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(* Title: Pure/theory.ML 
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ID: $Id$ 

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Author: Lawrence C Paulson and Markus Wenzel 

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Copyright 1996 University of Cambridge 

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Theories. 
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*) 
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(*this part made pervasive*) 
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signature BASIC_THEORY = 
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sig 
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type theory 
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exception THEORY of string * theory list 

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val rep_theory : theory > 

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{sign: Sign.sg, oraopt: (Sign.sg * exn > term) option, 
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new_axioms: term Symtab.table, parents: theory list} 

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val sign_of : theory > Sign.sg 
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val syn_of : theory > Syntax.syntax 

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val stamps_of_thy : theory > string ref list 

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val parents_of : theory > theory list 

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val subthy : theory * theory > bool 

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val eq_thy : theory * theory > bool 

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val proto_pure_thy : theory 

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val pure_thy : theory 

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val cpure_thy : theory 

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val cert_axm : Sign.sg > string * term > string * term 
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val read_axm : Sign.sg > string * string > string * term 
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val inferT_axm : Sign.sg > string * term > string * term 
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val merge_theories : theory * theory > theory 
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end 
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signature THEORY = 
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sig 
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include BASIC_THEORY 
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(*theory extendsion primitives*) 
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val add_classes : (class * class list) list > theory > theory 
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val add_classes_i : (class * class list) list > theory > theory 
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val add_classrel : (class * class) list > theory > theory 
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val add_classrel_i : (class * class) list > theory > theory 
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val add_defsort : sort > theory > theory 
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val add_defsort_i : sort > theory > theory 
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val add_types : (string * int * mixfix) list > theory > theory 
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val add_tyabbrs : (string * string list * string * mixfix) list 

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> theory > theory 
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val add_tyabbrs_i : (string * string list * typ * mixfix) list 
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> theory > theory 
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val add_arities : (string * sort list * sort) list > theory > theory 
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val add_arities_i : (string * sort list * sort) list > theory > theory 
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val add_consts : (string * string * mixfix) list > theory > theory 
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val add_consts_i : (string * typ * mixfix) list > theory > theory 

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val add_syntax : (string * string * mixfix) list > theory > theory 

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val add_syntax_i : (string * typ * mixfix) list > theory > theory 

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val add_modesyntax : string * bool > (string * string * mixfix) list > theory > theory 
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val add_modesyntax_i : string * bool > (string * typ * mixfix) list > theory > theory 

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val add_trfuns : 
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(string * (Syntax.ast list > Syntax.ast)) list * 
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(string * (term list > term)) list * 

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(string * (term list > term)) list * 

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(string * (Syntax.ast list > Syntax.ast)) list > theory > theory 

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val add_trfunsT : 
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(string * (typ > term list > term)) list > theory > theory 

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val add_tokentrfuns: 
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(string * string * (string > string * int)) list > theory > theory 

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val add_trrules : (string * string)Syntax.trrule list > theory > theory 
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val add_trrules_i : Syntax.ast Syntax.trrule list > theory > theory 
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val add_axioms : (string * string) list > theory > theory 

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val add_axioms_i : (string * term) list > theory > theory 

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val add_defs : (string * string) list > theory > theory 
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val add_defs_i : (string * term) list > theory > theory 
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val add_path : string > theory > theory 
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val add_space : string * string list > theory > theory 
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val add_name : string > theory > theory 
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val set_oracle : (Sign.sg * exn > term) > theory > theory 

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val merge_thy_list : bool > theory list > theory 

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end; 

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structure Theory: THEORY = 
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struct 
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(** datatype theory **) 

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datatype theory = 

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Theory of { 

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sign: Sign.sg, 

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oraopt: (Sign.sg * exn > term) option, 
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new_axioms: term Symtab.table, 
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parents: theory list}; 

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fun rep_theory (Theory args) = args; 

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(*errors involving theories*) 

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exception THEORY of string * theory list; 

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val sign_of = #sign o rep_theory; 

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val syn_of = #syn o Sign.rep_sg o sign_of; 

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(*stamps associated with a theory*) 

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val stamps_of_thy = #stamps o Sign.rep_sg o sign_of; 

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(*return the immediate ancestors*) 

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val parents_of = #parents o rep_theory; 

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(*compare theories*) 

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val subthy = Sign.subsig o pairself sign_of; 

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val eq_thy = Sign.eq_sg o pairself sign_of; 

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(* the Pure theories *) 

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val proto_pure_thy = 

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Theory {sign = Sign.proto_pure, oraopt = None, 
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new_axioms = Symtab.null, parents = []}; 

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val pure_thy = 

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Theory {sign = Sign.pure, oraopt = None, 
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new_axioms = Symtab.null, parents = []}; 

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val cpure_thy = 

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Theory {sign = Sign.cpure, oraopt = None, 
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new_axioms = Symtab.null, parents = []}; 

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(** extend theory **) 

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fun err_dup_axms names = 

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error ("Duplicate axiom name(s) " ^ commas_quote names); 

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fun ext_thy (thy as Theory {sign, oraopt, new_axioms, parents}) 
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sign1 new_axms = 

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let 
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val draft = Sign.is_draft sign; 

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val new_axioms1 = 

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Symtab.extend_new (if draft then new_axioms else Symtab.null, new_axms) 

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handle Symtab.DUPS names => err_dup_axms names; 

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val parents1 = if draft then parents else [thy]; 

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in 

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Theory {sign = sign1, oraopt = oraopt, 
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new_axioms = new_axioms1, parents = parents1} 

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end; 
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(* extend signature of a theory *) 

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fun ext_sg extfun decls (thy as Theory {sign, ...}) = 

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ext_thy thy (extfun decls sign) []; 

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val add_classes = ext_sg Sign.add_classes; 
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val add_classes_i = ext_sg Sign.add_classes_i; 
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val add_classrel = ext_sg Sign.add_classrel; 
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val add_classrel_i = ext_sg Sign.add_classrel_i; 
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val add_defsort = ext_sg Sign.add_defsort; 
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val add_defsort_i = ext_sg Sign.add_defsort_i; 
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val add_types = ext_sg Sign.add_types; 
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val add_tyabbrs = ext_sg Sign.add_tyabbrs; 

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val add_tyabbrs_i = ext_sg Sign.add_tyabbrs_i; 

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val add_arities = ext_sg Sign.add_arities; 

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val add_arities_i = ext_sg Sign.add_arities_i; 
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val add_consts = ext_sg Sign.add_consts; 
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val add_consts_i = ext_sg Sign.add_consts_i; 

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val add_syntax = ext_sg Sign.add_syntax; 

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val add_syntax_i = ext_sg Sign.add_syntax_i; 

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val add_modesyntax = curry (ext_sg Sign.add_modesyntax); 

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val add_modesyntax_i = curry (ext_sg Sign.add_modesyntax_i); 

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val add_trfuns = ext_sg Sign.add_trfuns; 

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val add_trfunsT = ext_sg Sign.add_trfunsT; 
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val add_tokentrfuns = ext_sg Sign.add_tokentrfuns; 
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val add_trrules = ext_sg Sign.add_trrules; 
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val add_trrules_i = ext_sg Sign.add_trrules_i; 

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val add_path = ext_sg Sign.add_path; 
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val add_space = ext_sg Sign.add_space; 
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val add_name = ext_sg Sign.add_name; 
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(* prepare axioms *) 

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fun err_in_axm name = 

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error ("The error(s) above occurred in axiom " ^ quote name); 

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fun no_vars tm = 

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if null (term_vars tm) andalso null (term_tvars tm) then tm 

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else error "Illegal schematic variable(s) in term"; 

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fun cert_axm sg (name, raw_tm) = 

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let 

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val (t, T, _) = Sign.certify_term sg raw_tm 

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handle TYPE (msg, _, _) => error msg 
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 TERM (msg, _) => error msg; 
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in 

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assert (T = propT) "Term not of type prop"; 

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(name, no_vars t) 

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end 

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handle ERROR => err_in_axm name; 

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(*Some duplication of code with read_def_cterm*) 

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fun read_axm sg (name, str) = 

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let val ts = Syntax.read (#syn (Sign.rep_sg sg)) propT str; 

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val (_, t, _) = 

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Sign.infer_types sg (K None) (K None) [] true (ts,propT); 

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in cert_axm sg (name,t) end 
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handle ERROR => err_in_axm name; 
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fun inferT_axm sg (name, pre_tm) = 

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let val t = #2(Sign.infer_types sg (K None) (K None) [] true 

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([pre_tm], propT)) 

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in (name, no_vars t) end 

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handle ERROR => err_in_axm name; 

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(* extend axioms of a theory *) 

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fun ext_axms prep_axm axms (thy as Theory {sign, ...}) = 

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let 

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val sign1 = Sign.make_draft sign; 

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val axioms = map (apsnd (Term.compress_term o Logic.varify) o 

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prep_axm sign) 

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axms; 

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in 

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ext_thy thy sign1 axioms 

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end; 

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val add_axioms = ext_axms read_axm; 

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val add_axioms_i = ext_axms cert_axm; 

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(** add constant definitions **) 
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(* all_axioms_of *) 
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(*results may contain duplicates!*) 
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fun ancestry_of thy = 
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thy :: List.concat (map ancestry_of (parents_of thy)); 
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val all_axioms_of = 
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List.concat o map (Symtab.dest o #new_axioms o rep_theory) o ancestry_of; 
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(* clash_types, clash_consts *) 
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(*check if types have common instance (ignoring sorts)*) 
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fun clash_types ty1 ty2 = 
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let 
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val ty1' = Type.varifyT ty1; 
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val ty2' = incr_tvar (maxidx_of_typ ty1' + 1) (Type.varifyT ty2); 
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in 
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Type.raw_unify (ty1', ty2') 
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end; 
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fun clash_consts (c1, ty1) (c2, ty2) = 
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c1 = c2 andalso clash_types ty1 ty2; 
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(* clash_defns *) 
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fun clash_defn c_ty (name, tm) = 
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let val (c, ty') = dest_Const (head_of (fst (Logic.dest_equals tm))) in 
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if clash_consts c_ty (c, ty') then Some (name, ty') else None 
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end handle TERM _ => None; 
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fun clash_defns c_ty axms = 
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distinct (mapfilter (clash_defn c_ty) axms); 
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(* dest_defn *) 
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fun dest_defn tm = 
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let 
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fun err msg = raise TERM (msg, [tm]); 
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277 

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val (lhs, rhs) = Logic.dest_equals (Logic.strip_imp_concl tm) 
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handle TERM _ => err "Not a metaequality (==)"; 
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val (head, args) = strip_comb lhs; 
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val (c, ty) = dest_Const head 
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handle TERM _ => err "Head of lhs not a constant"; 
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283 

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fun occs_const (Const c_ty') = (c_ty' = (c, ty)) 
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 occs_const (Abs (_, _, t)) = occs_const t 
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 occs_const (t $ u) = occs_const t orelse occs_const u 
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 occs_const _ = false; 
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val show_frees = commas_quote o map (fst o dest_Free); 
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val show_tfrees = commas_quote o map fst; 
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291 

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val lhs_dups = duplicates args; 
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val rhs_extras = gen_rems (op =) (term_frees rhs, args); 
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val rhs_extrasT = gen_rems (op =) (term_tfrees rhs, typ_tfrees ty); 
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in 
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if not (forall is_Free args) then 
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err "Arguments (on lhs) must be variables" 
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else if not (null lhs_dups) then 
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err ("Duplicate variables on lhs: " ^ show_frees lhs_dups) 
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else if not (null rhs_extras) then 
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err ("Extra variables on rhs: " ^ show_frees rhs_extras) 
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else if not (null rhs_extrasT) then 
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err ("Extra type variables on rhs: " ^ show_tfrees rhs_extrasT) 
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else if occs_const rhs then 
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err ("Constant to be defined occurs on rhs") 
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else (c, ty) 
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end; 
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309 

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(* check_defn *) 
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fun err_in_defn name msg = 
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(writeln msg; error ("The error(s) above occurred in definition " ^ quote name)); 
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fun check_defn sign (axms, (name, tm)) = 
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let 
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fun show_const (c, ty) = quote (Pretty.string_of (Pretty.block 
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[Pretty.str (c ^ " ::"), Pretty.brk 1, Sign.pretty_typ sign ty])); 
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fun show_defn c (dfn, ty') = show_const (c, ty') ^ " in " ^ dfn; 
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fun show_defns c = cat_lines o map (show_defn c); 
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val (c, ty) = dest_defn tm 
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handle TERM (msg, _) => err_in_defn name msg; 
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val defns = clash_defns (c, ty) axms; 
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in 
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if not (null defns) then 
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err_in_defn name ("Definition of " ^ show_const (c, ty) ^ 
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"\nclashes with " ^ show_defns c defns) 
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else (name, tm) :: axms 
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end; 
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(* add_defs *) 
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335 

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fun ext_defns prep_axm raw_axms thy = 
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let 
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val axms = map (prep_axm (sign_of thy)) raw_axms; 
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val all_axms = all_axioms_of thy; 
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in 
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foldl (check_defn (sign_of thy)) (all_axms, axms); 
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add_axioms_i axms thy 
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end; 
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val add_defs_i = ext_defns cert_axm; 
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val add_defs = ext_defns read_axm; 
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1539  350 
(** Set oracle of theory **) 
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(* FIXME support more than one oracle (!?) *) 
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fun set_oracle oracle 
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(thy as Theory {sign, oraopt = None, new_axioms, parents}) = 
356 
if Sign.is_draft sign then 

357 
Theory {sign = sign, 

358 
oraopt = Some oracle, 

359 
new_axioms = new_axioms, 

360 
parents = parents} 

361 
else raise THEORY ("Can only set oracle of a draft", [thy]) 

362 
 set_oracle _ thy = raise THEORY ("Oracle already set", [thy]); 

363 

1526  364 

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1526  366 
(** merge theories **) 
367 

368 
fun merge_thy_list mk_draft thys = 

369 
let 

370 
fun is_union thy = forall (fn t => subthy (t, thy)) thys; 

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val is_draft = Sign.is_draft o sign_of; 

372 

373 
fun add_sign (sg, Theory {sign, ...}) = 

374 
Sign.merge (sg, sign) handle TERM (msg, _) => error msg; 

375 
in 

1539  376 
case (find_first is_union thys, exists is_draft thys) of 
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(Some thy, _) => thy 
378 
 (None, true) => raise THEORY ("Illegal merge of draft theories", thys) 

379 
 (None, false) => Theory { 

380 
sign = 

381 
(if mk_draft then Sign.make_draft else I) 

382 
(foldl add_sign (Sign.proto_pure, thys)), 

1539  383 
oraopt = None, 
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new_axioms = Symtab.null, 
1539  385 
parents = thys} 
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end; 
387 

388 
fun merge_theories (thy1, thy2) = merge_thy_list false [thy1, thy2]; 

389 

390 

391 
end; 

392 

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structure BasicTheory: BASIC_THEORY = Theory; 
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open BasicTheory; 