wenzelm@22362: (* Title: Pure/more_thm.ML wenzelm@22362: ID: $Id$ wenzelm@22362: Author: Makarius wenzelm@22362: wenzelm@22907: Further operations on type ctyp/cterm/thm, outside the inference kernel. wenzelm@22362: *) wenzelm@22362: wenzelm@23169: infix aconvc; wenzelm@23169: wenzelm@22362: signature THM = wenzelm@22362: sig wenzelm@22362: include THM wenzelm@24948: val aconvc: cterm * cterm -> bool wenzelm@23491: val add_cterm_frees: cterm -> cterm list -> cterm list wenzelm@22907: val mk_binop: cterm -> cterm -> cterm -> cterm wenzelm@22907: val dest_binop: cterm -> cterm * cterm wenzelm@22907: val dest_implies: cterm -> cterm * cterm wenzelm@22907: val dest_equals: cterm -> cterm * cterm wenzelm@22907: val dest_equals_lhs: cterm -> cterm wenzelm@22907: val dest_equals_rhs: cterm -> cterm wenzelm@22907: val lhs_of: thm -> cterm wenzelm@22907: val rhs_of: thm -> cterm wenzelm@22362: val thm_ord: thm * thm -> order wenzelm@23599: val is_reflexive: thm -> bool wenzelm@22362: val eq_thm: thm * thm -> bool wenzelm@22362: val eq_thms: thm list * thm list -> bool wenzelm@22362: val eq_thm_thy: thm * thm -> bool wenzelm@22362: val eq_thm_prop: thm * thm -> bool wenzelm@22362: val equiv_thm: thm * thm -> bool wenzelm@24048: val is_dummy: thm -> bool wenzelm@22695: val plain_prop_of: thm -> term wenzelm@22695: val fold_terms: (term -> 'a -> 'a) -> thm -> 'a -> 'a wenzelm@24048: val add_thm: thm -> thm list -> thm list wenzelm@24048: val del_thm: thm -> thm list -> thm list wenzelm@24048: val merge_thms: thm list * thm list -> thm list wenzelm@22362: val axiomK: string wenzelm@22362: val assumptionK: string wenzelm@22362: val definitionK: string wenzelm@22362: val theoremK: string wenzelm@22362: val lemmaK: string wenzelm@22362: val corollaryK: string wenzelm@22362: val internalK: string wenzelm@22362: val rule_attribute: (Context.generic -> thm -> thm) -> attribute wenzelm@22362: val declaration_attribute: (thm -> Context.generic -> Context.generic) -> attribute wenzelm@22362: val theory_attributes: attribute list -> theory * thm -> theory * thm wenzelm@22362: val proof_attributes: attribute list -> Proof.context * thm -> Proof.context * thm wenzelm@22362: val no_attributes: 'a -> 'a * 'b list wenzelm@22362: val simple_fact: 'a -> ('a * 'b list) list wenzelm@22682: val read_def_cterms: wenzelm@22682: theory * (indexname -> typ option) * (indexname -> sort option) -> wenzelm@22682: string list -> bool -> (string * typ)list wenzelm@22682: -> cterm list * (indexname * typ)list wenzelm@22682: val read_cterm: theory -> string * typ -> cterm wenzelm@24980: val elim_implies: thm -> thm -> thm wenzelm@24980: val unvarify: thm -> thm wenzelm@26628: val close_derivation: thm -> thm wenzelm@24980: val add_axiom: term list -> bstring * term -> theory -> thm * theory haftmann@25518: val add_def: bool -> bool -> bstring * term -> theory -> thm * theory wenzelm@22362: end; wenzelm@22362: wenzelm@22362: structure Thm: THM = wenzelm@22362: struct wenzelm@22362: wenzelm@22695: (** basic operations **) wenzelm@22362: wenzelm@23491: (* collecting cterms *) wenzelm@23491: wenzelm@23491: val op aconvc = op aconv o pairself Thm.term_of; wenzelm@23491: wenzelm@23491: fun add_cterm_frees ct = wenzelm@23491: let wenzelm@23491: val cert = Thm.cterm_of (Thm.theory_of_cterm ct); wenzelm@23491: val t = Thm.term_of ct; wenzelm@23491: in Term.fold_aterms (fn v as Free _ => insert (op aconvc) (cert v) | _ => I) t end; wenzelm@23491: wenzelm@23491: wenzelm@22907: (* cterm constructors and destructors *) wenzelm@22907: wenzelm@22907: fun mk_binop c a b = Thm.capply (Thm.capply c a) b; wenzelm@22907: fun dest_binop ct = (Thm.dest_arg1 ct, Thm.dest_arg ct); wenzelm@22907: wenzelm@22907: fun dest_implies ct = wenzelm@22907: (case Thm.term_of ct of wenzelm@22907: Const ("==>", _) $ _ $ _ => dest_binop ct wenzelm@22907: | _ => raise TERM ("dest_implies", [Thm.term_of ct])); wenzelm@22907: wenzelm@22907: fun dest_equals ct = wenzelm@22907: (case Thm.term_of ct of wenzelm@22907: Const ("==", _) $ _ $ _ => dest_binop ct wenzelm@22907: | _ => raise TERM ("dest_equals", [Thm.term_of ct])); wenzelm@22907: wenzelm@22907: fun dest_equals_lhs ct = wenzelm@22907: (case Thm.term_of ct of wenzelm@22907: Const ("==", _) $ _ $ _ => Thm.dest_arg1 ct wenzelm@22907: | _ => raise TERM ("dest_equals_lhs", [Thm.term_of ct])); wenzelm@22907: wenzelm@22907: fun dest_equals_rhs ct = wenzelm@22907: (case Thm.term_of ct of wenzelm@22907: Const ("==", _) $ _ $ _ => Thm.dest_arg ct wenzelm@22907: | _ => raise TERM ("dest_equals_rhs", [Thm.term_of ct])); wenzelm@22907: wenzelm@22907: val lhs_of = dest_equals_lhs o Thm.cprop_of; wenzelm@22907: val rhs_of = dest_equals_rhs o Thm.cprop_of; wenzelm@22907: wenzelm@22907: wenzelm@22907: (* thm order: ignores theory context! *) wenzelm@22682: wenzelm@22362: fun thm_ord (th1, th2) = wenzelm@22362: let wenzelm@22362: val {shyps = shyps1, hyps = hyps1, tpairs = tpairs1, prop = prop1, ...} = Thm.rep_thm th1; wenzelm@22362: val {shyps = shyps2, hyps = hyps2, tpairs = tpairs2, prop = prop2, ...} = Thm.rep_thm th2; wenzelm@22362: in wenzelm@22362: (case Term.fast_term_ord (prop1, prop2) of wenzelm@22362: EQUAL => wenzelm@22362: (case list_ord (prod_ord Term.fast_term_ord Term.fast_term_ord) (tpairs1, tpairs2) of wenzelm@22362: EQUAL => wenzelm@22362: (case list_ord Term.fast_term_ord (hyps1, hyps2) of wenzelm@22362: EQUAL => list_ord Term.sort_ord (shyps1, shyps2) wenzelm@22362: | ord => ord) wenzelm@22362: | ord => ord) wenzelm@22362: | ord => ord) wenzelm@22362: end; wenzelm@22362: wenzelm@22682: wenzelm@22682: (* equality *) wenzelm@22682: wenzelm@23599: fun is_reflexive th = op aconv (Logic.dest_equals (Thm.prop_of th)) wenzelm@23599: handle TERM _ => false; wenzelm@23599: wenzelm@22362: fun eq_thm ths = wenzelm@22362: Context.joinable (pairself Thm.theory_of_thm ths) andalso wenzelm@22362: thm_ord ths = EQUAL; wenzelm@22362: wenzelm@22362: val eq_thms = eq_list eq_thm; wenzelm@22362: wenzelm@22362: val eq_thm_thy = eq_thy o pairself Thm.theory_of_thm; wenzelm@22362: val eq_thm_prop = op aconv o pairself Thm.full_prop_of; wenzelm@22362: wenzelm@22682: wenzelm@22682: (* pattern equivalence *) wenzelm@22682: wenzelm@22362: fun equiv_thm ths = wenzelm@22362: Pattern.equiv (Theory.merge (pairself Thm.theory_of_thm ths)) (pairself Thm.full_prop_of ths); wenzelm@22362: wenzelm@22362: wenzelm@22695: (* misc operations *) wenzelm@22695: wenzelm@24048: fun is_dummy thm = wenzelm@24048: (case try Logic.dest_term (Thm.concl_of thm) of wenzelm@24048: NONE => false wenzelm@24048: | SOME t => Term.is_dummy_pattern t); wenzelm@24048: wenzelm@22695: fun plain_prop_of raw_thm = wenzelm@22695: let wenzelm@22695: val thm = Thm.strip_shyps raw_thm; wenzelm@22695: fun err msg = raise THM ("plain_prop_of: " ^ msg, 0, [thm]); wenzelm@22695: val {hyps, prop, tpairs, ...} = Thm.rep_thm thm; wenzelm@22695: in wenzelm@22695: if not (null hyps) then wenzelm@22695: err "theorem may not contain hypotheses" wenzelm@22695: else if not (null (Thm.extra_shyps thm)) then wenzelm@22695: err "theorem may not contain sort hypotheses" wenzelm@22695: else if not (null tpairs) then wenzelm@22695: err "theorem may not contain flex-flex pairs" wenzelm@22695: else prop wenzelm@22695: end; wenzelm@22695: wenzelm@22695: fun fold_terms f th = wenzelm@22695: let val {tpairs, prop, hyps, ...} = Thm.rep_thm th wenzelm@22695: in fold (fn (t, u) => f t #> f u) tpairs #> f prop #> fold f hyps end; wenzelm@22695: wenzelm@22695: wenzelm@24048: (* lists of theorems in canonical order *) wenzelm@24048: wenzelm@24048: val add_thm = update eq_thm_prop; wenzelm@24048: val del_thm = remove eq_thm_prop; wenzelm@24048: val merge_thms = merge eq_thm_prop; wenzelm@24048: wenzelm@24048: wenzelm@22682: wenzelm@22682: (** theorem kinds **) wenzelm@22362: wenzelm@22362: val axiomK = "axiom"; wenzelm@22362: val assumptionK = "assumption"; wenzelm@22362: val definitionK = "definition"; wenzelm@22362: val theoremK = "theorem"; wenzelm@22362: val lemmaK = "lemma"; wenzelm@22362: val corollaryK = "corollary"; wenzelm@24775: val internalK = Markup.internalK; wenzelm@22362: wenzelm@22362: wenzelm@22682: wenzelm@22682: (** attributes **) wenzelm@22362: wenzelm@22362: fun rule_attribute f (x, th) = (x, f x th); wenzelm@22362: fun declaration_attribute f (x, th) = (f th x, th); wenzelm@22362: wenzelm@22362: fun apply_attributes mk dest = wenzelm@22362: let wenzelm@22362: fun app [] = I wenzelm@22362: | app ((f: attribute) :: fs) = fn (x, th) => f (mk x, th) |>> dest |> app fs; wenzelm@22362: in app end; wenzelm@22362: wenzelm@22362: val theory_attributes = apply_attributes Context.Theory Context.the_theory; wenzelm@22362: val proof_attributes = apply_attributes Context.Proof Context.the_proof; wenzelm@22362: wenzelm@22362: fun no_attributes x = (x, []); wenzelm@22362: fun simple_fact x = [(x, [])]; wenzelm@22362: wenzelm@22362: wenzelm@22682: (** read/certify terms (obsolete) **) (*exception ERROR*) wenzelm@22682: wenzelm@22682: fun read_def_cterms (thy, types, sorts) used freeze sTs = wenzelm@22682: let wenzelm@22682: val (ts', tye) = Sign.read_def_terms (thy, types, sorts) used freeze sTs; wenzelm@22682: val cts = map (Thm.cterm_of thy) ts' wenzelm@22682: handle TYPE (msg, _, _) => error msg wenzelm@22682: | TERM (msg, _) => error msg; wenzelm@22682: in (cts, tye) end; wenzelm@22682: wenzelm@22682: fun read_cterm thy sT = wenzelm@22682: let val ([ct], _) = read_def_cterms (thy, K NONE, K NONE) [] true [sT] wenzelm@22682: in ct end; wenzelm@22682: wenzelm@22682: wenzelm@24980: wenzelm@24980: (** basic derived rules **) wenzelm@24980: wenzelm@24980: (*Elimination of implication wenzelm@24980: A A ==> B wenzelm@24980: ------------ wenzelm@24980: B wenzelm@24980: *) wenzelm@24980: fun elim_implies thA thAB = Thm.implies_elim thAB thA; wenzelm@24980: wenzelm@24980: (*global schematic variables*) wenzelm@24980: fun unvarify th = wenzelm@24980: let wenzelm@24980: val thy = Thm.theory_of_thm th; wenzelm@24980: val cert = Thm.cterm_of thy; wenzelm@24980: val certT = Thm.ctyp_of thy; wenzelm@24980: wenzelm@24980: val prop = Thm.full_prop_of th; wenzelm@24980: val _ = map Logic.unvarify (prop :: Thm.hyps_of th) wenzelm@24980: handle TERM (msg, _) => raise THM (msg, 0, [th]); wenzelm@24980: wenzelm@24980: val instT0 = rev (Term.add_tvars prop []) |> map (fn v as ((a, _), S) => (v, TFree (a, S))); wenzelm@24980: val instT = map (fn (v, T) => (certT (TVar v), certT T)) instT0; wenzelm@24980: val inst = rev (Term.add_vars prop []) |> map (fn ((a, i), T) => wenzelm@24980: let val T' = TermSubst.instantiateT instT0 T wenzelm@24980: in (cert (Var ((a, i), T')), cert (Free ((a, T')))) end); wenzelm@24980: in Thm.instantiate (instT, inst) th end; wenzelm@24980: wenzelm@26628: fun close_derivation thm = wenzelm@26628: if Thm.get_name thm = "" then Thm.put_name "" thm wenzelm@26628: else thm; wenzelm@26628: wenzelm@24980: wenzelm@24980: wenzelm@24980: (** specification primitives **) wenzelm@24980: wenzelm@24980: fun add_axiom hyps (name, prop) thy = wenzelm@24980: let wenzelm@24980: val name' = if name = "" then "axiom_" ^ serial_string () else name; wenzelm@24980: val prop' = Logic.list_implies (hyps, prop); wenzelm@24980: val thy' = thy |> Theory.add_axioms_i [(name', prop')]; wenzelm@24980: val axm = unvarify (Thm.get_axiom_i thy' (Sign.full_name thy' name')); wenzelm@24980: val prems = map (Thm.assume o Thm.cterm_of thy') hyps; wenzelm@24980: val thm = fold elim_implies prems axm; wenzelm@24980: in (thm, thy') end; wenzelm@24980: haftmann@25518: fun add_def unchecked overloaded (name, prop) thy = wenzelm@24980: let wenzelm@24980: val tfrees = rev (map TFree (Term.add_tfrees prop [])); wenzelm@24980: val tfrees' = map (fn a => TFree (a, [])) (Name.invents Name.context Name.aT (length tfrees)); wenzelm@24980: val strip_sorts = tfrees ~~ tfrees'; wenzelm@24980: val recover_sorts = map (pairself (Thm.ctyp_of thy o Logic.varifyT)) (tfrees' ~~ tfrees); wenzelm@24980: wenzelm@24980: val prop' = Term.map_types (Term.map_atyps (perhaps (AList.lookup (op =) strip_sorts))) prop; haftmann@25518: val thy' = Theory.add_defs_i unchecked overloaded [(name, prop')] thy; wenzelm@24980: val axm' = Thm.get_axiom_i thy' (Sign.full_name thy' name); wenzelm@24980: val thm = unvarify (Thm.instantiate (recover_sorts, []) axm'); wenzelm@24980: in (thm, thy') end; wenzelm@24980: wenzelm@22362: open Thm; wenzelm@22362: wenzelm@22362: end; wenzelm@22362: wenzelm@23170: val op aconvc = Thm.aconvc; wenzelm@23170: wenzelm@22362: structure Thmtab = TableFun(type key = thm val ord = Thm.thm_ord);