(* Title: Pure/theory.ML
ID: $Id$
Author: Lawrence C Paulson and Markus Wenzel
Copyright 1996 University of Cambridge
The abstract type "theory" of theories.
*)
signature BASIC_THEORY =
sig
type theory
exception THEORY of string * theory list
val rep_theory: theory ->
{sign: Sign.sg,
const_deps: unit Graph.T,
axioms: term Symtab.table,
oracles: ((Sign.sg * Object.T -> term) * stamp) Symtab.table,
parents: theory list,
ancestors: theory list}
val sign_of: theory -> Sign.sg
val is_draft: theory -> bool
val syn_of: theory -> Syntax.syntax
val parents_of: theory -> theory list
val ancestors_of: theory -> theory list
val subthy: theory * theory -> bool
val eq_thy: theory * theory -> bool
val cert_axm: Sign.sg -> string * term -> string * term
val read_def_axm: Sign.sg * (indexname -> typ option) * (indexname -> sort option) ->
string list -> string * string -> string * term
val read_axm: Sign.sg -> string * string -> string * term
val inferT_axm: Sign.sg -> string * term -> string * term
end
signature THEORY =
sig
include BASIC_THEORY
val axiomK: string
val oracleK: string
(*theory extension primitives*)
val add_classes: (bclass * xclass list) list -> theory -> theory
val add_classes_i: (bclass * class list) list -> theory -> theory
val add_classrel: (xclass * xclass) list -> theory -> theory
val add_classrel_i: (class * class) list -> theory -> theory
val add_defsort: string -> theory -> theory
val add_defsort_i: sort -> theory -> theory
val add_types: (bstring * int * mixfix) list -> theory -> theory
val add_nonterminals: bstring list -> theory -> theory
val add_tyabbrs: (bstring * string list * string * mixfix) list
-> theory -> theory
val add_tyabbrs_i: (bstring * string list * typ * mixfix) list
-> theory -> theory
val add_arities: (xstring * string list * string) list -> theory -> theory
val add_arities_i: (string * sort list * sort) list -> theory -> theory
val add_consts: (bstring * string * mixfix) list -> theory -> theory
val add_consts_i: (bstring * typ * mixfix) list -> theory -> theory
val add_syntax: (bstring * string * mixfix) list -> theory -> theory
val add_syntax_i: (bstring * typ * mixfix) list -> theory -> theory
val add_modesyntax: string * bool -> (bstring * string * mixfix) list -> theory -> theory
val add_modesyntax_i: string * bool -> (bstring * typ * mixfix) list -> theory -> theory
val add_trfuns:
(string * (Syntax.ast list -> Syntax.ast)) list *
(string * (term list -> term)) list *
(string * (term list -> term)) list *
(string * (Syntax.ast list -> Syntax.ast)) list -> theory -> theory
val add_trfunsT:
(string * (bool -> typ -> term list -> term)) list -> theory -> theory
val add_tokentrfuns:
(string * string * (string -> string * real)) list -> theory -> theory
val add_mode_tokentrfuns: string -> (string * (string -> string * real)) list
-> theory -> theory
val add_trrules: (xstring * string) Syntax.trrule list -> theory -> theory
val add_trrules_i: Syntax.ast Syntax.trrule list -> theory -> theory
val add_axioms: (bstring * string) list -> theory -> theory
val add_axioms_i: (bstring * term) list -> theory -> theory
val add_oracle: bstring * (Sign.sg * Object.T -> term) -> theory -> theory
val add_defs: bool -> (bstring * string) list -> theory -> theory
val add_defs_i: bool -> (bstring * term) list -> theory -> theory
val add_path: string -> theory -> theory
val parent_path: theory -> theory
val root_path: theory -> theory
val hide_space: string * xstring list -> theory -> theory
val hide_space_i: string * string list -> theory -> theory
val hide_classes: string list -> theory -> theory
val hide_types: string list -> theory -> theory
val hide_consts: string list -> theory -> theory
val add_name: string -> theory -> theory
val copy: theory -> theory
val prep_ext: theory -> theory
val prep_ext_merge: theory list -> theory
val requires: theory -> string -> string -> unit
val assert_super: theory -> theory -> theory
val pre_pure: theory
end;
signature PRIVATE_THEORY =
sig
include THEORY
val init_data: Object.kind -> (Object.T * (Object.T -> Object.T) * (Object.T -> Object.T) *
(Object.T * Object.T -> Object.T) * (Sign.sg -> Object.T -> unit)) -> theory -> theory
val print_data: Object.kind -> theory -> unit
val get_data: Object.kind -> (Object.T -> 'a) -> theory -> 'a
val put_data: Object.kind -> ('a -> Object.T) -> 'a -> theory -> theory
end;
structure Theory: PRIVATE_THEORY =
struct
(** datatype theory **)
(*Note: dependencies are only tracked for non-overloaded constant definitions*)
datatype theory =
Theory of {
sign: Sign.sg,
const_deps: unit Graph.T,
axioms: term Symtab.table,
oracles: ((Sign.sg * Object.T -> term) * stamp) Symtab.table,
parents: theory list,
ancestors: theory list};
fun make_theory sign const_deps axioms oracles parents ancestors =
Theory {sign = sign, const_deps = const_deps, axioms = axioms, oracles = oracles,
parents = parents, ancestors = ancestors};
fun rep_theory (Theory args) = args;
val sign_of = #sign o rep_theory;
val is_draft = Sign.is_draft o sign_of;
val syn_of = #syn o Sign.rep_sg o sign_of;
val parents_of = #parents o rep_theory;
val ancestors_of = #ancestors o rep_theory;
(*errors involving theories*)
exception THEORY of string * theory list;
(*compare theories*)
val subthy = Sign.subsig o pairself sign_of;
val eq_thy = Sign.eq_sg o pairself sign_of;
(*check for some theory*)
fun requires thy name what =
if exists (equal name) (Sign.stamp_names_of (sign_of thy)) then ()
else error ("Require theory " ^ quote name ^ " as an ancestor for " ^ what);
fun assert_super thy1 thy2 =
if subthy (thy1, thy2) then thy2
else raise THEORY ("Not a super theory", [thy1, thy2]);
(*partial Pure theory*)
val pre_pure =
make_theory Sign.pre_pure Graph.empty Symtab.empty Symtab.empty [] [];
(** extend theory **)
(*name spaces*)
val axiomK = "axiom";
val oracleK = "oracle";
(* extend logical part of a theory *)
fun err_dup_axms names =
error ("Duplicate axiom name(s) " ^ commas_quote names);
fun err_dup_oras names =
error ("Duplicate oracles " ^ commas_quote names);
fun ext_theory thy ext_sg ext_deps new_axms new_oras =
let
val Theory {sign, const_deps, axioms, oracles, parents, ancestors} = thy;
val draft = Sign.is_draft sign;
val axioms' =
Symtab.extend (if draft then axioms else Symtab.empty, new_axms)
handle Symtab.DUPS names => err_dup_axms names;
val oracles' =
Symtab.extend (oracles, new_oras)
handle Symtab.DUPS names => err_dup_oras names;
val (parents', ancestors') =
if draft then (parents, ancestors) else ([thy], thy :: ancestors);
in
make_theory (ext_sg sign) (ext_deps const_deps) axioms' oracles' parents' ancestors'
end;
(* extend signature of a theory *)
fun ext_sign extfun decls thy = ext_theory thy (extfun decls) I [] [];
val add_classes = ext_sign Sign.add_classes;
val add_classes_i = ext_sign Sign.add_classes_i;
val add_classrel = ext_sign Sign.add_classrel;
val add_classrel_i = ext_sign Sign.add_classrel_i;
val add_defsort = ext_sign Sign.add_defsort;
val add_defsort_i = ext_sign Sign.add_defsort_i;
val add_types = ext_sign Sign.add_types;
val add_nonterminals = ext_sign Sign.add_nonterminals;
val add_tyabbrs = ext_sign Sign.add_tyabbrs;
val add_tyabbrs_i = ext_sign Sign.add_tyabbrs_i;
val add_arities = ext_sign Sign.add_arities;
val add_arities_i = ext_sign Sign.add_arities_i;
val add_consts = ext_sign Sign.add_consts;
val add_consts_i = ext_sign Sign.add_consts_i;
val add_syntax = ext_sign Sign.add_syntax;
val add_syntax_i = ext_sign Sign.add_syntax_i;
val add_modesyntax = curry (ext_sign Sign.add_modesyntax);
val add_modesyntax_i = curry (ext_sign Sign.add_modesyntax_i);
val add_trfuns = ext_sign Sign.add_trfuns;
val add_trfunsT = ext_sign Sign.add_trfunsT;
val add_tokentrfuns = ext_sign Sign.add_tokentrfuns;
fun add_mode_tokentrfuns m = add_tokentrfuns o map (fn (s, f) => (m, s, f));
val add_trrules = ext_sign Sign.add_trrules;
val add_trrules_i = ext_sign Sign.add_trrules_i;
val add_path = ext_sign Sign.add_path;
val parent_path = add_path "..";
val root_path = add_path "/";
val add_space = ext_sign Sign.add_space;
val hide_space = ext_sign Sign.hide_space;
val hide_space_i = ext_sign Sign.hide_space_i;
val hide_classes = curry hide_space_i Sign.classK;
val hide_types = curry hide_space_i Sign.typeK;
val hide_consts = curry hide_space_i Sign.constK;
val add_name = ext_sign Sign.add_name;
val copy = ext_sign (K Sign.copy) ();
val prep_ext = ext_sign (K Sign.prep_ext) ();
(** add axioms **)
(* prepare axioms *)
fun err_in_axm name =
error ("The error(s) above occurred in axiom " ^ quote name);
fun no_vars tm =
if null (term_vars tm) andalso null (term_tvars tm) then tm
else error "Illegal schematic variable(s) in term";
fun cert_axm sg (name, raw_tm) =
let
val (t, T, _) = Sign.certify_term sg raw_tm
handle TYPE (msg, _, _) => error msg
| TERM (msg, _) => error msg;
in
assert (T = propT) "Term not of type prop";
(name, no_vars t)
end
handle ERROR => err_in_axm name;
(*some duplication of code with read_def_cterm*)
fun read_def_axm (sg, types, sorts) used (name, str) =
let
val ts = Syntax.read (#syn (Sign.rep_sg sg)) propT str;
val (t, _) = Sign.infer_types sg types sorts used true (ts, propT);
in cert_axm sg (name, t) end
handle ERROR => err_in_axm name;
fun read_axm sg name_str = read_def_axm (sg, K None, K None) [] name_str;
fun inferT_axm sg (name, pre_tm) =
let
val (t, _) = Sign.infer_types sg (K None) (K None) [] true ([pre_tm], propT);
in (name, no_vars t) end
handle ERROR => err_in_axm name;
(* extend axioms of a theory *)
fun ext_axms prep_axm raw_axms (thy as Theory {sign, ...}) =
let
val raw_axms' = map (apfst (Sign.full_name sign)) raw_axms;
val axioms =
map (apsnd (Term.compress_term o Logic.varify) o prep_axm sign) raw_axms';
val ext_sg = Sign.add_space (axiomK, map fst axioms);
in ext_theory thy ext_sg I axioms [] end;
val add_axioms = ext_axms read_axm;
val add_axioms_i = ext_axms cert_axm;
(* add oracle **)
fun add_oracle (raw_name, oracle) (thy as Theory {sign, ...}) =
let
val name = Sign.full_name sign raw_name;
val ext_sg = Sign.add_space (oracleK, [name]);
in ext_theory thy ext_sg I [] [(name, (oracle, stamp ()))] end;
(** add constant definitions **)
(* clash_types, clash_consts *)
(*check if types have common instance (ignoring sorts)*)
fun clash_types ty1 ty2 =
let
val ty1' = Type.varifyT ty1;
val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2);
in Type.raw_unify (ty1', ty2') end;
fun clash_consts (c1, ty1) (c2, ty2) =
c1 = c2 andalso clash_types ty1 ty2;
(* clash_defns *)
fun clash_defn c_ty (name, tm) =
let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in
if clash_consts c_ty (c, ty') then Some (name, ty') else None
end handle TERM _ => None;
fun clash_defns c_ty axms =
distinct (mapfilter (clash_defn c_ty) axms);
(* overloading *)
datatype overloading = NoOverloading | Useless | Plain;
fun overloading sg declT defT =
let
val tsig = Sign.tsig_of sg;
val T = Term.incr_tvar (maxidx_of_typ declT + 1) (Type.varifyT defT);
in
if Type.typ_instance (tsig, declT, T) then NoOverloading
else if Type.typ_instance (tsig, Type.rem_sorts declT, Type.rem_sorts T) then Useless
else Plain
end;
(* dest_defn *)
fun dest_defn tm =
let
fun err msg = raise TERM (msg, [tm]);
val (lhs, rhs) = Logic.dest_equals (Logic.strip_imp_concl tm)
handle TERM _ => err "Not a meta-equality (==)";
val (head, args) = strip_comb lhs;
val c_ty as (c, ty) = dest_Const head
handle TERM _ => err "Head of lhs not a constant";
fun dest_free (Free (x, _)) = x
| dest_free (Const ("TYPE", Type ("itself", [TFree (x, _)]))) = x
| dest_free _ = raise Match;
val show_frees = commas_quote o map dest_free;
val show_tfrees = commas_quote o map fst;
val lhs_dups = duplicates args;
val rhs_extras = gen_rems (op =) (term_frees rhs, args);
val rhs_extrasT = gen_rems (op =) (term_tfrees rhs, typ_tfrees ty);
in
if not (forall (can dest_free) args) then
err "Arguments (on lhs) must be variables"
else if not (null lhs_dups) then
err ("Duplicate variables on lhs: " ^ show_frees lhs_dups)
else if not (null rhs_extras) then
err ("Extra variables on rhs: " ^ show_frees rhs_extras)
else if not (null rhs_extrasT) then
err ("Extra type variables on rhs: " ^ show_tfrees rhs_extrasT)
else if exists_Const (fn c_ty' => c_ty' = c_ty) rhs then
err ("Constant to be defined occurs on rhs")
else (c_ty, rhs)
end;
(* check_defn *)
fun err_in_defn sg name msg =
(error_msg msg;
error ("The error(s) above occurred in definition " ^ quote (Sign.full_name sg name)));
fun cycle_msg namess = "Cyclic dependency of constants:\n" ^
cat_lines (map (space_implode " -> " o map quote o rev) namess);
fun add_deps (c, cs) deps =
let fun declare (G, x) = Graph.new_node (x, ()) G handle Graph.DUP _ => G
in foldl declare (deps, c :: cs) |> Graph.add_deps_acyclic (c, cs) end;
fun check_defn sg overloaded ((deps, axms), def as (name, tm)) =
let
fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block
[Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sg ty]));
fun def_txt c_ty = "Definition of " ^ show_const c_ty;
fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn;
fun show_defns c = cat_lines o map (show_defn c);
val (c_ty as (c, ty), rhs) = dest_defn tm
handle TERM (msg, _) => err_in_defn sg name msg;
val c_decl =
(case Sign.const_type sg c of Some T => T
| None => err_in_defn sg name ("Undeclared constant " ^ quote c));
val clashed = clash_defns c_ty axms;
in
if not (null clashed) then
err_in_defn sg name (def_txt c_ty ^"\nclashes with "^ show_defns c clashed)
else
(case overloading sg c_decl ty of
NoOverloading =>
(add_deps (c, Term.add_term_consts (rhs, [])) deps
handle Graph.CYCLES namess => err_in_defn sg name (cycle_msg namess),
def :: axms)
| Useless =>
err_in_defn sg name (Library.setmp show_sorts true def_txt c_ty ^
"\nimposes additional sort constraints on the declared type of the constant.")
| Plain =>
(if not overloaded then
warning (def_txt c_ty ^ "\nis strictly less general than the declared type (see "
^ quote (Sign.full_name sg name) ^ ")")
else (); (deps, def :: axms)))
end;
(* add_defs *)
fun ext_defns prep_axm overloaded raw_axms thy =
let
val Theory {sign, const_deps, axioms, oracles, parents, ancestors} = thy;
val all_axioms = flat (map (Symtab.dest o #axioms o rep_theory) (thy :: ancestors));
val axms = map (prep_axm sign) raw_axms;
val (const_deps', _) = foldl (check_defn sign overloaded) ((const_deps, all_axioms), axms);
in
make_theory sign const_deps' axioms oracles parents ancestors
|> add_axioms_i axms
end;
val add_defs_i = ext_defns cert_axm;
val add_defs = ext_defns read_axm;
(** additional theory data **)
val init_data = curry (ext_sign Sign.init_data);
fun print_data kind = Sign.print_data kind o sign_of;
fun get_data kind f = Sign.get_data kind f o sign_of;
fun put_data kind f = ext_sign (Sign.put_data kind f);
(** merge theories **) (*exception ERROR*)
fun merge_sign (sg, thy) =
Sign.nontriv_merge (sg, sign_of thy) handle TERM (msg, _) => error msg;
(*merge list of theories from left to right, preparing extend*)
fun prep_ext_merge thys =
if null thys then
error "Merge: no parent theories"
else if exists is_draft thys then
error "Attempt to merge draft theories"
else
let
val sign' =
foldl merge_sign (sign_of (hd thys), tl thys)
|> Sign.prep_ext
|> Sign.add_path "/";
val depss = map (#const_deps o rep_theory) thys;
val deps' = foldl (Graph.merge_acyclic (K true)) (hd depss, tl depss)
handle Graph.CYCLES namess => error (cycle_msg namess);
val axioms' = Symtab.empty;
fun eq_ora ((_, (_, s1: stamp)), (_, (_, s2))) = s1 = s2;
val oracles' =
Symtab.make (gen_distinct eq_ora
(flat (map (Symtab.dest o #oracles o rep_theory) thys)))
handle Symtab.DUPS names => err_dup_oras names;
val parents' = gen_distinct eq_thy thys;
val ancestors' =
gen_distinct eq_thy (parents' @ flat (map ancestors_of thys));
in
make_theory sign' deps' axioms' oracles' parents' ancestors'
end;
end;
structure BasicTheory: BASIC_THEORY = Theory;
open BasicTheory;