^ axname);
+ collect_term_axioms (ax' :: axs, ax')
+ )
+ end
+ (* Term.term list * Term.typ -> Term.term list *)
+ and collect_sort_axioms (axs, T) =
+ let
+ (* string list *)
+ val sort = (case T of
+ TFree (_, sort) => sort
+ | TVar (_, sort) => sort
+ | _ => raise REFUTE ("collect_axioms", "type " ^
+ Sign.string_of_typ thy 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_definition 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.term_tvars ax of
+ [] =>
+ (axname, ax)
+ | [(idx, S)] =>
+ (axname, monomorphic_term (Vartab.make [(idx, (S, T))]) ax)
+ | _ =>
+ raise REFUTE ("collect_axioms", "class axiom " ^ axname ^ " (" ^
+ Sign.string_of_term thy ax ^
+ ") contains more than one type variable")))
+ class_axioms
+ in
+ fold collect_this_axiom monomorphic_class_axioms axs
+ end
+ (* Term.term list * Term.typ -> Term.term list *)
+ and collect_type_axioms (axs, T) =
+ case T of
+ (* simple types *)
+ Type ("prop", []) => axs
+ | Type ("fun", [T1, T2]) => collect_type_axioms
+ (collect_type_axioms (axs, T1), T2)
+ | Type ("set", [T1]) => collect_type_axioms (axs, T1)
+ (* axiomatic type classes *)
+ | Type ("itself", [T1]) => collect_type_axioms (axs, T1)
+ | Type (s, Ts) =>
+ (case DatatypePackage.get_datatype thy s of
+ SOME info => (* inductive datatype *)
+ (* only collect relevant type axioms for the argument types *)
+ Library.foldl collect_type_axioms (axs, Ts)
+ | 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 *)
+ Library.foldl collect_type_axioms (axs, Ts)))
+ (* axiomatic type classes *)
+ | TFree _ => collect_sort_axioms (axs, T)
+ (* axiomatic type classes *)
+ | TVar _ => collect_sort_axioms (axs, T)
+ (* Term.term list * Term.term -> Term.term list *)
+ and collect_term_axioms (axs, t) =
+ case t of
+ (* Pure *)
+ Const ("all", _) => axs
+ | Const ("==", _) => axs
+ | Const ("==>", _) => axs
+ (* axiomatic type classes *)
+ | Const ("TYPE", T) => collect_type_axioms (axs, T)
+ (* HOL *)
+ | Const ("Trueprop", _) => axs
+ | Const ("Not", _) => axs
+ (* redundant, since 'True' is also an IDT constructor *)
+ | Const ("True", _) => axs
+ (* redundant, since 'False' is also an IDT constructor *)
+ | Const ("False", _) => axs
+ | Const ("arbitrary", T) => collect_type_axioms (axs, T)
+ | Const ("The", T) =>
+ let
+ val ax = specialize_type thy ("The", T)
+ (lookup axioms "HOL.the_eq_trivial")
+ in
+ collect_this_axiom ("HOL.the_eq_trivial", ax) axs
+ end
+ | Const ("Hilbert_Choice.Eps", T) =>
+ let
+ val ax = specialize_type thy ("Hilbert_Choice.Eps", T)
+ (lookup axioms "Hilbert_Choice.someI")
+ in
+ collect_this_axiom ("Hilbert_Choice.someI", ax) axs
+ end
+ | Const ("All", T) => collect_type_axioms (axs, T)
+ | Const ("Ex", T) => collect_type_axioms (axs, T)
+ | Const ("op =", T) => collect_type_axioms (axs, T)
+ | Const ("op &", _) => axs
+ | Const ("op |", _) => axs
+ | Const ("op -->", _) => axs
+ (* sets *)
+ | Const ("Collect", T) => collect_type_axioms (axs, T)
+ | Const ("op :", T) => collect_type_axioms (axs, T)
+ (* other optimizations *)
+ | Const ("Finite_Set.card", T) => collect_type_axioms (axs, T)
+ | Const ("Finite_Set.Finites", T) => collect_type_axioms (axs, T)
+ | Const ("Finite_Set.finite", T) => collect_type_axioms (axs, T)
+ | Const ("Orderings.less", T as Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("bool", [])])])) =>
+ collect_type_axioms (axs, T)
+ | Const ("HOL.plus", T as Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
+ collect_type_axioms (axs, T)
+ | Const ("HOL.minus", T as Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
+ collect_type_axioms (axs, T)
+ | Const ("HOL.times", T as Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
+ collect_type_axioms (axs, T)
+ | Const ("List.op @", T) => collect_type_axioms (axs, T)
+ | Const ("Lfp.lfp", T) => collect_type_axioms (axs, T)
+ | Const ("Gfp.gfp", T) => collect_type_axioms (axs, T)
+ | Const ("fst", T) => collect_type_axioms (axs, T)
+ | Const ("snd", T) => collect_type_axioms (axs, T)
+ (* 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 inclass = Logic.mk_inclass (TVar (("'a", 0), [class]), class)
+ val ax_in = SOME (specialize_type thy (s, T) inclass)
+ (* type match may fail due to sort constraints *)
+ handle Type.TYPE_MATCH => NONE
+ val ax_1 = Option.map (fn ax => (Sign.string_of_term thy ax, ax))
+ ax_in
+ val ax_2 = Option.map (apsnd (specialize_type thy (s, T)))
+ (get_classdef thy class)
+ in
+ collect_type_axioms (fold collect_this_axiom
+ (map_filter I [ax_1, ax_2]) axs, T)
+ 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 (axs, T)
+ 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 (axs, T)
+ | Free (_, T) => collect_type_axioms (axs, T)
+ | Var (_, T) => collect_type_axioms (axs, T)
+ | Bound i => axs
+ | Abs (_, T, body) => collect_term_axioms
+ (collect_type_axioms (axs, T), body)
+ | t1 $ t2 => collect_term_axioms
+ (collect_term_axioms (axs, t1), t2)
+ (* Term.term list *)
+ val result = map close_form (collect_term_axioms ([], t))
+ val _ = writeln " ...done."
+ in
+ result
+ end;
(* ------------------------------------------------------------------------- *)
(* ground_types: collects all ground types in a term (including argument *)
@@ -960,61 +960,61 @@
(* are considered. *)
(* ------------------------------------------------------------------------- *)
- (* theory -> Term.term -> Term.typ list *)
+ (* theory -> Term.term -> Term.typ list *)
- fun ground_types thy t =
- let
- (* Term.typ * Term.typ list -> Term.typ list *)
- fun collect_types (T, acc) =
- if T mem acc then
- acc (* prevent infinite recursion (for IDTs) *)
- else
- (case T of
- Type ("fun", [T1, T2]) => collect_types (T1, collect_types (T2, acc))
- | Type ("prop", []) => acc
- | Type ("set", [T1]) => collect_types (T1, acc)
- | Type (s, Ts) =>
- (case DatatypePackage.get_datatype thy s of
- SOME info => (* inductive datatype *)
- let
- val index = #index info
- val descr = #descr info
- val (_, dtyps, constrs) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
- then
- raise REFUTE ("ground_types", "datatype argument (for type "
- ^ Sign.string_of_typ thy (Type (s, Ts))
- ^ ") is not a variable")
- else
- ())
- (* if the current type is a recursive IDT (i.e. a depth is *)
- (* required), add it to 'acc' *)
- val acc' = (if Library.exists (fn (_, ds) => Library.exists
- DatatypeAux.is_rec_type ds) constrs then
- insert (op =) T acc
- else
- acc)
- (* collect argument types *)
- val acc_args = foldr collect_types acc' Ts
- (* collect constructor types *)
- val acc_constrs = foldr collect_types acc_args (List.concat
- (map (fn (_, ds) => map (typ_of_dtyp descr typ_assoc) ds)
- constrs))
- in
- acc_constrs
- end
- | NONE =>
- (* not an inductive datatype, e.g. defined via "typedef" or *)
- (* "typedecl" *)
- insert (op =) T (foldr collect_types acc Ts))
- | TFree _ => insert (op =) T acc
- | TVar _ => insert (op =) T acc)
- in
- it_term_types collect_types (t, [])
- end;
+ fun ground_types thy t =
+ let
+ (* Term.typ * Term.typ list -> Term.typ list *)
+ fun collect_types (T, acc) =
+ if T mem acc then
+ acc (* prevent infinite recursion (for IDTs) *)
+ else
+ (case T of
+ Type ("fun", [T1, T2]) => collect_types (T1, collect_types (T2, acc))
+ | Type ("prop", []) => acc
+ | Type ("set", [T1]) => collect_types (T1, acc)
+ | Type (s, Ts) =>
+ (case DatatypePackage.get_datatype thy s of
+ SOME info => (* inductive datatype *)
+ let
+ val index = #index info
+ val descr = #descr info
+ val (_, dtyps, constrs) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
+ then
+ raise REFUTE ("ground_types", "datatype argument (for type "
+ ^ Sign.string_of_typ thy (Type (s, Ts))
+ ^ ") is not a variable")
+ else
+ ())
+ (* if the current type is a recursive IDT (i.e. a depth is *)
+ (* required), add it to 'acc' *)
+ val acc' = (if Library.exists (fn (_, ds) => Library.exists
+ DatatypeAux.is_rec_type ds) constrs then
+ insert (op =) T acc
+ else
+ acc)
+ (* collect argument types *)
+ val acc_args = foldr collect_types acc' Ts
+ (* collect constructor types *)
+ val acc_constrs = foldr collect_types acc_args (List.concat
+ (map (fn (_, ds) => map (typ_of_dtyp descr typ_assoc) ds)
+ constrs))
+ in
+ acc_constrs
+ end
+ | NONE =>
+ (* not an inductive datatype, e.g. defined via "typedef" or *)
+ (* "typedecl" *)
+ insert (op =) T (foldr collect_types acc Ts))
+ | TFree _ => insert (op =) T acc
+ | TVar _ => insert (op =) T acc)
+ in
+ it_term_types collect_types (t, [])
+ end;
(* ------------------------------------------------------------------------- *)
(* string_of_typ: (rather naive) conversion from types to strings, used to *)
@@ -1023,11 +1023,11 @@
(* list") are identified. *)
(* ------------------------------------------------------------------------- *)
- (* Term.typ -> string *)
+ (* Term.typ -> string *)
- fun string_of_typ (Type (s, _)) = s
- | string_of_typ (TFree (s, _)) = s
- | string_of_typ (TVar ((s,_), _)) = s;
+ 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 *)
@@ -1035,17 +1035,17 @@
(* 'sizes' *)
(* ------------------------------------------------------------------------- *)
- (* Term.typ list -> (string * int) list -> int -> (Term.typ * int) list *)
+ (* 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;
+ 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 *)
@@ -1054,70 +1054,70 @@
(* type may have a fixed size given in 'sizes' *)
(* ------------------------------------------------------------------------- *)
- (* (Term.typ * int) list -> (string * int) list -> int -> int ->
- (Term.typ * int) list option *)
+ (* (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 max len sum [] =
- 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 (valOf (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 = List.filter
- (not o (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 (snd (foldl_map (fn (ds, (T, _)) =>
- case AList.lookup (op =) sizes (string_of_typ T) of
- (* return the fixed size *)
- SOME n => (ds, (T, n))
- (* consume the head of 'ds', add 'minsize' *)
- | NONE => (tl ds, (T, minsize + hd ds)))
- (diffs', xs)))
- | NONE =>
- NONE
- end;
+ 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 max len sum [] =
+ 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 (valOf (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 = List.filter
+ (not o (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 (snd (foldl_map (fn (ds, (T, _)) =>
+ case AList.lookup (op =) sizes (string_of_typ T) of
+ (* return the fixed size *)
+ SOME n => (ds, (T, n))
+ (* consume the head of 'ds', add 'minsize' *)
+ | NONE => (tl ds, (T, minsize + hd ds)))
+ (diffs', xs)))
+ | 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 *)
+ (* interpretation -> prop_formula *)
- fun toTrue (Leaf [fm, _]) =
- fm
- | toTrue _ =
- raise REFUTE ("toTrue", "interpretation does not denote a Boolean value");
+ 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 *)
@@ -1125,12 +1125,12 @@
(* denotes "false" *)
(* ------------------------------------------------------------------------- *)
- (* interpretation -> prop_formula *)
+ (* interpretation -> prop_formula *)
- fun toFalse (Leaf [_, fm]) =
- fm
- | toFalse _ =
- raise REFUTE ("toFalse", "interpretation does not denote a Boolean value");
+ fun toFalse (Leaf [_, fm]) =
+ fm
+ | toFalse _ =
+ raise REFUTE ("toFalse", "interpretation does not denote a Boolean value");
(* ------------------------------------------------------------------------- *)
(* find_model: repeatedly calls 'interpret' with appropriate parameters, *)
@@ -1142,121 +1142,121 @@
(* negate : if true, find a model that makes 't' false (rather than true) *)
(* ------------------------------------------------------------------------- *)
- (* theory -> params -> Term.term -> bool -> unit *)
+ (* theory -> params -> Term.term -> bool -> unit *)
- fun find_model thy {sizes, minsize, maxsize, maxvars, maxtime, satsolver} t
- negate =
- let
- (* unit -> unit *)
- fun wrapper () =
- let
- val u = unfold_defs thy t
- val _ = writeln ("Unfolded term: " ^ Sign.string_of_term thy u)
- val axioms = collect_axioms thy u
- (* Term.typ list *)
- val types = Library.foldl (fn (acc, t') =>
- acc union (ground_types thy t')) ([], u :: axioms)
- val _ = writeln ("Ground types: "
- ^ (if null types then "none."
- else commas (map (Sign.string_of_typ thy) 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 _ = if Library.exists (fn
- Type (s, _) =>
- (case DatatypePackage.get_datatype thy s of
- SOME info => (* inductive datatype *)
- let
- val index = #index info
- val descr = #descr info
- val (_, _, constrs) = lookup descr index
- in
- (* recursive datatype? *)
- Library.exists (fn (_, ds) =>
- Library.exists DatatypeAux.is_rec_type ds) constrs
- end
- | NONE => false)
- | _ => false) types then
- warning ("Term contains a recursive datatype; "
- ^ "countermodel(s) may be spurious!")
- else
- ()
- (* (Term.typ * int) list -> unit *)
- fun find_model_loop universe =
- let
- val init_model = (universe, [])
- val init_args = {maxvars = maxvars, def_eq = false, next_idx = 1,
- bounds = [], wellformed = True}
- val _ = immediate_output ("Translating term (sizes: "
- ^ commas (map (fn (_, n) => string_of_int n) universe) ^ ") ...")
- (* translate 'u' and all axioms *)
- val ((model, args), intrs) = foldl_map (fn ((m, a), t') =>
- let
- val (i, m', a') = interpret thy m a t'
- in
- (* set 'def_eq' to 'true' *)
- ((m', {maxvars = #maxvars a', def_eq = true,
- next_idx = #next_idx a', bounds = #bounds a',
- wellformed = #wellformed a'}), i)
- end) ((init_model, init_args), u :: axioms)
- (* 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 = PropLogic.all (map toTrue (tl intrs))
- val fm = PropLogic.all [#wellformed args, fm_ax, fm_u]
- in
- immediate_output " invoking SAT solver...";
- (case SatSolver.invoke_solver satsolver fm of
- SatSolver.SATISFIABLE assignment =>
- (writeln " model found!";
- writeln ("*** Model found: ***\n" ^ print_model thy model
- (fn i => case assignment i of SOME b => b | NONE => true)))
- | SatSolver.UNSATISFIABLE _ =>
- (immediate_output " no model exists.\n";
- case next_universe universe sizes minsize maxsize of
- SOME universe' => find_model_loop universe'
- | NONE => writeln
- "Search terminated, no larger universe within the given limits.")
- | SatSolver.UNKNOWN =>
- (immediate_output " no model found.\n";
- case next_universe universe sizes minsize maxsize of
- SOME universe' => find_model_loop universe'
- | NONE => writeln
- "Search terminated, no larger universe within the given limits.")
- ) handle SatSolver.NOT_CONFIGURED =>
- error ("SAT solver " ^ quote satsolver ^ " is not configured.")
- end handle MAXVARS_EXCEEDED =>
- writeln ("\nSearch terminated, number of Boolean variables ("
- ^ string_of_int maxvars ^ " allowed) exceeded.")
- in
- find_model_loop (first_universe types sizes minsize)
- end
- in
- (* some parameter sanity checks *)
- assert (minsize>=1)
- ("\"minsize\" is " ^ string_of_int minsize ^ ", must be at least 1");
- assert (maxsize>=1)
- ("\"maxsize\" is " ^ string_of_int maxsize ^ ", must be at least 1");
- assert (maxsize>=minsize)
- ("\"maxsize\" (=" ^ string_of_int maxsize ^
- ") is less than \"minsize\" (=" ^ string_of_int minsize ^ ").");
- assert (maxvars>=0)
- ("\"maxvars\" is " ^ string_of_int maxvars ^ ", must be at least 0");
- assert (maxtime>=0)
- ("\"maxtime\" is " ^ string_of_int maxtime ^ ", must be at least 0");
- (* enter loop with or without time limit *)
- writeln ("Trying to find a model that "
- ^ (if negate then "refutes" else "satisfies") ^ ": "
- ^ Sign.string_of_term thy t);
- if maxtime>0 then (
- interrupt_timeout (Time.fromSeconds (Int.toLarge maxtime))
- wrapper ()
- handle Interrupt =>
- writeln ("\nSearch terminated, time limit (" ^ string_of_int maxtime
- ^ (if maxtime=1 then " second" else " seconds") ^ ") exceeded.")
- ) else
- wrapper ()
- end;
+ fun find_model thy {sizes, minsize, maxsize, maxvars, maxtime, satsolver} t
+ negate =
+ let
+ (* unit -> unit *)
+ fun wrapper () =
+ let
+ val u = unfold_defs thy t
+ val _ = writeln ("Unfolded term: " ^ Sign.string_of_term thy u)
+ val axioms = collect_axioms thy u
+ (* Term.typ list *)
+ val types = Library.foldl (fn (acc, t') =>
+ acc union (ground_types thy t')) ([], u :: axioms)
+ val _ = writeln ("Ground types: "
+ ^ (if null types then "none."
+ else commas (map (Sign.string_of_typ thy) 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 _ = if Library.exists (fn
+ Type (s, _) =>
+ (case DatatypePackage.get_datatype thy s of
+ SOME info => (* inductive datatype *)
+ let
+ val index = #index info
+ val descr = #descr info
+ val (_, _, constrs) = lookup descr index
+ in
+ (* recursive datatype? *)
+ Library.exists (fn (_, ds) =>
+ Library.exists DatatypeAux.is_rec_type ds) constrs
+ end
+ | NONE => false)
+ | _ => false) types then
+ warning ("Term contains a recursive datatype; "
+ ^ "countermodel(s) may be spurious!")
+ else
+ ()
+ (* (Term.typ * int) list -> unit *)
+ fun find_model_loop universe =
+ let
+ val init_model = (universe, [])
+ val init_args = {maxvars = maxvars, def_eq = false, next_idx = 1,
+ bounds = [], wellformed = True}
+ val _ = immediate_output ("Translating term (sizes: "
+ ^ commas (map (fn (_, n) => string_of_int n) universe) ^ ") ...")
+ (* translate 'u' and all axioms *)
+ val ((model, args), intrs) = foldl_map (fn ((m, a), t') =>
+ let
+ val (i, m', a') = interpret thy m a t'
+ in
+ (* set 'def_eq' to 'true' *)
+ ((m', {maxvars = #maxvars a', def_eq = true,
+ next_idx = #next_idx a', bounds = #bounds a',
+ wellformed = #wellformed a'}), i)
+ end) ((init_model, init_args), u :: axioms)
+ (* 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 = PropLogic.all (map toTrue (tl intrs))
+ val fm = PropLogic.all [#wellformed args, fm_ax, fm_u]
+ in
+ immediate_output " invoking SAT solver...";
+ (case SatSolver.invoke_solver satsolver fm of
+ SatSolver.SATISFIABLE assignment =>
+ (writeln " model found!";
+ writeln ("*** Model found: ***\n" ^ print_model thy model
+ (fn i => case assignment i of SOME b => b | NONE => true)))
+ | SatSolver.UNSATISFIABLE _ =>
+ (immediate_output " no model exists.\n";
+ case next_universe universe sizes minsize maxsize of
+ SOME universe' => find_model_loop universe'
+ | NONE => writeln
+ "Search terminated, no larger universe within the given limits.")
+ | SatSolver.UNKNOWN =>
+ (immediate_output " no model found.\n";
+ case next_universe universe sizes minsize maxsize of
+ SOME universe' => find_model_loop universe'
+ | NONE => writeln
+ "Search terminated, no larger universe within the given limits.")
+ ) handle SatSolver.NOT_CONFIGURED =>
+ error ("SAT solver " ^ quote satsolver ^ " is not configured.")
+ end handle MAXVARS_EXCEEDED =>
+ writeln ("\nSearch terminated, number of Boolean variables ("
+ ^ string_of_int maxvars ^ " allowed) exceeded.")
+ in
+ find_model_loop (first_universe types sizes minsize)
+ 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 *)
+ writeln ("Trying to find a model that "
+ ^ (if negate then "refutes" else "satisfies") ^ ": "
+ ^ Sign.string_of_term thy t);
+ if maxtime>0 then (
+ interrupt_timeout (Time.fromSeconds (Int.toLarge maxtime))
+ wrapper ()
+ handle Interrupt =>
+ writeln ("\nSearch terminated, time limit (" ^ string_of_int maxtime
+ ^ (if maxtime=1 then " second" else " seconds") ^ ") exceeded.")
+ ) else
+ wrapper ()
+ end;
(* ------------------------------------------------------------------------- *)
@@ -1269,10 +1269,10 @@
(* parameters *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * string) list -> Term.term -> unit *)
+ (* theory -> (string * string) list -> Term.term -> unit *)
- fun satisfy_term thy params t =
- find_model thy (actual_params thy params) t false;
+ fun satisfy_term thy params t =
+ find_model thy (actual_params thy params) t false;
(* ------------------------------------------------------------------------- *)
(* refute_term: calls 'find_model' to find a model that refutes 't' *)
@@ -1280,57 +1280,57 @@
(* parameters *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * string) list -> Term.term -> unit *)
+ (* theory -> (string * string) list -> Term.term -> unit *)
- fun refute_term thy params 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 _ = assert (null (term_tvars t))
- "Term to be refuted contains schematic type variables"
+ fun refute_term thy params 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_tvars t) orelse
+ error "Term to be refuted contains schematic type variables"
- (* existential closure over schematic variables *)
- (* (Term.indexname * Term.typ) list *)
- val vars = sort_wrt (fst o fst) (map dest_Var (term_vars t))
- (* Term.term *)
- val ex_closure = Library.foldl (fn (t', ((x, i), T)) =>
- (HOLogic.exists_const T) $
- Abs (x, T, abstract_over (Var ((x, i), T), t')))
- (t, vars)
- (* 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. *)
+ (* existential closure over schematic variables *)
+ (* (Term.indexname * Term.typ) list *)
+ val vars = sort_wrt (fst o fst) (map dest_Var (term_vars t))
+ (* Term.term *)
+ val ex_closure = Library.foldl (fn (t', ((x, i), T)) =>
+ (HOLogic.exists_const T) $
+ Abs (x, T, abstract_over (Var ((x, i), T), t')))
+ (t, vars)
+ (* 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 ("all", _) $ Abs (_, _, t)) = strip_all_body t
- | strip_all_body (Const ("Trueprop", _) $ t) = strip_all_body t
- | strip_all_body (Const ("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 ("all", _) $ Abs (a, T, t)) =
- (a, T) :: strip_all_vars t
- | strip_all_vars (Const ("Trueprop", _) $ t) =
- strip_all_vars t
- | strip_all_vars (Const ("All", _) $ Abs (a, T, t)) =
- (a, T) :: strip_all_vars t
- | strip_all_vars t =
- [] : (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 thy (actual_params thy params) subst_t true
- end;
+ (* 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 ("all", _) $ Abs (_, _, t)) = strip_all_body t
+ | strip_all_body (Const ("Trueprop", _) $ t) = strip_all_body t
+ | strip_all_body (Const ("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 ("all", _) $ Abs (a, T, t)) =
+ (a, T) :: strip_all_vars t
+ | strip_all_vars (Const ("Trueprop", _) $ t) =
+ strip_all_vars t
+ | strip_all_vars (Const ("All", _) $ Abs (a, T, t)) =
+ (a, T) :: strip_all_vars t
+ | strip_all_vars t =
+ [] : (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 thy (actual_params thy params) subst_t true
+ end;
(* ------------------------------------------------------------------------- *)
(* refute_subgoal: calls 'refute_term' on a specific subgoal *)
@@ -1339,10 +1339,10 @@
(* subgoal : 0-based index specifying the subgoal number *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (string * string) list -> Thm.thm -> int -> unit *)
+ (* theory -> (string * string) list -> Thm.thm -> int -> unit *)
- fun refute_subgoal thy params thm subgoal =
- refute_term thy params (List.nth (Thm.prems_of thm, subgoal));
+ fun refute_subgoal thy params thm subgoal =
+ refute_term thy params (List.nth (Thm.prems_of thm, subgoal));
(* ------------------------------------------------------------------------- *)
@@ -1355,71 +1355,71 @@
(* 'True'/'False' only (no Boolean variables) *)
(* ------------------------------------------------------------------------- *)
- (* interpretation -> interpretation list *)
+ (* interpretation -> interpretation list *)
- fun make_constants intr =
- 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 -> interpretation list *)
- fun unit_vectors_acc k vs =
- if k>n then [] else (unit_vector (k,n))::(unit_vectors_acc (k+1) vs)
- in
- unit_vectors_acc 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
- Library.foldl (fn (acc, x) => map (cons x) rec_pick @ acc) ([], xs)
- end
- in
- case intr of
- Leaf xs => unit_vectors (length xs)
- | Node xs => map (fn xs' => Node xs') (pick_all (length xs)
- (make_constants (hd xs)))
- end;
+ fun make_constants intr =
+ 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 -> interpretation list *)
+ fun unit_vectors_acc k vs =
+ if k>n then [] else (unit_vector (k,n))::(unit_vectors_acc (k+1) vs)
+ in
+ unit_vectors_acc 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
+ Library.foldl (fn (acc, x) => map (cons x) rec_pick @ acc) ([], xs)
+ end
+ in
+ case intr of
+ Leaf xs => unit_vectors (length xs)
+ | Node xs => map (fn xs' => Node xs') (pick_all (length xs)
+ (make_constants (hd xs)))
+ end;
(* ------------------------------------------------------------------------- *)
(* size_of_type: returns the number of constants in a type (i.e. 'length *)
(* (make_constants intr)', but implemented more efficiently) *)
(* ------------------------------------------------------------------------- *)
- (* interpretation -> int *)
+ (* interpretation -> int *)
- fun size_of_type intr =
- let
- (* power (a, b) computes a^b, for a>=0, b>=0 *)
- (* int * int -> int *)
- fun power (a, 0) = 1
- | power (a, 1) = a
- | power (a, b) = let val ab = power(a, b div 2) in
- ab * ab * power(a, b mod 2)
- end
- in
- case intr of
- Leaf xs => length xs
- | Node xs => power (size_of_type (hd xs), length xs)
- end;
+ fun size_of_type intr =
+ let
+ (* power (a, b) computes a^b, for a>=0, b>=0 *)
+ (* int * int -> int *)
+ fun power (a, 0) = 1
+ | power (a, 1) = a
+ | power (a, b) = let val ab = power(a, b div 2) in
+ ab * ab * power(a, b mod 2)
+ end
+ in
+ case intr of
+ Leaf xs => length xs
+ | Node xs => power (size_of_type (hd xs), length xs)
+ end;
(* ------------------------------------------------------------------------- *)
(* TT/FF: interpretations that denote "true" or "false", respectively *)
(* ------------------------------------------------------------------------- *)
- (* interpretation *)
+ (* interpretation *)
- val TT = Leaf [True, False];
+ val TT = Leaf [True, False];
- val FF = Leaf [False, True];
+ val FF = Leaf [False, True];
(* ------------------------------------------------------------------------- *)
(* make_equality: returns an interpretation that denotes (extensional) *)
@@ -1432,51 +1432,51 @@
(* '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. *)
+ (* 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 *)
+ (* 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 => PropLogic.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 => PropLogic.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 => PropLogic.all ((PropLogic.exists xs)
- :: (PropLogic.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 => PropLogic.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;
+ fun make_equality (i1, i2) =
+ let
+ (* interpretation * interpretation -> prop_formula *)
+ fun equal (i1, i2) =
+ (case i1 of
+ Leaf xs =>
+ (case i2 of
+ Leaf ys => PropLogic.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 => PropLogic.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 => PropLogic.all ((PropLogic.exists xs)
+ :: (PropLogic.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 => PropLogic.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) *)
@@ -1487,30 +1487,30 @@
(* to an undefined interpretation. *)
(* ------------------------------------------------------------------------- *)
- (* interpretation * interpretation -> 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 (PropLogic.dot_product (xs, ys),
- SAnd (PropLogic.all (map SNot xs), PropLogic.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 => PropLogic.all (map equal (xs ~~ ys))))
- (* interpretation *)
- val eq = equal (i1, i2)
- in
- Leaf [eq, SNot eq]
- end;
+ 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 (PropLogic.dot_product (xs, ys),
+ SAnd (PropLogic.all (map SNot xs), PropLogic.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 => PropLogic.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 *)
@@ -1518,86 +1518,86 @@
(* argument denoted by 'i2' *)
(* ------------------------------------------------------------------------- *)
- (* interpretation * interpretation -> interpretation *)
+ (* 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)")
- (* concatenates 'x' with every list in 'xss', returning a new list of *)
- (* lists *)
- (* 'a -> 'a list list -> 'a list list *)
- fun cons_list x xss =
- map (cons x) xss
- (* 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
- Library.foldl (fn (acc, x) => (cons_list x rec_pick) @ acc) ([], 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 PropLogic.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;
+ 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)")
+ (* concatenates 'x' with every list in 'xss', returning a new list of *)
+ (* lists *)
+ (* 'a -> 'a list list -> 'a list list *)
+ fun cons_list x xss =
+ map (cons x) xss
+ (* 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
+ Library.foldl (fn (acc, x) => (cons_list x rec_pick) @ acc) ([], 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 PropLogic.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 *)
+ (* 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
- foldr (fn (T, term) => Abs ("<eta_expand>", T, term))
- (Term.list_comb (t', map Bound (i-1 downto 0))) (List.take (Ts, i))
- end;
+ fun eta_expand t i =
+ let
+ val Ts = Term.binder_types (Term.fastype_of t)
+ val t' = Term.incr_boundvars i t
+ in
+ foldr (fn (T, term) => Abs ("<eta_expand>", T, term))
+ (Term.list_comb (t', map Bound (i-1 downto 0))) (List.take (Ts, i))
+ end;
(* ------------------------------------------------------------------------- *)
(* sum: returns the sum of a list 'xs' of integers *)
(* ------------------------------------------------------------------------- *)
- (* int list -> int *)
+ (* int list -> int *)
- fun sum xs = foldl op+ 0 xs;
+ fun sum xs = foldl op+ 0 xs;
(* ------------------------------------------------------------------------- *)
(* product: returns the product of a list 'xs' of integers *)
(* ------------------------------------------------------------------------- *)
- (* int list -> int *)
+ (* int list -> int *)
- fun product xs = foldl op* 1 xs;
+ fun product xs = foldl op* 1 xs;
(* ------------------------------------------------------------------------- *)
(* size_of_dtyp: the size of (an initial fragment of) an inductive data type *)
@@ -1605,1594 +1605,1594 @@
(* their arguments) of the size of the argument types *)
(* ------------------------------------------------------------------------- *)
- (* theory -> (Term.typ * int) list -> DatatypeAux.descr ->
- (DatatypeAux.dtyp * Term.typ) list ->
- (string * DatatypeAux.dtyp list) list -> int *)
+ (* theory -> (Term.typ * int) list -> DatatypeAux.descr ->
+ (DatatypeAux.dtyp * Term.typ) list ->
+ (string * DatatypeAux.dtyp list) list -> int *)
- fun size_of_dtyp thy typ_sizes descr typ_assoc constructors =
- sum (map (fn (_, dtyps) =>
- product (map (fn dtyp =>
- let
- val T = typ_of_dtyp descr typ_assoc dtyp
- val (i, _, _) = interpret thy (typ_sizes, [])
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- in
- size_of_type i
- end) dtyps)) constructors);
+ fun size_of_dtyp thy typ_sizes descr typ_assoc constructors =
+ sum (map (fn (_, dtyps) =>
+ product (map (fn dtyp =>
+ let
+ val T = typ_of_dtyp descr typ_assoc dtyp
+ val (i, _, _) = interpret thy (typ_sizes, [])
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ in
+ size_of_type i
+ end) dtyps)) constructors);
(* ------------------------------------------------------------------------- *)
(* INTERPRETERS: Actual Interpreters *)
(* ------------------------------------------------------------------------- *)
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* simply typed lambda calculus: Isabelle's basic term syntax, with type *)
- (* variables, function types, and propT *)
+ (* simply typed lambda calculus: Isabelle's basic term syntax, with type *)
+ (* variables, function types, and propT *)
- fun stlc_interpreter thy 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 lookup 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 (PropLogic.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 (interpret (... T1))' different copies *)
- (* of the interpretation for 'T2', which are then combined into a *)
- (* single new interpretation *)
- val (i1, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T1))
- (* 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 thy (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 i1)
- (* 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 (List.nth (#bounds args, i), model, args)
- | Abs (x, T, body) =>
- let
- (* create all constants of type 'T' *)
- val (i, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
- val constants = make_constants i
- (* interpret the 'body' separately for each constant *)
- val ((model', args'), bodies) = foldl_map
- (fn ((m, a), c) =>
- let
- (* add 'c' to 'bounds' *)
- val (i', m', a') = interpret thy 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' *)
- ((m', {maxvars = maxvars, def_eq = def_eq,
- next_idx = #next_idx a', bounds = bounds,
- wellformed = #wellformed a'}), i')
- end)
- ((model, args), constants)
- in
- SOME (Node bodies, model', args')
- end
- | t1 $ t2 =>
- let
- (* interpret 't1' and 't2' separately *)
- val (intr1, model1, args1) = interpret thy model args t1
- val (intr2, model2, args2) = interpret thy model1 args1 t2
- in
- SOME (interpretation_apply (intr1, intr2), model2, args2)
- end)
- end;
+ fun stlc_interpreter thy 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 lookup 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 (PropLogic.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 (interpret (... T1))' different copies *)
+ (* of the interpretation for 'T2', which are then combined into a *)
+ (* single new interpretation *)
+ val (i1, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T1))
+ (* 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 thy (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 i1)
+ (* 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 (List.nth (#bounds args, i), model, args)
+ | Abs (x, T, body) =>
+ let
+ (* create all constants of type 'T' *)
+ val (i, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
+ val constants = make_constants i
+ (* interpret the 'body' separately for each constant *)
+ val ((model', args'), bodies) = foldl_map
+ (fn ((m, a), c) =>
+ let
+ (* add 'c' to 'bounds' *)
+ val (i', m', a') = interpret thy 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' *)
+ ((m', {maxvars = maxvars, def_eq = def_eq,
+ next_idx = #next_idx a', bounds = bounds,
+ wellformed = #wellformed a'}), i')
+ end)
+ ((model, args), constants)
+ in
+ SOME (Node bodies, model', args')
+ end
+ | t1 $ t2 =>
+ let
+ (* interpret 't1' and 't2' separately *)
+ val (intr1, model1, args1) = interpret thy model args t1
+ val (intr2, model2, args2) = interpret thy model1 args1 t2
+ in
+ SOME (interpretation_apply (intr1, intr2), model2, args2)
+ end)
+ end;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- fun Pure_interpreter thy model args t =
- case t of
- Const ("all", _) $ t1 =>
- let
- val (i, m, a) = interpret thy model args t1
- in
- case i of
- Node xs =>
- (* 3-valued logic *)
- let
- val fmTrue = PropLogic.all (map toTrue xs)
- val fmFalse = PropLogic.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 ("all", _) =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("==", _) $ t1 $ t2 =>
- let
- val (i1, m1, a1) = interpret thy model args t1
- val (i2, m2, a2) = interpret thy 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 ("==", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("==", _) =>
- SOME (interpret thy model args (eta_expand t 2))
- | Const ("==>", _) $ t1 $ t2 =>
- (* 3-valued logic *)
- let
- val (i1, m1, a1) = interpret thy model args t1
- val (i2, m2, a2) = interpret thy m1 a1 t2
- val fmTrue = PropLogic.SOr (toFalse i1, toTrue i2)
- val fmFalse = PropLogic.SAnd (toTrue i1, toFalse i2)
- in
- SOME (Leaf [fmTrue, fmFalse], m2, a2)
- end
- | Const ("==>", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("==>", _) =>
- SOME (interpret thy model args (eta_expand t 2))
- | _ => NONE;
+ fun Pure_interpreter thy model args t =
+ case t of
+ Const ("all", _) $ t1 =>
+ let
+ val (i, m, a) = interpret thy model args t1
+ in
+ case i of
+ Node xs =>
+ (* 3-valued logic *)
+ let
+ val fmTrue = PropLogic.all (map toTrue xs)
+ val fmFalse = PropLogic.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 ("all", _) =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("==", _) $ t1 $ t2 =>
+ let
+ val (i1, m1, a1) = interpret thy model args t1
+ val (i2, m2, a2) = interpret thy 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 ("==", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("==", _) =>
+ SOME (interpret thy model args (eta_expand t 2))
+ | Const ("==>", _) $ t1 $ t2 =>
+ (* 3-valued logic *)
+ let
+ val (i1, m1, a1) = interpret thy model args t1
+ val (i2, m2, a2) = interpret thy m1 a1 t2
+ val fmTrue = PropLogic.SOr (toFalse i1, toTrue i2)
+ val fmFalse = PropLogic.SAnd (toTrue i1, toFalse i2)
+ in
+ SOME (Leaf [fmTrue, fmFalse], m2, a2)
+ end
+ | Const ("==>", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("==>", _) =>
+ SOME (interpret thy model args (eta_expand t 2))
+ | _ => NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- fun HOLogic_interpreter thy 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 ("Trueprop", _) =>
- SOME (Node [TT, FF], model, args)
- | Const ("Not", _) =>
- SOME (Node [FF, TT], model, args)
- (* redundant, since 'True' is also an IDT constructor *)
- | Const ("True", _) =>
- SOME (TT, model, args)
- (* redundant, since 'False' is also an IDT constructor *)
- | Const ("False", _) =>
- SOME (FF, model, args)
- | Const ("All", _) $ t1 => (* similar to "all" (Pure) *)
- let
- val (i, m, a) = interpret thy model args t1
- in
- case i of
- Node xs =>
- (* 3-valued logic *)
- let
- val fmTrue = PropLogic.all (map toTrue xs)
- val fmFalse = PropLogic.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 ("All", _) =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("Ex", _) $ t1 =>
- let
- val (i, m, a) = interpret thy model args t1
- in
- case i of
- Node xs =>
- (* 3-valued logic *)
- let
- val fmTrue = PropLogic.exists (map toTrue xs)
- val fmFalse = PropLogic.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 ("Ex", _) =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("op =", _) $ t1 $ t2 => (* similar to "==" (Pure) *)
- let
- val (i1, m1, a1) = interpret thy model args t1
- val (i2, m2, a2) = interpret thy m1 a1 t2
- in
- SOME (make_equality (i1, i2), m2, a2)
- end
- | Const ("op =", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("op =", _) =>
- SOME (interpret thy model args (eta_expand t 2))
- | Const ("op &", _) $ t1 $ t2 =>
- (* 3-valued logic *)
- let
- val (i1, m1, a1) = interpret thy model args t1
- val (i2, m2, a2) = interpret thy m1 a1 t2
- val fmTrue = PropLogic.SAnd (toTrue i1, toTrue i2)
- val fmFalse = PropLogic.SOr (toFalse i1, toFalse i2)
- in
- SOME (Leaf [fmTrue, fmFalse], m2, a2)
- end
- | Const ("op &", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("op &", _) =>
- SOME (interpret thy 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 ("op |", _) $ t1 $ t2 =>
- (* 3-valued logic *)
- let
- val (i1, m1, a1) = interpret thy model args t1
- val (i2, m2, a2) = interpret thy m1 a1 t2
- val fmTrue = PropLogic.SOr (toTrue i1, toTrue i2)
- val fmFalse = PropLogic.SAnd (toFalse i1, toFalse i2)
- in
- SOME (Leaf [fmTrue, fmFalse], m2, a2)
- end
- | Const ("op |", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("op |", _) =>
- SOME (interpret thy 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 ("op -->", _) $ t1 $ t2 => (* similar to "==>" (Pure) *)
- (* 3-valued logic *)
- let
- val (i1, m1, a1) = interpret thy model args t1
- val (i2, m2, a2) = interpret thy m1 a1 t2
- val fmTrue = PropLogic.SOr (toFalse i1, toTrue i2)
- val fmFalse = PropLogic.SAnd (toTrue i1, toFalse i2)
- in
- SOME (Leaf [fmTrue, fmFalse], m2, a2)
- end
- | Const ("op -->", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("op -->", _) =>
- SOME (interpret thy 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;
+ fun HOLogic_interpreter thy 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 ("Trueprop", _) =>
+ SOME (Node [TT, FF], model, args)
+ | Const ("Not", _) =>
+ SOME (Node [FF, TT], model, args)
+ (* redundant, since 'True' is also an IDT constructor *)
+ | Const ("True", _) =>
+ SOME (TT, model, args)
+ (* redundant, since 'False' is also an IDT constructor *)
+ | Const ("False", _) =>
+ SOME (FF, model, args)
+ | Const ("All", _) $ t1 => (* similar to "all" (Pure) *)
+ let
+ val (i, m, a) = interpret thy model args t1
+ in
+ case i of
+ Node xs =>
+ (* 3-valued logic *)
+ let
+ val fmTrue = PropLogic.all (map toTrue xs)
+ val fmFalse = PropLogic.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 ("All", _) =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("Ex", _) $ t1 =>
+ let
+ val (i, m, a) = interpret thy model args t1
+ in
+ case i of
+ Node xs =>
+ (* 3-valued logic *)
+ let
+ val fmTrue = PropLogic.exists (map toTrue xs)
+ val fmFalse = PropLogic.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 ("Ex", _) =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("op =", _) $ t1 $ t2 => (* similar to "==" (Pure) *)
+ let
+ val (i1, m1, a1) = interpret thy model args t1
+ val (i2, m2, a2) = interpret thy m1 a1 t2
+ in
+ SOME (make_equality (i1, i2), m2, a2)
+ end
+ | Const ("op =", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("op =", _) =>
+ SOME (interpret thy model args (eta_expand t 2))
+ | Const ("op &", _) $ t1 $ t2 =>
+ (* 3-valued logic *)
+ let
+ val (i1, m1, a1) = interpret thy model args t1
+ val (i2, m2, a2) = interpret thy m1 a1 t2
+ val fmTrue = PropLogic.SAnd (toTrue i1, toTrue i2)
+ val fmFalse = PropLogic.SOr (toFalse i1, toFalse i2)
+ in
+ SOME (Leaf [fmTrue, fmFalse], m2, a2)
+ end
+ | Const ("op &", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("op &", _) =>
+ SOME (interpret thy 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 ("op |", _) $ t1 $ t2 =>
+ (* 3-valued logic *)
+ let
+ val (i1, m1, a1) = interpret thy model args t1
+ val (i2, m2, a2) = interpret thy m1 a1 t2
+ val fmTrue = PropLogic.SOr (toTrue i1, toTrue i2)
+ val fmFalse = PropLogic.SAnd (toFalse i1, toFalse i2)
+ in
+ SOME (Leaf [fmTrue, fmFalse], m2, a2)
+ end
+ | Const ("op |", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("op |", _) =>
+ SOME (interpret thy 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 ("op -->", _) $ t1 $ t2 => (* similar to "==>" (Pure) *)
+ (* 3-valued logic *)
+ let
+ val (i1, m1, a1) = interpret thy model args t1
+ val (i2, m2, a2) = interpret thy m1 a1 t2
+ val fmTrue = PropLogic.SOr (toFalse i1, toTrue i2)
+ val fmFalse = PropLogic.SAnd (toTrue i1, toFalse i2)
+ in
+ SOME (Leaf [fmTrue, fmFalse], m2, a2)
+ end
+ | Const ("op -->", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("op -->", _) =>
+ SOME (interpret thy 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;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- fun set_interpreter thy model args t =
- (* "T set" is isomorphic to "T --> bool" *)
- 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 ("set", [T])) =>
- let
- val (intr, _, args') =
- interpret thy (typs, []) args (Free (x, T --> HOLogic.boolT))
- in
- SOME (intr, (typs, (t, intr)::terms), args')
- end
- | Var ((x, i), Type ("set", [T])) =>
- let
- val (intr, _, args') =
- interpret thy (typs, []) args (Var ((x,i), T --> HOLogic.boolT))
- in
- SOME (intr, (typs, (t, intr)::terms), args')
- end
- | Const (s, Type ("set", [T])) =>
- let
- val (intr, _, args') =
- interpret thy (typs, []) args (Const (s, T --> HOLogic.boolT))
- in
- SOME (intr, (typs, (t, intr)::terms), args')
- end
- (* 'Collect' == identity *)
- | Const ("Collect", _) $ t1 =>
- SOME (interpret thy model args t1)
- | Const ("Collect", _) =>
- SOME (interpret thy model args (eta_expand t 1))
- (* 'op :' == application *)
- | Const ("op :", _) $ t1 $ t2 =>
- SOME (interpret thy model args (t2 $ t1))
- | Const ("op :", _) $ t1 =>
- SOME (interpret thy model args (eta_expand t 1))
- | Const ("op :", _) =>
- SOME (interpret thy model args (eta_expand t 2))
- | _ => NONE)
- end;
+ fun set_interpreter thy model args t =
+ (* "T set" is isomorphic to "T --> bool" *)
+ 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 ("set", [T])) =>
+ let
+ val (intr, _, args') =
+ interpret thy (typs, []) args (Free (x, T --> HOLogic.boolT))
+ in
+ SOME (intr, (typs, (t, intr)::terms), args')
+ end
+ | Var ((x, i), Type ("set", [T])) =>
+ let
+ val (intr, _, args') =
+ interpret thy (typs, []) args (Var ((x,i), T --> HOLogic.boolT))
+ in
+ SOME (intr, (typs, (t, intr)::terms), args')
+ end
+ | Const (s, Type ("set", [T])) =>
+ let
+ val (intr, _, args') =
+ interpret thy (typs, []) args (Const (s, T --> HOLogic.boolT))
+ in
+ SOME (intr, (typs, (t, intr)::terms), args')
+ end
+ (* 'Collect' == identity *)
+ | Const ("Collect", _) $ t1 =>
+ SOME (interpret thy model args t1)
+ | Const ("Collect", _) =>
+ SOME (interpret thy model args (eta_expand t 1))
+ (* 'op :' == application *)
+ | Const ("op :", _) $ t1 $ t2 =>
+ SOME (interpret thy model args (t2 $ t1))
+ | Const ("op :", _) $ t1 =>
+ SOME (interpret thy model args (eta_expand t 1))
+ | Const ("op :", _) =>
+ SOME (interpret thy model args (eta_expand t 2))
+ | _ => NONE)
+ end;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* interprets variables and constants whose type is an IDT; *)
- (* constructors of IDTs however are properly interpreted by *)
- (* 'IDT_constructor_interpreter' *)
+ (* interprets variables and constants whose type is an IDT; *)
+ (* constructors of IDTs however are properly interpreted by *)
+ (* 'IDT_constructor_interpreter' *)
- fun IDT_interpreter thy model args t =
- let
- val (typs, terms) = model
- (* Term.typ -> (interpretation * model * arguments) option *)
- fun interpret_term (Type (s, Ts)) =
- (case DatatypePackage.get_datatype 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))
- 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) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
- then
- raise REFUTE ("IDT_interpreter",
- "datatype argument (for type "
- ^ Sign.string_of_typ thy (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 thy 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 (PropLogic.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;
+ fun IDT_interpreter thy model args t =
+ let
+ val (typs, terms) = model
+ (* Term.typ -> (interpretation * model * arguments) option *)
+ fun interpret_term (Type (s, Ts)) =
+ (case DatatypePackage.get_datatype 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))
+ 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) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
+ then
+ raise REFUTE ("IDT_interpreter",
+ "datatype argument (for type "
+ ^ Sign.string_of_typ thy (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 thy 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 (PropLogic.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;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- fun IDT_constructor_interpreter thy 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
- Const (s, T) =>
- (case body_type T of
- Type (s', Ts') =>
- (case DatatypePackage.get_datatype thy s' of
- SOME info => (* body type is an inductive datatype *)
- let
- val index = #index info
- val descr = #descr info
- val (_, dtyps, constrs) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
- then
- raise REFUTE ("IDT_constructor_interpreter",
- "datatype argument (for type "
- ^ Sign.string_of_typ thy (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)::cs =>
- let
- (* compute the total size of the datatype (with the *)
- (* current depth) *)
- val (i, _, _) = interpret thy (typs, []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type (s', Ts')))
- val total = size_of_type i
- (* int option -- only /recursive/ IDTs have an associated *)
- (* depth *)
- val depth = AList.lookup (op =) typs (Type (s', Ts'))
- val typs' = (case depth of NONE => typs | SOME n =>
- AList.update (op =) (Type (s', Ts'), n-1) typs)
- (* returns an interpretation where everything is mapped to *)
- (* "undefined" *)
- (* DatatypeAux.dtyp list -> interpretation *)
- fun make_undef [] =
- Leaf (replicate total False)
- | make_undef (d::ds) =
- let
- (* compute the current size of the type 'd' *)
- val T = typ_of_dtyp descr typ_assoc d
- val (i, _, _) = interpret thy (typs, []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size = size_of_type i
- in
- Node (replicate size (make_undef ds))
- end
- (* returns the interpretation for a constructor at depth 1 *)
- (* int * DatatypeAux.dtyp list -> int * interpretation *)
- fun make_constr (offset, []) =
- if offset<total then
- (offset+1, Leaf ((replicate offset False) @ True ::
- (replicate (total-offset-1) False)))
- else
- raise REFUTE ("IDT_constructor_interpreter",
- "offset >= total")
- | make_constr (offset, d::ds) =
- let
- (* compute the current and the old size of the type 'd' *)
- val T = typ_of_dtyp descr typ_assoc d
- val (i, _, _) = interpret thy (typs, []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size = size_of_type i
- val (i', _, _) = interpret thy (typs', []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size' = size_of_type i'
- (* sanity check *)
- val _ = if size < size' then
- raise REFUTE ("IDT_constructor_interpreter",
- "current size is less than old size")
- else ()
- (* int * interpretation list *)
- val (new_offset, intrs) = foldl_map make_constr
- (offset, replicate size' ds)
- (* interpretation list *)
- val undefs = replicate (size - size') (make_undef ds)
- in
- (* elements that exist at the previous depth are *)
- (* mapped to a defined value, while new elements are *)
- (* mapped to "undefined" by the recursive constructor *)
- (new_offset, Node (intrs @ undefs))
- end
- (* extends the interpretation for a constructor (both *)
- (* recursive and non-recursive) obtained at depth n (n>=1) *)
- (* to depth n+1 *)
- (* int * DatatypeAux.dtyp list * interpretation
- -> int * interpretation *)
- fun extend_constr (offset, [], Leaf xs) =
- 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 *)
- val k = find_index_eq True xs
- in
- if k=(~1) then
- (* if the element was mapped to "undefined" before, *)
- (* map it to the value given by 'offset' now (and *)
- (* extend the length of the leaf) *)
- (offset+1, unit_vector (offset+1, total))
- else
- (* if the element was already mapped to a defined *)
- (* value, map it to the same value again, just *)
- (* extend the length of the leaf, do not increment *)
- (* the 'offset' *)
- (offset, unit_vector (k+1, total))
- end
- | extend_constr (_, [], Node _) =
- raise REFUTE ("IDT_constructor_interpreter",
- "interpretation for constructor (with no arguments left)"
- ^ " is a node")
- | extend_constr (offset, d::ds, Node xs) =
- let
- (* compute the size of the type 'd' *)
- val T = typ_of_dtyp descr typ_assoc d
- val (i, _, _) = interpret thy (typs, []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size = size_of_type i
- (* sanity check *)
- val _ = if size < length xs then
- raise REFUTE ("IDT_constructor_interpreter",
- "new size of type is less than old size")
- else ()
- (* extend the existing interpretations *)
- (* int * interpretation list *)
- val (new_offset, intrs) = foldl_map (fn (off, i) =>
- extend_constr (off, ds, i)) (offset, xs)
- (* new elements of the type 'd' are mapped to *)
- (* "undefined" *)
- val undefs = replicate (size - length xs) (make_undef ds)
- in
- (new_offset, Node (intrs @ undefs))
- end
- | extend_constr (_, d::ds, Leaf _) =
- raise REFUTE ("IDT_constructor_interpreter",
- "interpretation for constructor (with arguments left)"
- ^ " is a leaf")
- (* returns 'true' iff the constructor has a recursive *)
- (* argument *)
- (* DatatypeAux.dtyp list -> bool *)
- fun is_rec_constr ds =
- Library.exists DatatypeAux.is_rec_type ds
- (* constructors before 'Const (s, T)' generate elements of *)
- (* the datatype *)
- val offset = size_of_dtyp thy typs' descr typ_assoc constrs1
- in
- case depth of
- NONE => (* equivalent to a depth of 1 *)
- SOME (snd (make_constr (offset, ctypes)), model, args)
- | SOME 0 =>
- raise REFUTE ("IDT_constructor_interpreter", "depth is 0")
- | SOME 1 =>
- SOME (snd (make_constr (offset, ctypes)), model, args)
- | SOME n => (* n > 1 *)
- let
- (* interpret the constructor at depth-1 *)
- val (iC, _, _) = interpret thy (typs', []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Const (s, T))
- (* elements generated by the constructor at depth-1 *)
- (* must be added to 'offset' *)
- (* interpretation -> int *)
- fun number_of_defined_elements (Leaf xs) =
- if find_index_eq True xs = (~1) then 0 else 1
- | number_of_defined_elements (Node xs) =
- sum (map number_of_defined_elements xs)
- (* int *)
- val offset' = offset + number_of_defined_elements iC
- in
- SOME (snd (extend_constr (offset', ctypes, iC)), model,
- args)
- end
- 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;
+ fun IDT_constructor_interpreter thy 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
+ Const (s, T) =>
+ (case body_type T of
+ Type (s', Ts') =>
+ (case DatatypePackage.get_datatype thy s' of
+ SOME info => (* body type is an inductive datatype *)
+ let
+ val index = #index info
+ val descr = #descr info
+ val (_, dtyps, constrs) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
+ then
+ raise REFUTE ("IDT_constructor_interpreter",
+ "datatype argument (for type "
+ ^ Sign.string_of_typ thy (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)::cs =>
+ let
+ (* compute the total size of the datatype (with the *)
+ (* current depth) *)
+ val (i, _, _) = interpret thy (typs, []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type (s', Ts')))
+ val total = size_of_type i
+ (* int option -- only /recursive/ IDTs have an associated *)
+ (* depth *)
+ val depth = AList.lookup (op =) typs (Type (s', Ts'))
+ val typs' = (case depth of NONE => typs | SOME n =>
+ AList.update (op =) (Type (s', Ts'), n-1) typs)
+ (* returns an interpretation where everything is mapped to *)
+ (* "undefined" *)
+ (* DatatypeAux.dtyp list -> interpretation *)
+ fun make_undef [] =
+ Leaf (replicate total False)
+ | make_undef (d::ds) =
+ let
+ (* compute the current size of the type 'd' *)
+ val T = typ_of_dtyp descr typ_assoc d
+ val (i, _, _) = interpret thy (typs, []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size = size_of_type i
+ in
+ Node (replicate size (make_undef ds))
+ end
+ (* returns the interpretation for a constructor at depth 1 *)
+ (* int * DatatypeAux.dtyp list -> int * interpretation *)
+ fun make_constr (offset, []) =
+ if offset<total then
+ (offset+1, Leaf ((replicate offset False) @ True ::
+ (replicate (total-offset-1) False)))
+ else
+ raise REFUTE ("IDT_constructor_interpreter",
+ "offset >= total")
+ | make_constr (offset, d::ds) =
+ let
+ (* compute the current and the old size of the type 'd' *)
+ val T = typ_of_dtyp descr typ_assoc d
+ val (i, _, _) = interpret thy (typs, []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size = size_of_type i
+ val (i', _, _) = interpret thy (typs', []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size' = size_of_type i'
+ (* sanity check *)
+ val _ = if size < size' then
+ raise REFUTE ("IDT_constructor_interpreter",
+ "current size is less than old size")
+ else ()
+ (* int * interpretation list *)
+ val (new_offset, intrs) = foldl_map make_constr
+ (offset, replicate size' ds)
+ (* interpretation list *)
+ val undefs = replicate (size - size') (make_undef ds)
+ in
+ (* elements that exist at the previous depth are *)
+ (* mapped to a defined value, while new elements are *)
+ (* mapped to "undefined" by the recursive constructor *)
+ (new_offset, Node (intrs @ undefs))
+ end
+ (* extends the interpretation for a constructor (both *)
+ (* recursive and non-recursive) obtained at depth n (n>=1) *)
+ (* to depth n+1 *)
+ (* int * DatatypeAux.dtyp list * interpretation
+ -> int * interpretation *)
+ fun extend_constr (offset, [], Leaf xs) =
+ 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 *)
+ val k = find_index_eq True xs
+ in
+ if k=(~1) then
+ (* if the element was mapped to "undefined" before, *)
+ (* map it to the value given by 'offset' now (and *)
+ (* extend the length of the leaf) *)
+ (offset+1, unit_vector (offset+1, total))
+ else
+ (* if the element was already mapped to a defined *)
+ (* value, map it to the same value again, just *)
+ (* extend the length of the leaf, do not increment *)
+ (* the 'offset' *)
+ (offset, unit_vector (k+1, total))
+ end
+ | extend_constr (_, [], Node _) =
+ raise REFUTE ("IDT_constructor_interpreter",
+ "interpretation for constructor (with no arguments left)"
+ ^ " is a node")
+ | extend_constr (offset, d::ds, Node xs) =
+ let
+ (* compute the size of the type 'd' *)
+ val T = typ_of_dtyp descr typ_assoc d
+ val (i, _, _) = interpret thy (typs, []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size = size_of_type i
+ (* sanity check *)
+ val _ = if size < length xs then
+ raise REFUTE ("IDT_constructor_interpreter",
+ "new size of type is less than old size")
+ else ()
+ (* extend the existing interpretations *)
+ (* int * interpretation list *)
+ val (new_offset, intrs) = foldl_map (fn (off, i) =>
+ extend_constr (off, ds, i)) (offset, xs)
+ (* new elements of the type 'd' are mapped to *)
+ (* "undefined" *)
+ val undefs = replicate (size - length xs) (make_undef ds)
+ in
+ (new_offset, Node (intrs @ undefs))
+ end
+ | extend_constr (_, d::ds, Leaf _) =
+ raise REFUTE ("IDT_constructor_interpreter",
+ "interpretation for constructor (with arguments left)"
+ ^ " is a leaf")
+ (* returns 'true' iff the constructor has a recursive *)
+ (* argument *)
+ (* DatatypeAux.dtyp list -> bool *)
+ fun is_rec_constr ds =
+ Library.exists DatatypeAux.is_rec_type ds
+ (* constructors before 'Const (s, T)' generate elements of *)
+ (* the datatype *)
+ val offset = size_of_dtyp thy typs' descr typ_assoc constrs1
+ in
+ case depth of
+ NONE => (* equivalent to a depth of 1 *)
+ SOME (snd (make_constr (offset, ctypes)), model, args)
+ | SOME 0 =>
+ raise REFUTE ("IDT_constructor_interpreter", "depth is 0")
+ | SOME 1 =>
+ SOME (snd (make_constr (offset, ctypes)), model, args)
+ | SOME n => (* n > 1 *)
+ let
+ (* interpret the constructor at depth-1 *)
+ val (iC, _, _) = interpret thy (typs', []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Const (s, T))
+ (* elements generated by the constructor at depth-1 *)
+ (* must be added to 'offset' *)
+ (* interpretation -> int *)
+ fun number_of_defined_elements (Leaf xs) =
+ if find_index_eq True xs = (~1) then 0 else 1
+ | number_of_defined_elements (Node xs) =
+ sum (map number_of_defined_elements xs)
+ (* int *)
+ val offset' = offset + number_of_defined_elements iC
+ in
+ SOME (snd (extend_constr (offset', ctypes, iC)), model,
+ args)
+ end
+ 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;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* 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. *)
+ (* 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 thy model args t =
- (* 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 the datatype given by *)
- (* 'info', or of a mutually recursive datatype *)
- let
- val index = #index info
- val descr = #descr info
- val (dtname, dtyps, _) = lookup descr index
- (* number of all constructors, including those of different *)
- (* (mutually recursive) datatypes within the same descriptor *)
- (* 'descr' *)
- val mconstrs_count = sum (map (fn (_, (_, _, cs)) => length cs)
- descr)
- val params_count = length params
- (* the type of a recursion operator: *)
- (* [T1, ..., Tn, IDT] ---> Tresult *)
- val IDT = List.nth (binder_types T, mconstrs_count)
- in
- if (fst o dest_Type) IDT <> dtname then
- (* recursion operator of a mutually recursive datatype *)
- NONE
- else if mconstrs_count < params_count then
- (* too many actual parameters; for now we'll use the *)
- (* 'stlc_interpreter' to strip off one application *)
- NONE
- else if mconstrs_count > params_count 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 thy model args (eta_expand t
- (mconstrs_count - params_count)))
- else (* mconstrs_count = params_count *)
- let
- (* interpret each parameter separately *)
- val ((model', args'), p_intrs) = foldl_map (fn ((m, a), p) =>
- let
- val (i, m', a') = interpret thy m a p
- in
- ((m', a'), i)
- end) ((model, args), params)
- val (typs, _) = model'
- val typ_assoc = dtyps ~~ (snd o dest_Type) IDT
- (* 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
- (DatatypeAux.DtRec idx)
- in
- (idx, map (fn (cname, cargs) =>
- (#1 o interpret thy (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
- (* the recursion operator is a function that maps every *)
- (* element of the inductive datatype (and of mutually *)
- (* recursive types) to an element of some result type; an *)
- (* array entry of NONE means that the actual result has *)
- (* not been computed yet *)
- (* (int * interpretation option Array.array) list *)
- val INTRS = map (fn (idx, _) =>
- let
- val T = typ_of_dtyp descr typ_assoc
- (DatatypeAux.DtRec idx)
- val (i, _, _) = interpret thy (typs, []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size = size_of_type i
- in
- (idx, Array.array (size, NONE))
- end) descr
- (* 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_eq True xs = elem then
- SOME []
- else
- NONE
- | get_args (Node xs) elem =
- let
- (* interpretation * 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 element "
- ^ string_of_int elem ^ " in datatype "
- ^ Sign.string_of_typ thy IDT ^ " (datatype index "
- ^ string_of_int idx ^ ")")
- | 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, lookup mc_intrs idx)
- end
- (* returns the number of constructors in datatypes that *)
- (* occur in the descriptor 'descr' before the datatype *)
- (* given by 'idx' *)
- fun get_coffset idx =
- let
- fun get_coffset_acc _ [] =
- raise REFUTE ("IDT_recursion_interpreter", "index "
- ^ string_of_int idx ^ " not found in descriptor")
- | get_coffset_acc sum ((i, (_, _, cs))::descr') =
- if i=idx then
- sum
- else
- get_coffset_acc (sum + length cs) descr'
- in
- get_coffset_acc 0 descr
- end
- (* computes one entry in INTRS, 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 =
- case Array.sub (lookup INTRS idx, elem) of
- SOME result =>
- (* simply return the previously computed result *)
- result
- | NONE =>
- let
- (* int * int list *)
- val (c, args) = get_cargs idx elem
- (* interpretation * int list -> interpretation *)
- fun select_subtree (tr, []) =
- tr (* return the whole tree *)
- | select_subtree (Leaf _, _) =
- raise REFUTE ("IDT_recursion_interpreter",
- "interpretation for parameter is a leaf; "
- ^ "cannot select a subtree")
- | select_subtree (Node tr, x::xs) =
- select_subtree (List.nth (tr, x), xs)
- (* select the correct subtree of the parameter *)
- (* corresponding to constructor 'c' *)
- val p_intr = select_subtree (List.nth
- (p_intrs, get_coffset idx + c), args)
- (* find the indices of the constructor's recursive *)
- (* arguments *)
- val (_, _, constrs) = lookup descr idx
- val constr_args = (snd o List.nth) (constrs, c)
- val rec_args = List.filter
- (DatatypeAux.is_rec_type o fst) (constr_args ~~ args)
- val rec_args' = map (fn (dtyp, elem) =>
- (DatatypeAux.dest_DtRec dtyp, elem)) rec_args
- (* apply 'p_intr' to recursively computed results *)
- val result = foldl (fn ((idx, elem), intr) =>
- interpretation_apply (intr,
- compute_array_entry idx elem)) p_intr rec_args'
- (* update 'INTRS' *)
- val _ = Array.update (lookup INTRS idx, elem,
- SOME result)
- in
- result
- end
- (* compute all entries in INTRS for the current datatype *)
- (* (given by 'index') *)
- (* TODO: we can use Array.modifyi instead once PolyML's *)
- (* Array signature conforms to the ML standard *)
- (* (int * 'a -> 'a) -> 'a array -> unit *)
- fun modifyi f arr =
- let
- val size = Array.length arr
- fun modifyi_loop i =
- if i < size then (
- Array.update (arr, i, f (i, Array.sub (arr, i)));
- modifyi_loop (i+1)
- ) else
- ()
- in
- modifyi_loop 0
- end
- val _ = modifyi (fn (i, _) =>
- SOME (compute_array_entry index i)) (lookup INTRS index)
- (* 'a Array.array -> 'a list *)
- fun toList arr =
- Array.foldr op:: [] arr
- in
- (* return the part of 'INTRS' that corresponds to the *)
- (* current datatype *)
- SOME ((Node o map Option.valOf o toList o lookup INTRS)
- index, model', args')
- end
- end
- else
- NONE (* not a recursion operator of this datatype *)
- ) (DatatypePackage.get_datatypes thy) NONE
- | _ => (* head of term is not a constant *)
- NONE;
+ fun IDT_recursion_interpreter thy model args t =
+ (* 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 the datatype given by *)
+ (* 'info', or of a mutually recursive datatype *)
+ let
+ val index = #index info
+ val descr = #descr info
+ val (dtname, dtyps, _) = lookup descr index
+ (* number of all constructors, including those of different *)
+ (* (mutually recursive) datatypes within the same descriptor *)
+ (* 'descr' *)
+ val mconstrs_count = sum (map (fn (_, (_, _, cs)) => length cs)
+ descr)
+ val params_count = length params
+ (* the type of a recursion operator: *)
+ (* [T1, ..., Tn, IDT] ---> Tresult *)
+ val IDT = List.nth (binder_types T, mconstrs_count)
+ in
+ if (fst o dest_Type) IDT <> dtname then
+ (* recursion operator of a mutually recursive datatype *)
+ NONE
+ else if mconstrs_count < params_count then
+ (* too many actual parameters; for now we'll use the *)
+ (* 'stlc_interpreter' to strip off one application *)
+ NONE
+ else if mconstrs_count > params_count 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 thy model args (eta_expand t
+ (mconstrs_count - params_count)))
+ else (* mconstrs_count = params_count *)
+ let
+ (* interpret each parameter separately *)
+ val ((model', args'), p_intrs) = foldl_map (fn ((m, a), p) =>
+ let
+ val (i, m', a') = interpret thy m a p
+ in
+ ((m', a'), i)
+ end) ((model, args), params)
+ val (typs, _) = model'
+ val typ_assoc = dtyps ~~ (snd o dest_Type) IDT
+ (* 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
+ (DatatypeAux.DtRec idx)
+ in
+ (idx, map (fn (cname, cargs) =>
+ (#1 o interpret thy (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
+ (* the recursion operator is a function that maps every *)
+ (* element of the inductive datatype (and of mutually *)
+ (* recursive types) to an element of some result type; an *)
+ (* array entry of NONE means that the actual result has *)
+ (* not been computed yet *)
+ (* (int * interpretation option Array.array) list *)
+ val INTRS = map (fn (idx, _) =>
+ let
+ val T = typ_of_dtyp descr typ_assoc
+ (DatatypeAux.DtRec idx)
+ val (i, _, _) = interpret thy (typs, []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size = size_of_type i
+ in
+ (idx, Array.array (size, NONE))
+ end) descr
+ (* 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_eq True xs = elem then
+ SOME []
+ else
+ NONE
+ | get_args (Node xs) elem =
+ let
+ (* interpretation * 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 element "
+ ^ string_of_int elem ^ " in datatype "
+ ^ Sign.string_of_typ thy IDT ^ " (datatype index "
+ ^ string_of_int idx ^ ")")
+ | 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, lookup mc_intrs idx)
+ end
+ (* returns the number of constructors in datatypes that *)
+ (* occur in the descriptor 'descr' before the datatype *)
+ (* given by 'idx' *)
+ fun get_coffset idx =
+ let
+ fun get_coffset_acc _ [] =
+ raise REFUTE ("IDT_recursion_interpreter", "index "
+ ^ string_of_int idx ^ " not found in descriptor")
+ | get_coffset_acc sum ((i, (_, _, cs))::descr') =
+ if i=idx then
+ sum
+ else
+ get_coffset_acc (sum + length cs) descr'
+ in
+ get_coffset_acc 0 descr
+ end
+ (* computes one entry in INTRS, 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 =
+ case Array.sub (lookup INTRS idx, elem) of
+ SOME result =>
+ (* simply return the previously computed result *)
+ result
+ | NONE =>
+ let
+ (* int * int list *)
+ val (c, args) = get_cargs idx elem
+ (* interpretation * int list -> interpretation *)
+ fun select_subtree (tr, []) =
+ tr (* return the whole tree *)
+ | select_subtree (Leaf _, _) =
+ raise REFUTE ("IDT_recursion_interpreter",
+ "interpretation for parameter is a leaf; "
+ ^ "cannot select a subtree")
+ | select_subtree (Node tr, x::xs) =
+ select_subtree (List.nth (tr, x), xs)
+ (* select the correct subtree of the parameter *)
+ (* corresponding to constructor 'c' *)
+ val p_intr = select_subtree (List.nth
+ (p_intrs, get_coffset idx + c), args)
+ (* find the indices of the constructor's recursive *)
+ (* arguments *)
+ val (_, _, constrs) = lookup descr idx
+ val constr_args = (snd o List.nth) (constrs, c)
+ val rec_args = List.filter
+ (DatatypeAux.is_rec_type o fst) (constr_args ~~ args)
+ val rec_args' = map (fn (dtyp, elem) =>
+ (DatatypeAux.dest_DtRec dtyp, elem)) rec_args
+ (* apply 'p_intr' to recursively computed results *)
+ val result = foldl (fn ((idx, elem), intr) =>
+ interpretation_apply (intr,
+ compute_array_entry idx elem)) p_intr rec_args'
+ (* update 'INTRS' *)
+ val _ = Array.update (lookup INTRS idx, elem,
+ SOME result)
+ in
+ result
+ end
+ (* compute all entries in INTRS for the current datatype *)
+ (* (given by 'index') *)
+ (* TODO: we can use Array.modifyi instead once PolyML's *)
+ (* Array signature conforms to the ML standard *)
+ (* (int * 'a -> 'a) -> 'a array -> unit *)
+ fun modifyi f arr =
+ let
+ val size = Array.length arr
+ fun modifyi_loop i =
+ if i < size then (
+ Array.update (arr, i, f (i, Array.sub (arr, i)));
+ modifyi_loop (i+1)
+ ) else
+ ()
+ in
+ modifyi_loop 0
+ end
+ val _ = modifyi (fn (i, _) =>
+ SOME (compute_array_entry index i)) (lookup INTRS index)
+ (* 'a Array.array -> 'a list *)
+ fun toList arr =
+ Array.foldr op:: [] arr
+ in
+ (* return the part of 'INTRS' that corresponds to the *)
+ (* current datatype *)
+ SOME ((Node o map Option.valOf o toList o lookup INTRS)
+ index, model', args')
+ end
+ end
+ else
+ NONE (* not a recursion operator of this datatype *)
+ ) (DatatypePackage.get_datatypes thy) NONE
+ | _ => (* head of term is not a constant *)
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'card' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* 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 thy model args t =
- case t of
- Const ("Finite_Set.card",
- Type ("fun", [Type ("set", [T]), Type ("nat", [])])) =>
- let
- val (i_nat, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("nat", [])))
- val size_nat = size_of_type i_nat
- val (i_set, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("set", [T])))
- val constants = make_constants i_set
- (* interpretation -> int *)
- fun number_of_elements (Node xs) =
- Library.foldl (fn (n, x) =>
- 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"))
- (0, xs)
- | number_of_elements (Leaf _) =
- raise REFUTE ("Finite_Set_card_interpreter",
- "interpretation for set type is a leaf")
- (* takes an interpretation for a set and returns an interpretation *)
- (* for a 'nat' *)
- (* interpretation -> interpretation *)
- fun card i =
- let
- val n = number_of_elements i
- in
- if n<size_nat then
- Leaf ((replicate n False) @ True ::
- (replicate (size_nat-n-1) False))
- else
- Leaf (replicate size_nat False)
- end
- in
- SOME (Node (map card constants), model, args)
- end
- | _ =>
- NONE;
+ fun Finite_Set_card_interpreter thy model args t =
+ case t of
+ Const ("Finite_Set.card",
+ Type ("fun", [Type ("set", [T]), Type ("nat", [])])) =>
+ let
+ val (i_nat, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("nat", [])))
+ val size_nat = size_of_type i_nat
+ val (i_set, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("set", [T])))
+ val constants = make_constants i_set
+ (* interpretation -> int *)
+ fun number_of_elements (Node xs) =
+ Library.foldl (fn (n, x) =>
+ 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"))
+ (0, xs)
+ | number_of_elements (Leaf _) =
+ raise REFUTE ("Finite_Set_card_interpreter",
+ "interpretation for set type is a leaf")
+ (* takes an interpretation for a set and returns an interpretation *)
+ (* for a 'nat' *)
+ (* interpretation -> interpretation *)
+ fun card i =
+ let
+ val n = number_of_elements i
+ in
+ if n<size_nat then
+ Leaf ((replicate n False) @ True ::
+ (replicate (size_nat-n-1) False))
+ else
+ Leaf (replicate size_nat False)
+ end
+ in
+ SOME (Node (map card constants), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'Finites' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* only an optimization: 'Finites' could in principle be interpreted with *)
+ (* interpreters available already (using its definition), but the code *)
+ (* below is more efficient *)
- fun Finite_Set_Finites_interpreter thy model args t =
- case t of
- Const ("Finite_Set.Finites", Type ("set", [Type ("set", [T])])) =>
- let
- val (i_set, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("set", [T])))
- val size_set = size_of_type i_set
- in
- (* we only consider finite models anyway, hence EVERY set is in *)
- (* "Finites" *)
- SOME (Node (replicate size_set TT), model, args)
- end
- | _ =>
- NONE;
+ fun Finite_Set_Finites_interpreter thy model args t =
+ case t of
+ Const ("Finite_Set.Finites", Type ("set", [Type ("set", [T])])) =>
+ let
+ val (i_set, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("set", [T])))
+ val size_set = size_of_type i_set
+ in
+ (* we only consider finite models anyway, hence EVERY set is in *)
+ (* "Finites" *)
+ SOME (Node (replicate size_set TT), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'finite' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* 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 thy model args t =
- case t of
- Const ("Finite_Set.finite",
- Type ("fun", [Type ("set", [T]), Type ("bool", [])])) $ _ =>
- (* we only consider finite models anyway, hence EVERY set is *)
- (* "finite" *)
- SOME (TT, model, args)
- | Const ("Finite_Set.finite",
- Type ("fun", [Type ("set", [T]), Type ("bool", [])])) =>
- let
- val (i_set, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("set", [T])))
- val size_set = size_of_type i_set
- in
- (* we only consider finite models anyway, hence EVERY set is *)
- (* "finite" *)
- SOME (Node (replicate size_set TT), model, args)
- end
- | _ =>
- NONE;
+ fun Finite_Set_finite_interpreter thy model args t =
+ case t of
+ Const ("Finite_Set.finite",
+ Type ("fun", [Type ("set", [T]), Type ("bool", [])])) $ _ =>
+ (* we only consider finite models anyway, hence EVERY set is *)
+ (* "finite" *)
+ SOME (TT, model, args)
+ | Const ("Finite_Set.finite",
+ Type ("fun", [Type ("set", [T]), Type ("bool", [])])) =>
+ let
+ val (i_set, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("set", [T])))
+ val size_set = size_of_type i_set
+ in
+ (* we only consider finite models anyway, hence EVERY set is *)
+ (* "finite" *)
+ SOME (Node (replicate size_set TT), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'Orderings.less' could in principle be *)
- (* interpreted with interpreters available already (using its definition), *)
- (* but the code below is more efficient *)
+ (* only an optimization: 'Orderings.less' could in principle be *)
+ (* interpreted with interpreters available already (using its definition), *)
+ (* but the code below is more efficient *)
- fun Nat_less_interpreter thy model args t =
- case t of
- Const ("Orderings.less", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("bool", [])])])) =>
- let
- val (i_nat, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("nat", [])))
- val size_nat = size_of_type i_nat
- (* int -> interpretation *)
- (* the 'n'-th nat is not less than the first 'n' nats, while it *)
- (* is less than the remaining 'size_nat - n' nats *)
- fun less n = Node ((replicate n FF) @ (replicate (size_nat - n) TT))
- in
- SOME (Node (map less (1 upto size_nat)), model, args)
- end
- | _ =>
- NONE;
+ fun Nat_less_interpreter thy model args t =
+ case t of
+ Const ("Orderings.less", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("bool", [])])])) =>
+ let
+ val (i_nat, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("nat", [])))
+ val size_nat = size_of_type i_nat
+ (* int -> interpretation *)
+ (* the 'n'-th nat is not less than the first 'n' nats, while it *)
+ (* is less than the remaining 'size_nat - n' nats *)
+ fun less n = Node ((replicate n FF) @ (replicate (size_nat - n) TT))
+ in
+ SOME (Node (map less (1 upto size_nat)), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'HOL.plus' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* only an optimization: 'HOL.plus' could in principle be interpreted with *)
+ (* interpreters available already (using its definition), but the code *)
+ (* below is more efficient *)
- fun Nat_plus_interpreter thy model args t =
- case t of
- Const ("HOL.plus", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
- let
- val (i_nat, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("nat", [])))
- val size_nat = size_of_type i_nat
- (* int -> int -> interpretation *)
- fun plus m n =
- let
- val element = (m+n)+1
- in
- if element > size_nat then
- Leaf (replicate size_nat False)
- else
- Leaf ((replicate (element-1) False) @ True ::
- (replicate (size_nat - element) False))
- end
- in
- SOME (Node (map (fn m => Node (map (plus m) (0 upto size_nat-1)))
- (0 upto size_nat-1)), model, args)
- end
- | _ =>
- NONE;
+ fun Nat_plus_interpreter thy model args t =
+ case t of
+ Const ("HOL.plus", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
+ let
+ val (i_nat, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("nat", [])))
+ val size_nat = size_of_type i_nat
+ (* int -> int -> interpretation *)
+ fun plus m n =
+ let
+ val element = (m+n)+1
+ in
+ if element > size_nat then
+ Leaf (replicate size_nat False)
+ else
+ Leaf ((replicate (element-1) False) @ True ::
+ (replicate (size_nat - element) False))
+ end
+ in
+ SOME (Node (map (fn m => Node (map (plus m) (0 upto size_nat-1)))
+ (0 upto size_nat-1)), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'HOL.minus' could in principle be interpreted *)
- (* with interpreters available already (using its definition), but the *)
- (* code below is more efficient *)
+ (* only an optimization: 'HOL.minus' could in principle be interpreted *)
+ (* with interpreters available already (using its definition), but the *)
+ (* code below is more efficient *)
- fun Nat_minus_interpreter thy model args t =
- case t of
- Const ("HOL.minus", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
- let
- val (i_nat, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("nat", [])))
- val size_nat = size_of_type i_nat
- (* int -> int -> interpretation *)
- fun minus m n =
- let
- val element = Int.max (m-n, 0) + 1
- in
- Leaf ((replicate (element-1) False) @ True ::
- (replicate (size_nat - element) False))
- end
- in
- SOME (Node (map (fn m => Node (map (minus m) (0 upto size_nat-1)))
- (0 upto size_nat-1)), model, args)
- end
- | _ =>
- NONE;
+ fun Nat_minus_interpreter thy model args t =
+ case t of
+ Const ("HOL.minus", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
+ let
+ val (i_nat, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("nat", [])))
+ val size_nat = size_of_type i_nat
+ (* int -> int -> interpretation *)
+ fun minus m n =
+ let
+ val element = Int.max (m-n, 0) + 1
+ in
+ Leaf ((replicate (element-1) False) @ True ::
+ (replicate (size_nat - element) False))
+ end
+ in
+ SOME (Node (map (fn m => Node (map (minus m) (0 upto size_nat-1)))
+ (0 upto size_nat-1)), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'HOL.times' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* only an optimization: 'HOL.times' could in principle be interpreted with *)
+ (* interpreters available already (using its definition), but the code *)
+ (* below is more efficient *)
- fun Nat_times_interpreter thy model args t =
- case t of
- Const ("HOL.times", Type ("fun", [Type ("nat", []),
- Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
- let
- val (i_nat, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("nat", [])))
- val size_nat = size_of_type i_nat
- (* nat -> nat -> interpretation *)
- fun mult m n =
- let
- val element = (m*n)+1
- in
- if element > size_nat then
- Leaf (replicate size_nat False)
- else
- Leaf ((replicate (element-1) False) @ True ::
- (replicate (size_nat - element) False))
- end
- in
- SOME (Node (map (fn m => Node (map (mult m) (0 upto size_nat-1)))
- (0 upto size_nat-1)), model, args)
- end
- | _ =>
- NONE;
+ fun Nat_times_interpreter thy model args t =
+ case t of
+ Const ("HOL.times", Type ("fun", [Type ("nat", []),
+ Type ("fun", [Type ("nat", []), Type ("nat", [])])])) =>
+ let
+ val (i_nat, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("nat", [])))
+ val size_nat = size_of_type i_nat
+ (* nat -> nat -> interpretation *)
+ fun mult m n =
+ let
+ val element = (m*n)+1
+ in
+ if element > size_nat then
+ Leaf (replicate size_nat False)
+ else
+ Leaf ((replicate (element-1) False) @ True ::
+ (replicate (size_nat - element) False))
+ end
+ in
+ SOME (Node (map (fn m => Node (map (mult m) (0 upto size_nat-1)))
+ (0 upto size_nat-1)), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'op @' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* only an optimization: 'op @' could in principle be interpreted with *)
+ (* interpreters available already (using its definition), but the code *)
+ (* below is more efficient *)
- fun List_append_interpreter thy model args t =
- case t of
- Const ("List.op @", Type ("fun", [Type ("List.list", [T]), Type ("fun",
- [Type ("List.list", [_]), Type ("List.list", [_])])])) =>
- let
- val (i_elem, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size_elem = size_of_type i_elem
- val (i_list, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("List.list", [T])))
- val size_list = size_of_type i_list
- (* power (a, b) computes a^b, for a>=0, b>=0 *)
- (* int * int -> int *)
- fun power (a, 0) = 1
- | power (a, 1) = a
- | power (a, b) =
- let val ab = power(a, b div 2) in ab * ab * power(a, b mod 2) end
- (* log (a, b) computes floor(log_a(b)), i.e. the largest integer x *)
- (* s.t. a^x <= b, for a>=2, b>=1 *)
- (* int * int -> int *)
- fun log (a, b) =
- let
- fun logloop (ax, x) =
- if ax > b then x-1 else logloop (a * ax, x+1)
- in
- logloop (1, 0)
- end
- (* nat -> nat -> interpretation *)
- fun append m n =
- let
- (* The following formula depends on the order in which lists are *)
- (* enumerated by the 'IDT_constructor_interpreter'. It took me *)
- (* a little while to come up with this formula. *)
- val element = n + m * (if size_elem = 1 then 1
- else power (size_elem, log (size_elem, n+1))) + 1
- in
- if element > size_list then
- Leaf (replicate size_list False)
- else
- Leaf ((replicate (element-1) False) @ True ::
- (replicate (size_list - element) False))
- end
- in
- SOME (Node (map (fn m => Node (map (append m) (0 upto size_list-1)))
- (0 upto size_list-1)), model, args)
- end
- | _ =>
- NONE;
+ fun List_append_interpreter thy model args t =
+ case t of
+ Const ("List.op @", Type ("fun", [Type ("List.list", [T]), Type ("fun",
+ [Type ("List.list", [_]), Type ("List.list", [_])])])) =>
+ let
+ val (i_elem, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size_elem = size_of_type i_elem
+ val (i_list, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("List.list", [T])))
+ val size_list = size_of_type i_list
+ (* power (a, b) computes a^b, for a>=0, b>=0 *)
+ (* int * int -> int *)
+ fun power (a, 0) = 1
+ | power (a, 1) = a
+ | power (a, b) =
+ let val ab = power(a, b div 2) in ab * ab * power(a, b mod 2) end
+ (* log (a, b) computes floor(log_a(b)), i.e. the largest integer x *)
+ (* s.t. a^x <= b, for a>=2, b>=1 *)
+ (* int * int -> int *)
+ fun log (a, b) =
+ let
+ fun logloop (ax, x) =
+ if ax > b then x-1 else logloop (a * ax, x+1)
+ in
+ logloop (1, 0)
+ end
+ (* nat -> nat -> interpretation *)
+ fun append m n =
+ let
+ (* The following formula depends on the order in which lists are *)
+ (* enumerated by the 'IDT_constructor_interpreter'. It took me *)
+ (* a little while to come up with this formula. *)
+ val element = n + m * (if size_elem = 1 then 1
+ else power (size_elem, log (size_elem, n+1))) + 1
+ in
+ if element > size_list then
+ Leaf (replicate size_list False)
+ else
+ Leaf ((replicate (element-1) False) @ True ::
+ (replicate (size_list - element) False))
+ end
+ in
+ SOME (Node (map (fn m => Node (map (append m) (0 upto size_list-1)))
+ (0 upto size_list-1)), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'lfp' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* 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_lfp_interpreter thy model args t =
- case t of
- Const ("Lfp.lfp", Type ("fun", [Type ("fun",
- [Type ("set", [T]), Type ("set", [_])]), Type ("set", [_])])) =>
- let
- val (i_elem, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size_elem = size_of_type i_elem
- (* 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_set, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("set", [T])))
- val i_sets = make_constants i_set
- (* all functions that map sets to sets *)
- val (i_fun, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy",
- Type ("fun", [Type ("set", [T]), Type ("set", [T])])))
- val i_funs = make_constants i_fun
- (* "lfp(f) == Inter({u. f(u) <= u})" *)
- (* interpretation * interpretation -> bool *)
- fun is_subset (Node subs, Node sups) =
- List.all (fn (sub, sup) => (sub = FF) orelse (sup = TT))
- (subs ~~ sups)
- | is_subset (_, _) =
- raise REFUTE ("Lfp_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_lfp_interpreter",
- "intersection: interpretation for set is not a node")
- (* interpretation -> interpretaion *)
- fun lfp (Node resultsets) =
- foldl (fn ((set, resultset), acc) =>
- if is_subset (resultset, set) then
- intersection (acc, set)
- else
- acc) i_univ (i_sets ~~ resultsets)
- | lfp _ =
- raise REFUTE ("Lfp_lfp_interpreter",
- "lfp: interpretation for function is not a node")
- in
- SOME (Node (map lfp i_funs), model, args)
- end
- | _ =>
- NONE;
+ fun Lfp_lfp_interpreter thy model args t =
+ case t of
+ Const ("Lfp.lfp", Type ("fun", [Type ("fun",
+ [Type ("set", [T]), Type ("set", [_])]), Type ("set", [_])])) =>
+ let
+ val (i_elem, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size_elem = size_of_type i_elem
+ (* 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_set, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("set", [T])))
+ val i_sets = make_constants i_set
+ (* all functions that map sets to sets *)
+ val (i_fun, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy",
+ Type ("fun", [Type ("set", [T]), Type ("set", [T])])))
+ val i_funs = make_constants i_fun
+ (* "lfp(f) == Inter({u. f(u) <= u})" *)
+ (* interpretation * interpretation -> bool *)
+ fun is_subset (Node subs, Node sups) =
+ List.all (fn (sub, sup) => (sub = FF) orelse (sup = TT))
+ (subs ~~ sups)
+ | is_subset (_, _) =
+ raise REFUTE ("Lfp_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_lfp_interpreter",
+ "intersection: interpretation for set is not a node")
+ (* interpretation -> interpretaion *)
+ fun lfp (Node resultsets) =
+ foldl (fn ((set, resultset), acc) =>
+ if is_subset (resultset, set) then
+ intersection (acc, set)
+ else
+ acc) i_univ (i_sets ~~ resultsets)
+ | lfp _ =
+ raise REFUTE ("Lfp_lfp_interpreter",
+ "lfp: interpretation for function is not a node")
+ in
+ SOME (Node (map lfp i_funs), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'gfp' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* 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_gfp_interpreter thy model args t =
- case t of
- Const ("Gfp.gfp", Type ("fun", [Type ("fun",
- [Type ("set", [T]), Type ("set", [_])]), Type ("set", [_])])) =>
- let nonfix union (* because "union" is used below *)
- val (i_elem, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", T))
- val size_elem = size_of_type i_elem
- (* 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_set, _, _) = interpret thy model
- {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", Type ("set", [T])))
- val i_sets = make_constants i_set
- (* all functions that map sets to sets *)
- val (i_fun, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy",
- Type ("fun", [Type ("set", [T]), Type ("set", [T])])))
- val i_funs = make_constants i_fun
- (* "gfp(f) == Union({u. u <= f(u)})" *)
- (* interpretation * interpretation -> bool *)
- fun is_subset (Node subs, Node sups) =
- List.all (fn (sub, sup) => (sub = FF) orelse (sup = TT))
- (subs ~~ sups)
- | is_subset (_, _) =
- raise REFUTE ("Gfp_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_gfp_interpreter",
- "union: interpretation for set is not a node")
- (* interpretation -> interpretaion *)
- fun gfp (Node resultsets) =
- foldl (fn ((set, resultset), acc) =>
- if is_subset (set, resultset) then
- union (acc, set)
- else
- acc) i_univ (i_sets ~~ resultsets)
- | gfp _ =
- raise REFUTE ("Gfp_gfp_interpreter",
- "gfp: interpretation for function is not a node")
- in
- SOME (Node (map gfp i_funs), model, args)
- end
- | _ =>
- NONE;
+ fun Gfp_gfp_interpreter thy model args t =
+ case t of
+ Const ("Gfp.gfp", Type ("fun", [Type ("fun",
+ [Type ("set", [T]), Type ("set", [_])]), Type ("set", [_])])) =>
+ let nonfix union (* because "union" is used below *)
+ val (i_elem, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", T))
+ val size_elem = size_of_type i_elem
+ (* 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_set, _, _) = interpret thy model
+ {maxvars=0, def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", Type ("set", [T])))
+ val i_sets = make_constants i_set
+ (* all functions that map sets to sets *)
+ val (i_fun, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy",
+ Type ("fun", [Type ("set", [T]), Type ("set", [T])])))
+ val i_funs = make_constants i_fun
+ (* "gfp(f) == Union({u. u <= f(u)})" *)
+ (* interpretation * interpretation -> bool *)
+ fun is_subset (Node subs, Node sups) =
+ List.all (fn (sub, sup) => (sub = FF) orelse (sup = TT))
+ (subs ~~ sups)
+ | is_subset (_, _) =
+ raise REFUTE ("Gfp_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_gfp_interpreter",
+ "union: interpretation for set is not a node")
+ (* interpretation -> interpretaion *)
+ fun gfp (Node resultsets) =
+ foldl (fn ((set, resultset), acc) =>
+ if is_subset (set, resultset) then
+ union (acc, set)
+ else
+ acc) i_univ (i_sets ~~ resultsets)
+ | gfp _ =
+ raise REFUTE ("Gfp_gfp_interpreter",
+ "gfp: interpretation for function is not a node")
+ in
+ SOME (Node (map gfp i_funs), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'fst' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* 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 thy model args t =
- case t of
- Const ("fst", Type ("fun", [Type ("*", [T, U]), _])) =>
- let
- val (iT, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
- val is_T = make_constants iT
- val (iU, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", U))
- val size_U = size_of_type iU
- in
- SOME (Node (List.concat (map (replicate size_U) is_T)), model, args)
- end
- | _ =>
- NONE;
+ fun Product_Type_fst_interpreter thy model args t =
+ case t of
+ Const ("fst", Type ("fun", [Type ("*", [T, U]), _])) =>
+ let
+ val (iT, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
+ val is_T = make_constants iT
+ val (iU, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", U))
+ val size_U = size_of_type iU
+ in
+ SOME (Node (List.concat (map (replicate size_U) is_T)), model, args)
+ end
+ | _ =>
+ NONE;
- (* theory -> model -> arguments -> Term.term ->
- (interpretation * model * arguments) option *)
+ (* theory -> model -> arguments -> Term.term ->
+ (interpretation * model * arguments) option *)
- (* only an optimization: 'snd' could in principle be interpreted with *)
- (* interpreters available already (using its definition), but the code *)
- (* below is more efficient *)
+ (* 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 thy model args t =
- case t of
- Const ("snd", Type ("fun", [Type ("*", [T, U]), _])) =>
- let
- val (iT, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
- val size_T = size_of_type iT
- val (iU, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", U))
- val is_U = make_constants iU
- in
- SOME (Node (List.concat (replicate size_T is_U)), model, args)
- end
- | _ =>
- NONE;
+ fun Product_Type_snd_interpreter thy model args t =
+ case t of
+ Const ("snd", Type ("fun", [Type ("*", [T, U]), _])) =>
+ let
+ val (iT, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
+ val size_T = size_of_type iT
+ val (iU, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", U))
+ val is_U = make_constants iU
+ in
+ SOME (Node (List.concat (replicate size_T is_U)), model, args)
+ end
+ | _ =>
+ NONE;
(* ------------------------------------------------------------------------- *)
(* PRINTERS *)
(* ------------------------------------------------------------------------- *)
- (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
- Term.term option *)
+ (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
+ Term.term option *)
- fun stlc_printer thy model t intr assignment =
- let
- (* Term.term -> Term.typ option *)
- fun typeof (Free (_, T)) = SOME T
- | typeof (Var (_, T)) = SOME T
- | typeof (Const (_, T)) = SOME T
- | typeof _ = NONE
- (* string -> string *)
- fun strip_leading_quote s =
- (implode o (fn [] => [] | x::xs => if x="'" then xs else x::xs)
- o explode) s
- (* 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 (PropLogic.eval assignment) xs
- | index_from_interpretation _ =
- raise REFUTE ("stlc_printer",
- "interpretation for ground type is not a leaf")
- in
- case typeof t of
- SOME T =>
- (case T of
- Type ("fun", [T1, T2]) =>
- let
- (* create all constants of type 'T1' *)
- val (i, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T1))
- val constants = make_constants i
- (* 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 thy model (Free ("dummy", T1)) arg assignment,
- print thy model (Free ("dummy", 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 ("{}", HOLogic_setT)
- val HOLogic_insert =
- Const ("insert", HOLogic_prodT --> HOLogic_setT --> HOLogic_setT)
- in
- SOME (foldr (fn (pair, acc) => HOLogic_insert $ pair $ acc)
- HOLogic_empty_set pairs)
- end
- | Type ("prop", []) =>
- (case index_from_interpretation intr of
- ~1 => SOME (HOLogic.mk_Trueprop (Const ("arbitrary", HOLogic.boolT)))
- | 0 => SOME (HOLogic.mk_Trueprop HOLogic.true_const)
- | 1 => SOME (HOLogic.mk_Trueprop HOLogic.false_const)
- | _ => raise REFUTE ("stlc_interpreter",
- "illegal interpretation for a propositional value"))
- | Type _ => if index_from_interpretation intr = (~1) then
- SOME (Const ("arbitrary", 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 ("arbitrary", 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 ("arbitrary", T))
- else
- SOME (Const (string_of_typ T ^
- string_of_int (index_from_interpretation intr), T)))
- | NONE =>
- NONE
- end;
+ fun stlc_printer thy model t intr assignment =
+ let
+ (* Term.term -> Term.typ option *)
+ fun typeof (Free (_, T)) = SOME T
+ | typeof (Var (_, T)) = SOME T
+ | typeof (Const (_, T)) = SOME T
+ | typeof _ = NONE
+ (* string -> string *)
+ fun strip_leading_quote s =
+ (implode o (fn [] => [] | x::xs => if x="'" then xs else x::xs)
+ o explode) s
+ (* 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 (PropLogic.eval assignment) xs
+ | index_from_interpretation _ =
+ raise REFUTE ("stlc_printer",
+ "interpretation for ground type is not a leaf")
+ in
+ case typeof t of
+ SOME T =>
+ (case T of
+ Type ("fun", [T1, T2]) =>
+ let
+ (* create all constants of type 'T1' *)
+ val (i, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T1))
+ val constants = make_constants i
+ (* 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 thy model (Free ("dummy", T1)) arg assignment,
+ print thy model (Free ("dummy", 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 ("{}", HOLogic_setT)
+ val HOLogic_insert =
+ Const ("insert", HOLogic_prodT --> HOLogic_setT --> HOLogic_setT)
+ in
+ SOME (foldr (fn (pair, acc) => HOLogic_insert $ pair $ acc)
+ HOLogic_empty_set pairs)
+ end
+ | Type ("prop", []) =>
+ (case index_from_interpretation intr of
+ ~1 => SOME (HOLogic.mk_Trueprop (Const ("arbitrary", HOLogic.boolT)))
+ | 0 => SOME (HOLogic.mk_Trueprop HOLogic.true_const)
+ | 1 => SOME (HOLogic.mk_Trueprop HOLogic.false_const)
+ | _ => raise REFUTE ("stlc_interpreter",
+ "illegal interpretation for a propositional value"))
+ | Type _ => if index_from_interpretation intr = (~1) then
+ SOME (Const ("arbitrary", 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 ("arbitrary", 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 ("arbitrary", T))
+ else
+ SOME (Const (string_of_typ T ^
+ string_of_int (index_from_interpretation intr), T)))
+ | NONE =>
+ NONE
+ end;
- (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
- string option *)
+ (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
+ string option *)
- fun set_printer thy model t intr assignment =
- let
- (* Term.term -> Term.typ option *)
- fun typeof (Free (_, T)) = SOME T
- | typeof (Var (_, T)) = SOME T
- | typeof (Const (_, T)) = SOME T
- | typeof _ = NONE
- in
- case typeof t of
- SOME (Type ("set", [T])) =>
- let
- (* create all constants of type 'T' *)
- val (i, _, _) = interpret thy model {maxvars=0, def_eq=false,
- next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
- val constants = make_constants i
- (* 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 PropLogic.eval assignment fmTrue then
- SOME (print thy model (Free ("dummy", T)) arg assignment)
- else (* if PropLogic.eval assignment fmFalse then *)
- NONE
- | _ =>
- raise REFUTE ("set_printer",
- "illegal interpretation for a Boolean value"))
- (constants ~~ results)
- (* Term.typ *)
- val HOLogic_setT = HOLogic.mk_setT T
- (* Term.term *)
- val HOLogic_empty_set = Const ("{}", HOLogic_setT)
- val HOLogic_insert =
- Const ("insert", T --> HOLogic_setT --> HOLogic_setT)
- in
- SOME (Library.foldl (fn (acc, elem) => HOLogic_insert $ elem $ acc)
- (HOLogic_empty_set, elements))
- end
- | _ =>
- NONE
- end;
+ fun set_printer thy model t intr assignment =
+ let
+ (* Term.term -> Term.typ option *)
+ fun typeof (Free (_, T)) = SOME T
+ | typeof (Var (_, T)) = SOME T
+ | typeof (Const (_, T)) = SOME T
+ | typeof _ = NONE
+ in
+ case typeof t of
+ SOME (Type ("set", [T])) =>
+ let
+ (* create all constants of type 'T' *)
+ val (i, _, _) = interpret thy model {maxvars=0, def_eq=false,
+ next_idx=1, bounds=[], wellformed=True} (Free ("dummy", T))
+ val constants = make_constants i
+ (* 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 PropLogic.eval assignment fmTrue then
+ SOME (print thy model (Free ("dummy", T)) arg assignment)
+ else (* if PropLogic.eval assignment fmFalse then *)
+ NONE
+ | _ =>
+ raise REFUTE ("set_printer",
+ "illegal interpretation for a Boolean value"))
+ (constants ~~ results)
+ (* Term.typ *)
+ val HOLogic_setT = HOLogic.mk_setT T
+ (* Term.term *)
+ val HOLogic_empty_set = Const ("{}", HOLogic_setT)
+ val HOLogic_insert =
+ Const ("insert", T --> HOLogic_setT --> HOLogic_setT)
+ in
+ SOME (Library.foldl (fn (acc, elem) => HOLogic_insert $ elem $ acc)
+ (HOLogic_empty_set, elements))
+ end
+ | _ =>
+ NONE
+ end;
- (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
- Term.term option *)
+ (* theory -> model -> Term.term -> interpretation -> (int -> bool) ->
+ Term.term option *)
- fun IDT_printer thy model t intr assignment =
- let
- (* Term.term -> Term.typ option *)
- fun typeof (Free (_, T)) = SOME T
- | typeof (Var (_, T)) = SOME T
- | typeof (Const (_, T)) = SOME T
- | typeof _ = NONE
- in
- case typeof t of
- SOME (Type (s, Ts)) =>
- (case DatatypePackage.get_datatype thy s of
- SOME info => (* inductive datatype *)
- let
- val (typs, _) = model
- val index = #index info
- val descr = #descr info
- val (_, dtyps, constrs) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
- then
- raise REFUTE ("IDT_printer", "datatype argument (for type " ^
- Sign.string_of_typ thy (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 (PropLogic.eval assignment) xs
- | Node _ => raise REFUTE ("IDT_printer",
- "interpretation is not a leaf"))
- in
- if element < 0 then
- SOME (Const ("arbitrary", 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 *)
- (* string * DatatypeAux.dtyp list ->
- (Term.term * int list) option *)
- 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 thy (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_eq 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
- (* Term.term * DatatypeAux.dtyp list * int list *)
- val (cTerm, cargs, args) =
- (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
- val (i, _, _) = interpret thy (typs, []) {maxvars=0,
- def_eq=false, next_idx=1, bounds=[], wellformed=True}
- (Free ("dummy", dT))
- (* 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 i
- in
- print thy (typs, []) (Free ("dummy", dT))
- (List.nth (consts, n)) assignment
- end) (cargs ~~ args)
- in
- SOME (Library.foldl op$ (cTerm, argsTerms))
- end
- end
- | NONE => (* not an inductive datatype *)
- NONE)
- | _ => (* a (free or schematic) type variable *)
- NONE
- end;
+ fun IDT_printer thy model t intr assignment =
+ let
+ (* Term.term -> Term.typ option *)
+ fun typeof (Free (_, T)) = SOME T
+ | typeof (Var (_, T)) = SOME T
+ | typeof (Const (_, T)) = SOME T
+ | typeof _ = NONE
+ in
+ case typeof t of
+ SOME (Type (s, Ts)) =>
+ (case DatatypePackage.get_datatype thy s of
+ SOME info => (* inductive datatype *)
+ let
+ val (typs, _) = model
+ val index = #index info
+ val descr = #descr info
+ val (_, dtyps, constrs) = lookup 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 DatatypeAux.DtTFree _ => false | _ => true) dtyps
+ then
+ raise REFUTE ("IDT_printer", "datatype argument (for type " ^
+ Sign.string_of_typ thy (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 (PropLogic.eval assignment) xs
+ | Node _ => raise REFUTE ("IDT_printer",
+ "interpretation is not a leaf"))
+ in
+ if element < 0 then
+ SOME (Const ("arbitrary", 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 *)
+ (* string * DatatypeAux.dtyp list ->
+ (Term.term * int list) option *)
+ 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 thy (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_eq 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
+ (* Term.term * DatatypeAux.dtyp list * int list *)
+ val (cTerm, cargs, args) =
+ (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
+ val (i, _, _) = interpret thy (typs, []) {maxvars=0,
+ def_eq=false, next_idx=1, bounds=[], wellformed=True}
+ (Free ("dummy", dT))
+ (* 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 i
+ in
+ print thy (typs, []) (Free ("dummy", dT))
+ (List.nth (consts, n)) assignment
+ end) (cargs ~~ args)
+ in
+ SOME (Library.foldl op$ (cTerm, argsTerms))
+ end
+ end
+ | NONE => (* not an inductive datatype *)
+ NONE)
+ | _ => (* a (free or schematic) type variable *)
+ NONE
+ end;
(* ------------------------------------------------------------------------- *)
@@ -3207,31 +3207,31 @@
(* subterms that are then passed to other interpreters! *)
(* ------------------------------------------------------------------------- *)
- (* (theory -> theory) list *)
+ (* (theory -> theory) list *)
- val setup =
- RefuteData.init #>
- 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.Finites" Finite_Set_Finites_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.op @" List_append_interpreter #>
- add_interpreter "Lfp.lfp" Lfp_lfp_interpreter #>
- add_interpreter "Gfp.gfp" Gfp_gfp_interpreter #>
- add_interpreter "fst" Product_Type_fst_interpreter #>
- add_interpreter "snd" Product_Type_snd_interpreter #>
- add_printer "stlc" stlc_printer #>
- add_printer "set" set_printer #>
- add_printer "IDT" IDT_printer;
+ val setup =
+ RefuteData.init #>
+ 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.Finites" Finite_Set_Finites_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.op @" List_append_interpreter #>
+ add_interpreter "Lfp.lfp" Lfp_lfp_interpreter #>
+ add_interpreter "Gfp.gfp" Gfp_gfp_interpreter #>
+ add_interpreter "fst" Product_Type_fst_interpreter #>
+ add_interpreter "snd" Product_Type_snd_interpreter #>
+ add_printer "stlc" stlc_printer #>
+ add_printer "set" set_printer #>
+ add_printer "IDT" IDT_printer;
end (* structure Refute *)