--- 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;
+