# HG changeset patch # User wenzelm # Date 760280103 -3600 # Node ID 7532f95d7f447ea3d7b5f3006454c240dfd4ae1b # Parent c9b984c0a674cb9ddfb5b67a9c24824feb603b3e removed eq_sg, pprint_sg, print_sg (now in sign.ML); removed cterm_fun, read_ctyp (now in thm.ML); print_theory: now shows all contents; diff -r c9b984c0a674 -r 7532f95d7f44 src/Pure/drule.ML --- a/src/Pure/drule.ML Thu Feb 03 13:53:44 1994 +0100 +++ b/src/Pure/drule.ML Thu Feb 03 13:55:03 1994 +0100 @@ -1,6 +1,6 @@ -(* Title: Pure/drule.ML +(* Title: Pure/drule.ML ID: $Id$ - Author: Lawrence C Paulson, Cambridge University Computer Laboratory + Author: Lawrence C Paulson, Cambridge University Computer Laboratory Copyright 1993 University of Cambridge Derived rules and other operations on theorems and theories @@ -14,14 +14,12 @@ local open Thm in val asm_rl: thm val assume_ax: theory -> string -> thm - val cterm_fun: (term -> term) -> (cterm -> cterm) val COMP: thm * thm -> thm val compose: thm * int * thm -> thm list val cterm_instantiate: (cterm*cterm)list -> thm -> thm val cut_rl: thm val equal_abs_elim: cterm -> thm -> thm val equal_abs_elim_list: cterm list -> thm -> thm - val eq_sg: Sign.sg * Sign.sg -> bool val eq_thm: thm * thm -> bool val eq_thm_sg: thm * thm -> bool val flexpair_abs_elim_list: cterm list -> thm -> thm @@ -36,7 +34,6 @@ val MRS: thm list * thm -> thm val pprint_cterm: cterm -> pprint_args -> unit val pprint_ctyp: ctyp -> pprint_args -> unit - val pprint_sg: Sign.sg -> pprint_args -> unit val pprint_theory: theory -> pprint_args -> unit val pprint_thm: thm -> pprint_args -> unit val pretty_thm: thm -> Sign.Syntax.Pretty.T @@ -44,16 +41,14 @@ val print_ctyp: ctyp -> unit val print_goals: int -> thm -> unit val print_goals_ref: (int -> thm -> unit) ref - val print_sg: Sign.sg -> unit val print_theory: theory -> unit val print_thm: thm -> unit val prth: thm -> thm val prthq: thm Sequence.seq -> thm Sequence.seq val prths: thm list -> thm list - val read_ctyp: Sign.sg -> string -> ctyp val read_instantiate: (string*string)list -> thm -> thm val read_instantiate_sg: Sign.sg -> (string*string)list -> thm -> thm - val read_insts: + val read_insts: Sign.sg -> (indexname -> typ option) * (indexname -> sort option) -> (indexname -> typ option) * (indexname -> sort option) -> (string*string)list @@ -82,7 +77,7 @@ end end; -functor DruleFun (structure Logic: LOGIC and Thm: THM)(* : DRULE *) = (* FIXME *) +functor DruleFun (structure Logic: LOGIC and Thm: THM): DRULE = struct structure Thm = Thm; structure Sign = Thm.Sign; @@ -93,12 +88,6 @@ (**** More derived rules and operations on theorems ****) -fun cterm_fun f ct = - let val {sign,t,...} = rep_cterm ct in cterm_of sign (f t) end; - -fun read_ctyp sign = ctyp_of sign o Sign.read_typ(sign, K None); - - (** reading of instantiations **) fun indexname cs = case Syntax.scan_varname cs of (v,[]) => v @@ -136,7 +125,8 @@ in (map (fn (ixn,T) => (ixn,ctyp_of sign T)) tye', cterms) end; -(*** Printing of theorems ***) + +(*** Printing of theories, theorems, etc. ***) (*If false, hypotheses are printed as dots*) val show_hyps = ref true; @@ -144,11 +134,11 @@ fun pretty_thm th = let val {sign, hyps, prop,...} = rep_thm th val hsymbs = if null hyps then [] - else if !show_hyps then - [Pretty.brk 2, - Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)] - else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @ - [Pretty.str"]"]; + else if !show_hyps then + [Pretty.brk 2, + Pretty.lst("[","]") (map (Sign.pretty_term sign) hyps)] + else Pretty.str" [" :: map (fn _ => Pretty.str".") hyps @ + [Pretty.str"]"]; in Pretty.blk(0, Sign.pretty_term sign prop :: hsymbs) end; val string_of_thm = Pretty.string_of o pretty_thm; @@ -163,38 +153,49 @@ (*Print and return a sequence of theorems, separated by blank lines. *) fun prthq thseq = - (Sequence.prints (fn _ => print_thm) 100000 thseq; - thseq); + (Sequence.prints (fn _ => print_thm) 100000 thseq; thseq); (*Print and return a list of theorems, separated by blank lines. *) fun prths ths = (print_list_ln print_thm ths; ths); -(*Other printing commands*) -fun pprint_ctyp cT = - let val {sign,T} = rep_ctyp cT in Sign.pprint_typ sign T end; + +(* other printing commands *) -fun string_of_ctyp cT = - let val {sign,T} = rep_ctyp cT in Sign.string_of_typ sign T end; +fun pprint_ctyp cT = + let val {sign, T} = rep_ctyp cT in Sign.pprint_typ sign T end; + +fun string_of_ctyp cT = + let val {sign, T} = rep_ctyp cT in Sign.string_of_typ sign T end; val print_ctyp = writeln o string_of_ctyp; -fun pprint_cterm ct = - let val {sign,t,...} = rep_cterm ct in Sign.pprint_term sign t end; +fun pprint_cterm ct = + let val {sign, t, ...} = rep_cterm ct in Sign.pprint_term sign t end; -fun string_of_cterm ct = - let val {sign,t,...} = rep_cterm ct in Sign.string_of_term sign t end; +fun string_of_cterm ct = + let val {sign, t, ...} = rep_cterm ct in Sign.string_of_term sign t end; val print_cterm = writeln o string_of_cterm; -fun pretty_sg sg = - Pretty.lst ("{", "}") (map (Pretty.str o !) (#stamps (Sign.rep_sg sg))); + +(* print theory *) + +val pprint_theory = Sign.pprint_sg o sign_of; -val pprint_sg = Pretty.pprint o pretty_sg; +fun print_theory thy = + let + fun prt_thm (name, thm) = Pretty.block + [Pretty.str (name ^ ":"), Pretty.brk 1, Pretty.quote (pretty_thm thm)]; -val pprint_theory = pprint_sg o sign_of; + val sg = sign_of thy; + val axioms = (* FIXME should rather fix axioms_of *) + sort (fn ((x, _), (y, _)) => x <= y) + (gen_distinct eq_fst (axioms_of thy)); + in + Sign.print_sg sg; + Pretty.writeln (Pretty.big_list "axioms:" (map prt_thm axioms)) + end; -val print_sg = writeln o Pretty.string_of o pretty_sg; -val print_theory = print_sg o sign_of; (** Print thm A1,...,An/B in "goal style" -- premises as numbered subgoals **) @@ -205,26 +206,26 @@ let val {sign, hyps, prop,...} = rep_thm th; fun printgoals (_, []) = () | printgoals (n, A::As) = - let val prettyn = Pretty.str(" " ^ string_of_int n ^ ". "); - val prettyA = Sign.pretty_term sign A - in prettyprints[prettyn,prettyA]; - printgoals (n+1,As) + let val prettyn = Pretty.str(" " ^ string_of_int n ^ ". "); + val prettyA = Sign.pretty_term sign A + in prettyprints[prettyn,prettyA]; + printgoals (n+1,As) end; fun prettypair(t,u) = Pretty.blk(0, [Sign.pretty_term sign t, Pretty.str" =?=", Pretty.brk 1, - Sign.pretty_term sign u]); + Sign.pretty_term sign u]); fun printff [] = () | printff tpairs = - writeln("\nFlex-flex pairs:\n" ^ - Pretty.string_of(Pretty.lst("","") (map prettypair tpairs))) + writeln("\nFlex-flex pairs:\n" ^ + Pretty.string_of(Pretty.lst("","") (map prettypair tpairs))) val (tpairs,As,B) = Logic.strip_horn(prop); val ngoals = length As -in +in writeln (Sign.string_of_term sign B); if ngoals=0 then writeln"No subgoals!" - else if ngoals>maxgoals + else if ngoals>maxgoals then (printgoals (1, take(maxgoals,As)); - writeln("A total of " ^ string_of_int ngoals ^ " subgoals...")) + writeln("A total of " ^ string_of_int ngoals ^ " subgoals...")) else printgoals (1, As); printff tpairs end; @@ -232,7 +233,7 @@ (*"hook" for user interfaces: allows print_goals to be replaced*) val print_goals_ref = ref print_goals; -(*** Find the type (sort) associated with a (T)Var or (T)Free in a term +(*** Find the type (sort) associated with a (T)Var or (T)Free in a term Used for establishing default types (of variables) and sorts (of type variables) when reading another term. Index -1 indicates that a (T)Free rather than a (T)Var is wanted. @@ -240,13 +241,13 @@ fun types_sorts thm = let val {prop,hyps,...} = rep_thm thm; - val big = list_comb(prop,hyps); (* bogus term! *) - val vars = map dest_Var (term_vars big); - val frees = map dest_Free (term_frees big); - val tvars = term_tvars big; - val tfrees = term_tfrees big; - fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i)); - fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); + val big = list_comb(prop,hyps); (* bogus term! *) + val vars = map dest_Var (term_vars big); + val frees = map dest_Free (term_frees big); + val tvars = term_tvars big; + val tfrees = term_tfrees big; + fun typ(a,i) = if i<0 then assoc(frees,a) else assoc(vars,(a,i)); + fun sort(a,i) = if i<0 then assoc(tfrees,a) else assoc(tvars,(a,i)); in (typ,sort) end; (** Standardization of rules **) @@ -254,31 +255,31 @@ (*Generalization over a list of variables, IGNORING bad ones*) fun forall_intr_list [] th = th | forall_intr_list (y::ys) th = - let val gth = forall_intr_list ys th - in forall_intr y gth handle THM _ => gth end; + let val gth = forall_intr_list ys th + in forall_intr y gth handle THM _ => gth end; (*Generalization over all suitable Free variables*) fun forall_intr_frees th = let val {prop,sign,...} = rep_thm th in forall_intr_list - (map (cterm_of sign) (sort atless (term_frees prop))) + (map (cterm_of sign) (sort atless (term_frees prop))) th end; (*Replace outermost quantified variable by Var of given index. Could clash with Vars already present.*) -fun forall_elim_var i th = +fun forall_elim_var i th = let val {prop,sign,...} = rep_thm th in case prop of - Const("all",_) $ Abs(a,T,_) => - forall_elim (cterm_of sign (Var((a,i), T))) th - | _ => raise THM("forall_elim_var", i, [th]) + Const("all",_) $ Abs(a,T,_) => + forall_elim (cterm_of sign (Var((a,i), T))) th + | _ => raise THM("forall_elim_var", i, [th]) end; (*Repeat forall_elim_var until all outer quantifiers are removed*) -fun forall_elim_vars i th = +fun forall_elim_vars i th = forall_elim_vars i (forall_elim_var i th) - handle THM _ => th; + handle THM _ => th; (*Specialization over a list of cterms*) fun forall_elim_list cts th = foldr (uncurry forall_elim) (rev cts, th); @@ -290,21 +291,21 @@ fun implies_elim_list impth ths = foldl (uncurry implies_elim) (impth,ths); (*Reset Var indexes to zero, renaming to preserve distinctness*) -fun zero_var_indexes th = +fun zero_var_indexes th = let val {prop,sign,...} = rep_thm th; val vars = term_vars prop val bs = foldl add_new_id ([], map (fn Var((a,_),_)=>a) vars) - val inrs = add_term_tvars(prop,[]); - val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); - val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms') - val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye; - fun varpairs([],[]) = [] - | varpairs((var as Var(v,T)) :: vars, b::bs) = - let val T' = typ_subst_TVars tye T - in (cterm_of sign (Var(v,T')), - cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs) - end - | varpairs _ = raise TERM("varpairs", []); + val inrs = add_term_tvars(prop,[]); + val nms' = rev(foldl add_new_id ([], map (#1 o #1) inrs)); + val tye = map (fn ((v,rs),a) => (v, TVar((a,0),rs))) (inrs ~~ nms') + val ctye = map (fn (v,T) => (v,ctyp_of sign T)) tye; + fun varpairs([],[]) = [] + | varpairs((var as Var(v,T)) :: vars, b::bs) = + let val T' = typ_subst_TVars tye T + in (cterm_of sign (Var(v,T')), + cterm_of sign (Var((b,0),T'))) :: varpairs(vars,bs) + end + | varpairs _ = raise TERM("varpairs", []); in instantiate (ctye, varpairs(vars,rev bs)) th end; @@ -312,22 +313,22 @@ all generality expressed by Vars having index 0.*) fun standard th = let val {maxidx,...} = rep_thm th - in varifyT (zero_var_indexes (forall_elim_vars(maxidx+1) + in varifyT (zero_var_indexes (forall_elim_vars(maxidx+1) (forall_intr_frees(implies_intr_hyps th)))) end; -(*Assume a new formula, read following the same conventions as axioms. +(*Assume a new formula, read following the same conventions as axioms. Generalizes over Free variables, creates the assumption, and then strips quantifiers. Example is [| ALL x:?A. ?P(x) |] ==> [| ?P(?a) |] - [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ] *) + [ !(A,P,a)[| ALL x:A. P(x) |] ==> [| P(a) |] ] *) fun assume_ax thy sP = let val sign = sign_of thy - val prop = Logic.close_form (term_of (read_cterm sign - (sP, propT))) + val prop = Logic.close_form (term_of (read_cterm sign + (sP, propT))) in forall_elim_vars 0 (assume (cterm_of sign prop)) end; -(*Resolution: exactly one resolvent must be produced.*) +(*Resolution: exactly one resolvent must be produced.*) fun tha RSN (i,thb) = case Sequence.chop (2, biresolution false [(false,tha)] i thb) of ([th],_) => th @@ -338,7 +339,7 @@ fun tha RS thb = tha RSN (1,thb); (*For joining lists of rules*) -fun thas RLN (i,thbs) = +fun thas RLN (i,thbs) = let val resolve = biresolution false (map (pair false) thas) i fun resb thb = Sequence.list_of_s (resolve thb) handle THM _ => [] in flat (map resb thbs) end; @@ -347,27 +348,27 @@ (*Resolve a list of rules against bottom_rl from right to left; makes proof trees*) -fun rls MRS bottom_rl = +fun rls MRS bottom_rl = let fun rs_aux i [] = bottom_rl - | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls) + | rs_aux i (rl::rls) = rl RSN (i, rs_aux (i+1) rls) in rs_aux 1 rls end; (*As above, but for rule lists*) -fun rlss MRL bottom_rls = +fun rlss MRL bottom_rls = let fun rs_aux i [] = bottom_rls - | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss) + | rs_aux i (rls::rlss) = rls RLN (i, rs_aux (i+1) rlss) in rs_aux 1 rlss end; -(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R +(*compose Q and [...,Qi,Q(i+1),...]==>R to [...,Q(i+1),...]==>R with no lifting or renaming! Q may contain ==> or meta-quants ALWAYS deletes premise i *) -fun compose(tha,i,thb) = +fun compose(tha,i,thb) = Sequence.list_of_s (bicompose false (false,tha,0) i thb); (*compose Q and [Q1,Q2,...,Qk]==>R to [Q2,...,Qk]==>R getting unique result*) fun tha COMP thb = case compose(tha,1,thb) of - [th] => th + [th] => th | _ => raise THM("COMP", 1, [tha,thb]); (*Instantiate theorem th, reading instantiations under signature sg*) @@ -387,18 +388,18 @@ let val {sign=signt, t=t, T= T, ...} = rep_cterm ct and {sign=signu, t=u, T= U, ...} = rep_cterm cu val sign' = Sign.merge(sign, Sign.merge(signt, signu)) - val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye) - handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u]) + val tye' = Type.unify (#tsig(Sign.rep_sg sign')) ((T,U), tye) + handle Type.TUNIFY => raise TYPE("add_types", [T,U], [t,u]) in (sign', tye') end; in -fun cterm_instantiate ctpairs0 th = +fun cterm_instantiate ctpairs0 th = let val (sign,tye) = foldr add_types (ctpairs0, (#sign(rep_thm th),[])) val tsig = #tsig(Sign.rep_sg sign); fun instT(ct,cu) = let val inst = subst_TVars tye - in (cterm_fun inst ct, cterm_fun inst cu) end + in (cterm_fun inst ct, cterm_fun inst cu) end fun ctyp2 (ix,T) = (ix, ctyp_of sign T) in instantiate (map ctyp2 tye, map instT ctpairs0) th end - handle TERM _ => + handle TERM _ => raise THM("cterm_instantiate: incompatible signatures",0,[th]) | TYPE _ => raise THM("cterm_instantiate: types", 0, [th]) end; @@ -406,21 +407,18 @@ (** theorem equality test is exported and used by BEST_FIRST **) -(*equality of signatures means exact identity -- by ref equality*) -fun eq_sg (sg1,sg2) = (#stamps(Sign.rep_sg sg1) = #stamps(Sign.rep_sg sg2)); - -(*equality of theorems uses equality of signatures and +(*equality of theorems uses equality of signatures and the a-convertible test for terms*) -fun eq_thm (th1,th2) = +fun eq_thm (th1,th2) = let val {sign=sg1, hyps=hyps1, prop=prop1, ...} = rep_thm th1 - and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2 - in eq_sg (sg1,sg2) andalso - aconvs(hyps1,hyps2) andalso - prop1 aconv prop2 + and {sign=sg2, hyps=hyps2, prop=prop2, ...} = rep_thm th2 + in Sign.eq_sg (sg1,sg2) andalso + aconvs(hyps1,hyps2) andalso + prop1 aconv prop2 end; (*Do the two theorems have the same signature?*) -fun eq_thm_sg (th1,th2) = eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); +fun eq_thm_sg (th1,th2) = Sign.eq_sg(#sign(rep_thm th1), #sign(rep_thm th2)); (*Useful "distance" function for BEST_FIRST*) val size_of_thm = size_of_term o #prop o rep_thm; @@ -449,13 +447,13 @@ (*In [A1,...,An]==>B, rewrite the selected A's only -- for rewrite_goals_tac*) (*Do not rewrite flex-flex pairs*) -fun goals_conv pred cv = +fun goals_conv pred cv = let fun gconv i ct = let val (A,B) = Thm.dest_cimplies ct val (thA,j) = case term_of A of Const("=?=",_)$_$_ => (reflexive A, i) | _ => (if pred i then cv A else reflexive A, i+1) - in combination (combination refl_cimplies thA) (gconv j B) end + in combination (combination refl_cimplies thA) (gconv j B) end handle TERM _ => reflexive ct in gconv 1 end; @@ -504,10 +502,10 @@ fun err th = raise THM("flexpair_inst: ", 0, [th]) fun flexpair_inst def th = let val {prop = Const _ $ t $ u, sign,...} = rep_thm th - val cterm = cterm_of sign - fun cvar a = cterm(Var((a,0),alpha)) - val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)] - def + val cterm = cterm_of sign + fun cvar a = cterm(Var((a,0),alpha)) + val def' = cterm_instantiate [(cvar"t", cterm t), (cvar"u", cterm u)] + def in equal_elim def' th end handle THM _ => err th | bind => err th @@ -517,7 +515,7 @@ end; (*Version for flexflex pairs -- this supports lifting.*) -fun flexpair_abs_elim_list cts = +fun flexpair_abs_elim_list cts = flexpair_intr o equal_abs_elim_list cts o flexpair_elim; @@ -527,17 +525,17 @@ val asm_rl = trivial(read_cterm Sign.pure ("PROP ?psi",propT)); (*Meta-level cut rule: [| V==>W; V |] ==> W *) -val cut_rl = trivial(read_cterm Sign.pure - ("PROP ?psi ==> PROP ?theta", propT)); +val cut_rl = trivial(read_cterm Sign.pure + ("PROP ?psi ==> PROP ?theta", propT)); -(*Generalized elim rule for one conclusion; cut_rl with reversed premises: +(*Generalized elim rule for one conclusion; cut_rl with reversed premises: [| PROP V; PROP V ==> PROP W |] ==> PROP W *) val revcut_rl = let val V = read_cterm Sign.pure ("PROP V", propT) and VW = read_cterm Sign.pure ("PROP V ==> PROP W", propT); - in standard (implies_intr V - (implies_intr VW - (implies_elim (assume VW) (assume V)))) + in standard (implies_intr V + (implies_intr VW + (implies_elim (assume VW) (assume V)))) end; (* (!!x. PROP ?V) == PROP ?V Allows removal of redundant parameters*) @@ -546,8 +544,9 @@ and QV = read_cterm Sign.pure ("!!x::'a. PROP V", propT) and x = read_cterm Sign.pure ("x", TFree("'a",["logic"])); in standard (equal_intr (implies_intr QV (forall_elim x (assume QV))) - (implies_intr V (forall_intr x (assume V)))) + (implies_intr V (forall_intr x (assume V)))) end; end end; +