author | wenzelm |
Sun, 07 May 2006 00:22:05 +0200 | |
changeset 19585 | 70a1ce3b23ae |
parent 19574 | 7c761751e998 |
child 19642 | ea7162f84677 |
permissions | -rw-r--r-- |
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axiomatic type class 'package' for Pure (alpha version);
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(* Title: Pure/axclass.ML |
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axiomatic type class 'package' for Pure (alpha version);
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parents:
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ID: $Id$ |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
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Author: Markus Wenzel, TU Muenchen |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
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parents:
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19511 | 5 |
Type classes as parameter records and predicates, with explicit |
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definitions and proofs. |
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axiomatic type class 'package' for Pure (alpha version);
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parents:
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*) |
dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
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parents:
diff
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dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
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parents:
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signature AX_CLASS = |
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sig |
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val get_definition: theory -> class -> {def: thm, intro: thm, axioms: thm list} |
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val class_intros: theory -> thm list |
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val params_of: theory -> class -> string list |
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val all_params_of: theory -> sort -> string list |
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val print_axclasses: theory -> unit |
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val cert_classrel: theory -> class * class -> class * class |
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val read_classrel: theory -> xstring * xstring -> class * class |
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val add_classrel: thm -> theory -> theory |
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val add_arity: thm -> theory -> theory |
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val prove_classrel: class * class -> tactic -> theory -> theory |
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val prove_arity: string * sort list * sort -> tactic -> theory -> theory |
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val define_class: bstring * xstring list -> string list -> |
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((bstring * Attrib.src list) * string list) list -> theory -> class * theory |
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val define_class_i: bstring * class list -> string list -> |
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((bstring * attribute list) * term list) list -> theory -> class * theory |
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val axiomatize_class: bstring * xstring list -> theory -> theory |
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val axiomatize_class_i: bstring * class list -> theory -> theory |
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val axiomatize_classrel: (xstring * xstring) list -> theory -> theory |
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val axiomatize_classrel_i: (class * class) list -> theory -> theory |
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val axiomatize_arity: xstring * string list * string -> theory -> theory |
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val axiomatize_arity_i: arity -> theory -> theory |
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type cache |
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val cache: cache |
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val of_sort: theory -> typ * sort -> cache -> thm list * cache (*exception Sorts.CLASS_ERROR*) |
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end; |
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axiomatic type class 'package' for Pure (alpha version);
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parents:
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structure AxClass: AX_CLASS = |
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dd3d3d6467db
axiomatic type class 'package' for Pure (alpha version);
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parents:
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struct |
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axiomatic type class 'package' for Pure (alpha version);
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parents:
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(** theory data **) |
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(* class parameters (canonical order) *) |
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type param = string * class; |
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fun add_param pp ((x, c): param) params = |
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(case AList.lookup (op =) params x of |
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NONE => (x, c) :: params |
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| SOME c' => error ("Duplicate class parameter " ^ quote x ^ |
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" for " ^ Pretty.string_of_sort pp [c] ^ |
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(if c = c' then "" else " and " ^ Pretty.string_of_sort pp [c']))); |
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fun merge_params _ ([], qs) = qs |
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| merge_params pp (ps, qs) = |
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fold_rev (fn q => if member (op =) ps q then I else add_param pp q) qs ps; |
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||
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(* axclasses *) |
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val introN = "intro"; |
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val superN = "super"; |
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val axiomsN = "axioms"; |
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datatype axclass = AxClass of |
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{def: thm, |
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intro: thm, |
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axioms: thm list}; |
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||
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type axclasses = axclass Symtab.table * param list; |
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fun make_axclass (def, intro, axioms) = |
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AxClass {def = def, intro = intro, axioms = axioms}; |
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fun merge_axclasses pp ((tab1, params1), (tab2, params2)) : axclasses = |
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(Symtab.merge (K true) (tab1, tab2), merge_params pp (params1, params2)); |
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(* instances *) |
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val classrelN = "classrel"; |
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val arityN = "arity"; |
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type instances = |
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((class * class) * thm) list * |
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((class * sort list) * thm) list Symtab.table; |
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fun merge_instances ((classrel1, arities1): instances, (classrel2, arities2)) = |
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(merge (eq_fst op =) (classrel1, classrel2), |
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Symtab.join (K (merge (eq_fst op =))) (arities1, arities2)); |
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(* setup data *) |
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structure AxClassData = TheoryDataFun |
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(struct |
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val name = "Pure/axclass"; |
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type T = axclasses * instances; |
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val empty : T = ((Symtab.empty, []), ([], Symtab.empty)); |
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val copy = I; |
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val extend = I; |
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fun merge pp ((axclasses1, instances1), (axclasses2, instances2)) = |
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(merge_axclasses pp (axclasses1, axclasses2), (merge_instances (instances1, instances2))); |
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fun print _ _ = (); |
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end); |
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val _ = Context.add_setup AxClassData.init; |
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(* maintain axclasses *) |
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val get_axclasses = #1 o AxClassData.get; |
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fun map_axclasses f = AxClassData.map (apfst f); |
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val lookup_def = Symtab.lookup o #1 o get_axclasses; |
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fun get_definition thy c = |
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(case lookup_def thy c of |
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SOME (AxClass info) => info |
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| NONE => error ("Undefined type class " ^ quote c)); |
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fun class_intros thy = |
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let |
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fun add_intro c = |
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(case lookup_def thy c of SOME (AxClass {intro, ...}) => cons intro | _ => I); |
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val classes = Sign.classes thy; |
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in map (Thm.class_triv thy) classes @ fold add_intro classes [] end; |
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fun get_params thy pred = |
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let val params = #2 (get_axclasses thy); |
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in fold (fn (x, c) => if pred c then cons x else I) params [] end; |
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fun params_of thy c = get_params thy (fn c' => c' = c); |
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fun all_params_of thy S = get_params thy (fn c => Sign.subsort thy (S, [c])); |
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(* maintain instances *) |
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val get_instances = #2 o AxClassData.get; |
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fun map_instances f = AxClassData.map (apsnd f); |
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fun the_classrel thy (c1, c2) = |
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(case AList.lookup (op =) (#1 (get_instances thy)) (c1, c2) of |
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SOME th => Thm.transfer thy th |
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| NONE => error ("Unproven class relation " ^ Sign.string_of_classrel thy [c1, c2])); |
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fun put_classrel arg = map_instances (fn (classrel, arities) => |
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(insert (eq_fst op =) arg classrel, arities)); |
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fun the_arity thy a (c, Ss) = |
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(case AList.lookup (op =) (Symtab.lookup_list (#2 (get_instances thy)) a) (c, Ss) of |
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SOME th => Thm.transfer thy th |
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| NONE => error ("Unproven type arity " ^ Sign.string_of_arity thy (a, Ss, [c]))); |
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fun put_arity ((t, Ss, c), th) = map_instances (fn (classrel, arities) => |
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(classrel, arities |> Symtab.insert_list (eq_fst op =) (t, ((c, Ss), th)))); |
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(* print data *) |
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fun print_axclasses thy = |
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let |
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val axclasses = #1 (get_axclasses thy); |
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val ctxt = ProofContext.init thy; |
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fun pretty_axclass (class, AxClass {def, intro, axioms}) = |
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Pretty.block (Pretty.fbreaks |
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[Pretty.block |
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[Pretty.str "class ", ProofContext.pretty_sort ctxt [class], Pretty.str ":"], |
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Pretty.strs ("parameters:" :: params_of thy class), |
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ProofContext.pretty_fact ctxt ("def", [def]), |
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ProofContext.pretty_fact ctxt (introN, [intro]), |
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ProofContext.pretty_fact ctxt (axiomsN, axioms)]); |
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in Pretty.writeln (Pretty.chunks (map pretty_axclass (Symtab.dest axclasses))) end; |
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axiomatic type class 'package' for Pure (alpha version);
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parents:
diff
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(** instances **) |
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(* class relations *) |
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fun cert_classrel thy raw_rel = |
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sane interfaces for tactical instance proofs (do not expand defs of theory, proper handling of sort instances);
wenzelm
parents:
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diff
changeset
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let |
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val (c1, c2) = pairself (Sign.certify_class thy) raw_rel; |
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val _ = Type.add_classrel (Sign.pp thy) (c1, c2) (Sign.tsig_of thy); |
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val _ = |
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(case subtract (op =) (all_params_of thy [c1]) (all_params_of thy [c2]) of |
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[] => () |
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| xs => raise TYPE ("Class " ^ Sign.string_of_sort thy [c1] ^ " lacks parameter(s) " ^ |
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commas_quote xs ^ " of " ^ Sign.string_of_sort thy [c2], [], [])); |
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in (c1, c2) end; |
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fun read_classrel thy raw_rel = |
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cert_classrel thy (pairself (Sign.read_class thy) raw_rel) |
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handle TYPE (msg, _, _) => error msg; |
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(* primitive rules *) |
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fun add_classrel th thy = |
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let |
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fun err () = raise THM ("add_classrel: malformed class relation", 0, [th]); |
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val prop = Drule.plain_prop_of (Thm.transfer thy th); |
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val rel = Logic.dest_classrel prop handle TERM _ => err (); |
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val (c1, c2) = cert_classrel thy rel handle TYPE _ => err (); |
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in |
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thy |
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|> Sign.primitive_classrel (c1, c2) |
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|> put_classrel ((c1, c2), Drule.unconstrainTs th) |
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end; |
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wenzelm
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changeset
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fun add_arity th thy = |
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parents:
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diff
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let |
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fun err () = raise THM ("add_arity: malformed type arity", 0, [th]); |
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val prop = Drule.plain_prop_of (Thm.transfer thy th); |
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val (t, Ss, c) = Logic.dest_arity prop handle TERM _ => err (); |
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val _ = if map (Sign.certify_sort thy) Ss = Ss then () else err (); |
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in |
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thy |
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|> Sign.primitive_arity (t, Ss, [c]) |
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|> put_arity ((t, Ss, c), Drule.unconstrainTs th) |
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end; |
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axiomatic type class 'package' for Pure (alpha version);
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parents:
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axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
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(* tactical proofs *) |
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fun prove_classrel raw_rel tac thy = |
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let |
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val (c1, c2) = cert_classrel thy raw_rel; |
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val th = Goal.prove thy [] [] (Logic.mk_classrel (c1, c2)) (fn _ => tac) handle ERROR msg => |
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changeset
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cat_error msg ("The error(s) above occurred while trying to prove class relation " ^ |
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quote (Sign.string_of_classrel thy [c1, c2])); |
19511 | 235 |
in |
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thy |
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|> PureThy.add_thms [((classrelN ^ "_" ^ serial_string (), th), [])] |
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|-> (fn [th'] => add_classrel th') |
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end; |
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axiomatic type class 'package' for Pure (alpha version);
wenzelm
parents:
diff
changeset
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changeset
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fun prove_arity raw_arity tac thy = |
15876
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wenzelm
parents:
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diff
changeset
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let |
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diff
changeset
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243 |
val arity = Sign.cert_arity thy raw_arity; |
19405 | 244 |
val props = Logic.mk_arities arity; |
17956 | 245 |
val ths = Goal.prove_multi thy [] [] props |
18678 | 246 |
(fn _ => Tactic.precise_conjunction_tac (length props) 1 THEN tac) handle ERROR msg => |
19243
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moved read_class, read/cert_classrel/arity to sign.ML;
wenzelm
parents:
19134
diff
changeset
|
247 |
cat_error msg ("The error(s) above occurred while trying to prove type arity " ^ |
5dcb899a8486
moved read_class, read/cert_classrel/arity to sign.ML;
wenzelm
parents:
19134
diff
changeset
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248 |
quote (Sign.string_of_arity thy arity)); |
19511 | 249 |
in |
250 |
thy |
|
251 |
|> PureThy.add_thms (ths |> map (fn th => ((arityN ^ "_" ^ serial_string (), th), []))) |
|
252 |
|-> fold add_arity |
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253 |
end; |
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257 |
(** class definitions **) |
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259 |
local |
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260 |
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261 |
fun def_class prep_class prep_att prep_propp |
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262 |
(bclass, raw_super) params raw_specs thy = |
|
263 |
let |
|
264 |
val ctxt = ProofContext.init thy; |
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265 |
val pp = ProofContext.pp ctxt; |
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266 |
||
267 |
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268 |
(* prepare specification *) |
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269 |
||
270 |
val bconst = Logic.const_of_class bclass; |
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271 |
val class = Sign.full_name thy bclass; |
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272 |
val super = map (prep_class thy) raw_super |> Sign.certify_sort thy; |
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274 |
fun prep_axiom t = |
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275 |
(case Term.add_tfrees t [] of |
|
276 |
[(a, S)] => |
|
277 |
if Sign.subsort thy (super, S) then t |
|
278 |
else error ("Sort constraint of type variable " ^ |
|
279 |
setmp show_sorts true (Pretty.string_of_typ pp) (TFree (a, S)) ^ |
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280 |
" needs to be weaker than " ^ Pretty.string_of_sort pp super) |
|
281 |
| [] => t |
|
282 |
| _ => error ("Multiple type variables in class axiom:\n" ^ Pretty.string_of_term pp t)) |
|
283 |
|> map_term_types (Term.map_atyps (fn TFree _ => Term.aT [] | U => U)) |
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284 |
|> Logic.close_form; |
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285 |
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19585 | 286 |
val axiomss = prep_propp (ctxt, map (map (rpair []) o snd) raw_specs) |
19511 | 287 |
|> snd |> map (map (prep_axiom o fst)); |
288 |
val name_atts = Attrib.map_specs (prep_att thy) raw_specs |> map fst; |
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289 |
||
290 |
||
291 |
(* definition *) |
|
292 |
||
293 |
val conjs = map (curry Logic.mk_inclass (Term.aT [])) super @ flat axiomss; |
|
294 |
val class_eq = |
|
295 |
Logic.mk_equals (Logic.mk_inclass (Term.aT [], class), Logic.mk_conjunction_list conjs); |
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296 |
||
297 |
val ([def], def_thy) = |
|
298 |
thy |
|
299 |
|> Sign.primitive_class (bclass, super) |
|
300 |
|> PureThy.add_defs_i false [((Thm.def_name bconst, class_eq), [])]; |
|
301 |
val (raw_intro, (raw_classrel, raw_axioms)) = |
|
302 |
(Conjunction.split_defined (length conjs) def) ||> chop (length super); |
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19392 | 303 |
|
19418
03b01c9314fc
reworded add_axclass(_i): canonical specification format,
wenzelm
parents:
19405
diff
changeset
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304 |
|
19511 | 305 |
(* facts *) |
306 |
||
307 |
val class_triv = Thm.class_triv def_thy class; |
|
308 |
val ([(_, [intro]), (_, classrel), (_, axioms)], facts_thy) = |
|
309 |
def_thy |
|
310 |
|> PureThy.note_thmss_qualified "" bconst |
|
311 |
[((introN, []), [([Drule.standard raw_intro], [])]), |
|
312 |
((superN, []), [(map Drule.standard raw_classrel, [])]), |
|
313 |
((axiomsN, []), [(map (fn th => Drule.standard (class_triv RS th)) raw_axioms, [])])]; |
|
314 |
||
315 |
||
316 |
(* result *) |
|
317 |
||
318 |
val result_thy = |
|
319 |
facts_thy |
|
19574 | 320 |
|> fold put_classrel (map (pair class) super ~~ classrel) |
19511 | 321 |
|> Sign.add_path bconst |
322 |
|> PureThy.note_thmss_i "" (name_atts ~~ map Thm.simple_fact (unflat axiomss axioms)) |> snd |
|
323 |
|> Sign.restore_naming facts_thy |
|
19574 | 324 |
|> map_axclasses (fn (axclasses, parameters) => |
19511 | 325 |
(Symtab.update (class, make_axclass (def, intro, axioms)) axclasses, |
19574 | 326 |
fold (fn x => add_param pp (x, class)) params parameters)); |
19511 | 327 |
|
328 |
in (class, result_thy) end; |
|
329 |
||
330 |
in |
|
331 |
||
332 |
val define_class = def_class Sign.read_class Attrib.attribute ProofContext.read_propp; |
|
333 |
val define_class_i = def_class Sign.certify_class (K I) ProofContext.cert_propp; |
|
334 |
||
335 |
end; |
|
336 |
||
337 |
||
19531 | 338 |
|
19511 | 339 |
(** axiomatizations **) |
340 |
||
341 |
local |
|
342 |
||
343 |
fun axiomatize kind add prep arg thy = |
|
344 |
let val specs = arg |> prep thy |> map (fn prop => ((kind ^ "_" ^ serial_string (), prop), [])) |
|
345 |
in thy |> PureThy.add_axioms_i specs |-> fold add end; |
|
346 |
||
347 |
fun ax_classrel prep = |
|
348 |
axiomatize classrelN add_classrel (fn thy => map (prep thy #> Logic.mk_classrel)); |
|
349 |
||
350 |
fun ax_arity prep = |
|
351 |
axiomatize arityN add_arity (fn thy => prep thy #> Logic.mk_arities); |
|
352 |
||
353 |
fun ax_class prep_class prep_classrel (bclass, raw_super) thy = |
|
354 |
let |
|
355 |
val class = Sign.full_name thy bclass; |
|
356 |
val super = map (prep_class thy) raw_super |> Sign.certify_sort thy; |
|
357 |
in |
|
358 |
thy |
|
359 |
|> Sign.primitive_class (bclass, super) |
|
360 |
|> ax_classrel prep_classrel (map (fn c => (class, c)) super) |
|
361 |
end; |
|
362 |
||
363 |
in |
|
364 |
||
365 |
val axiomatize_class = ax_class Sign.read_class read_classrel; |
|
366 |
val axiomatize_class_i = ax_class Sign.certify_class cert_classrel; |
|
367 |
val axiomatize_classrel = ax_classrel read_classrel; |
|
368 |
val axiomatize_classrel_i = ax_classrel cert_classrel; |
|
369 |
val axiomatize_arity = ax_arity Sign.read_arity; |
|
370 |
val axiomatize_arity_i = ax_arity Sign.cert_arity; |
|
371 |
||
372 |
end; |
|
373 |
||
374 |
||
375 |
||
376 |
(** explicit derivations -- cached **) |
|
377 |
||
19574 | 378 |
datatype cache = Types of (class * thm) list Typtab.table; |
379 |
val cache = Types Typtab.empty; |
|
380 |
||
19511 | 381 |
local |
19503 | 382 |
|
19574 | 383 |
fun lookup_type (Types cache) = AList.lookup (op =) o Typtab.lookup_list cache; |
384 |
fun insert_type T der (Types cache) = Types (Typtab.insert_list (eq_fst op =) (T, der) cache); |
|
19503 | 385 |
|
19522 | 386 |
fun derive_type _ (_, []) = [] |
387 |
| derive_type thy (typ, sort) = |
|
388 |
let |
|
19528 | 389 |
val vars = Term.fold_atyps |
19522 | 390 |
(fn T as TFree (_, S) => insert (eq_fst op =) (T, S) |
391 |
| T as TVar (_, S) => insert (eq_fst op =) (T, S) |
|
19528 | 392 |
| _ => I) typ []; |
19574 | 393 |
val hyps = vars |
394 |
|> map (fn (T, S) => (T, Drule.sort_triv thy (T, S) ~~ S)); |
|
19528 | 395 |
val ths = (typ, sort) |
396 |
|> Sorts.of_sort_derivation (Sign.pp thy) (Sign.classes_of thy, Sign.arities_of thy) |
|
19574 | 397 |
{classrel = |
398 |
fn (th, c1) => fn c2 => th RS the_classrel thy (c1, c2), |
|
399 |
constructor = |
|
400 |
fn a => fn dom => fn c => |
|
401 |
let val Ss = map (map snd) dom and ths = maps (map fst) dom |
|
402 |
in ths MRS the_arity thy a (c, Ss) end, |
|
403 |
variable = |
|
404 |
the_default [] o AList.lookup (op =) hyps}; |
|
405 |
in ths end; |
|
19503 | 406 |
|
19511 | 407 |
in |
408 |
||
19574 | 409 |
fun of_sort thy (typ, sort) cache = |
410 |
let |
|
411 |
val sort' = filter (is_none o lookup_type cache typ) sort; |
|
412 |
val ths' = derive_type thy (typ, sort') |
|
413 |
handle ERROR msg => cat_error msg ("The error(s) above occurred for sort derivation: " ^ |
|
414 |
Sign.string_of_typ thy typ ^ " :: " ^ Sign.string_of_sort thy sort'); |
|
415 |
val cache' = cache |> fold (insert_type typ) (sort' ~~ ths'); |
|
416 |
val ths = |
|
417 |
sort |> map (fn c => |
|
418 |
Goal.finish (the (lookup_type cache' typ c) RS |
|
419 |
Goal.init (Thm.cterm_of thy (Logic.mk_inclass (typ, c)))) |
|
420 |
|> Thm.adjust_maxidx_thm); |
|
421 |
in (ths, cache') end; |
|
19503 | 422 |
|
19511 | 423 |
end; |
19418
03b01c9314fc
reworded add_axclass(_i): canonical specification format,
wenzelm
parents:
19405
diff
changeset
|
424 |
|
15876
a67343c6ab2a
sane interfaces for tactical instance proofs (do not expand defs of theory, proper handling of sort instances);
wenzelm
parents:
15853
diff
changeset
|
425 |
end; |