--- a/src/Pure/thm.ML Wed Feb 02 11:15:22 1994 +0100
+++ b/src/Pure/thm.ML Thu Feb 03 13:53:08 1994 +0100
@@ -1,16 +1,17 @@
-(* Title: Pure/thm.ML
+(* Title: Pure/thm.ML
ID: $Id$
- Author: Lawrence C Paulson, Cambridge University Computer Laboratory
+ Author: Lawrence C Paulson, Cambridge University Computer Laboratory
Copyright 1994 University of Cambridge
-NO REP_CTERM!!
+The abstract types "theory" and "thm".
+Also "cterm" / "ctyp" (certified terms / typs under a signature).
-The abstract types "theory" and "thm"
-Also "cterm" / "ctyp" (certified terms / typs under a signature).
+TODO:
+ NO REP_CTERM!!
*)
-signature THM =
- sig
+signature THM =
+sig
structure Envir : ENVIR
structure Sequence : SEQUENCE
structure Sign : SIGN
@@ -25,42 +26,44 @@
(*Certified terms/types; previously in sign.ML*)
val cterm_of: Sign.sg -> term -> cterm
val ctyp_of: Sign.sg -> typ -> ctyp
+ val read_ctyp: Sign.sg -> string -> ctyp
val read_cterm: Sign.sg -> string * typ -> cterm
val rep_cterm: cterm -> {T: typ, t: term, sign: Sign.sg, maxidx: int}
val rep_ctyp: ctyp -> {T: typ, sign: Sign.sg}
val term_of: cterm -> term
val typ_of: ctyp -> typ
- (*End of cterm/ctyp functions*)
+ val cterm_fun: (term -> term) -> (cterm -> cterm)
+ (*End of cterm/ctyp functions*)
val abstract_rule: string -> cterm -> thm -> thm
val add_congs: meta_simpset * thm list -> meta_simpset
val add_prems: meta_simpset * thm list -> meta_simpset
val add_simps: meta_simpset * thm list -> meta_simpset
val assume: cterm -> thm
- val assumption: int -> thm -> thm Sequence.seq
+ val assumption: int -> thm -> thm Sequence.seq
val axioms_of: theory -> (string * thm) list
- val beta_conversion: cterm -> thm
- val bicompose: bool -> bool * thm * int -> int -> thm -> thm Sequence.seq
- val biresolution: bool -> (bool*thm)list -> int -> thm -> thm Sequence.seq
- val combination: thm -> thm -> thm
- val concl_of: thm -> term
+ val beta_conversion: cterm -> thm
+ val bicompose: bool -> bool * thm * int -> int -> thm -> thm Sequence.seq
+ val biresolution: bool -> (bool*thm)list -> int -> thm -> thm Sequence.seq
+ val combination: thm -> thm -> thm
+ val concl_of: thm -> term
val cprop_of: thm -> cterm
val del_simps: meta_simpset * thm list -> meta_simpset
val dest_cimplies: cterm -> cterm*cterm
val dest_state: thm * int -> (term*term)list * term list * term * term
val empty_mss: meta_simpset
- val eq_assumption: int -> thm -> thm
+ val eq_assumption: int -> thm -> thm
val equal_intr: thm -> thm -> thm
val equal_elim: thm -> thm -> thm
val extend_theory: theory -> string
- -> (class * class list) list * sort
- * (string list * int)list
- * (string * indexname list * string) list
- * (string list * (sort list * class))list
- * (string list * string)list * Sign.Syntax.sext option
- -> (string*string)list -> theory
- val extensional: thm -> thm
- val flexflex_rule: thm -> thm Sequence.seq
- val flexpair_def: thm
+ -> (class * class list) list * sort
+ * (string list * int)list
+ * (string * string list * string) list
+ * (string list * (sort list * class))list
+ * (string list * string)list * Sign.Syntax.sext option
+ -> (string*string)list -> theory
+ val extensional: thm -> thm
+ val flexflex_rule: thm -> thm Sequence.seq
+ val flexpair_def: thm
val forall_elim: cterm -> thm -> thm
val forall_intr: cterm -> thm -> thm
val freezeT: thm -> thm
@@ -68,7 +71,7 @@
val implies_elim: thm -> thm -> thm
val implies_intr: cterm -> thm -> thm
val implies_intr_hyps: thm -> thm
- val instantiate: (indexname*ctyp)list * (cterm*cterm)list
+ val instantiate: (indexname*ctyp)list * (cterm*cterm)list
-> thm -> thm
val lift_rule: (thm * int) -> thm -> thm
val merge_theories: theory * theory -> theory
@@ -82,32 +85,29 @@
val read_def_cterm :
Sign.sg * (indexname -> typ option) * (indexname -> sort option) ->
string * typ -> cterm * (indexname * typ) list
- val reflexive: cterm -> thm
+ val reflexive: cterm -> thm
val rename_params_rule: string list * int -> thm -> thm
val rep_thm: thm -> {prop: term, hyps: term list, maxidx: int, sign: Sign.sg}
val rewrite_cterm:
bool*bool -> meta_simpset -> (meta_simpset -> thm -> thm option)
-> cterm -> thm
val set_mk_rews: meta_simpset * (thm -> thm list) -> meta_simpset
- val sign_of: theory -> Sign.sg
+ val sign_of: theory -> Sign.sg
val syn_of: theory -> Sign.Syntax.syntax
val stamps_of_thm: thm -> string ref list
val stamps_of_thy: theory -> string ref list
- val symmetric: thm -> thm
+ val symmetric: thm -> thm
val tpairs_of: thm -> (term*term)list
val trace_simp: bool ref
val transitive: thm -> thm -> thm
val trivial: cterm -> thm
val varifyT: thm -> thm
- end;
-
-
+end;
-functor ThmFun (structure Logic: LOGIC and Unify: UNIFY and Pattern:PATTERN
- and Net:NET
- sharing type Pattern.type_sig = Unify.Sign.Type.type_sig)
- (*: THM *) (* FIXME debug *) =
+functor ThmFun (structure Logic: LOGIC and Unify: UNIFY and Pattern: PATTERN
+ and Net:NET sharing type Pattern.type_sig = Unify.Sign.Type.type_sig)(*: THM *) (* FIXME debug *) =
struct
+
structure Sequence = Unify.Sequence;
structure Envir = Unify.Envir;
structure Sign = Unify.Sign;
@@ -116,71 +116,83 @@
structure Symtab = Sign.Symtab;
-(** Certified Types **)
+(** certified types **)
+
+(*certified typs under a signature*)
+
+datatype ctyp = Ctyp of {sign: Sign.sg, T: typ};
+
+fun rep_ctyp (Ctyp args) = args;
+fun typ_of (Ctyp {T, ...}) = T;
+
+fun ctyp_of sign T =
+ Ctyp {sign = sign, T = Sign.certify_typ sign T};
+
+fun read_ctyp sign s =
+ Ctyp {sign = sign, T = Sign.read_typ (sign, K None) s};
-(*Certified typs under a signature*)
-datatype ctyp = Ctyp of {sign: Sign.sg, T: typ};
-fun rep_ctyp(Ctyp ctyp) = ctyp;
-fun typ_of (Ctyp{sign,T}) = T;
+(** certified terms **)
-fun ctyp_of sign T =
- case Type.type_errors (#tsig(Sign.rep_sg sign)) (T,[]) of
- [] => Ctyp{sign= sign,T= T}
- | errs => error (cat_lines ("Error in type:" :: errs));
+(*certified terms under a signature, with checked typ and maxidx of Vars*)
-(** Certified Terms **)
-
-(*Certified terms under a signature, with checked typ and maxidx of Vars*)
-datatype cterm = Cterm of {sign: Sign.sg, t: term, T: typ, maxidx: int};
+datatype cterm = Cterm of {sign: Sign.sg, t: term, T: typ, maxidx: int};
fun rep_cterm (Cterm args) = args;
+fun term_of (Cterm {t, ...}) = t;
-(*Return the underlying term*)
-fun term_of (Cterm{t,...}) = t;
+(*create a cterm by checking a "raw" term with respect to a signature*)
+fun cterm_of sign tm =
+ let val (t, T, maxidx) = Sign.certify_term sign tm
+ in Cterm {sign = sign, t = t, T = T, maxidx = maxidx}
+ end handle TYPE (msg, _, _)
+ => raise TERM ("Term not in signature\n" ^ msg, [tm]);
-(*Create a cterm by checking a "raw" term with respect to a signature*)
-fun cterm_of sign t =
- case Sign.term_errors sign t of
- [] => Cterm{sign=sign, t=t, T= type_of t, maxidx= maxidx_of_term t}
- | errs => raise TERM(cat_lines("Term not in signature"::errs), [t]);
+fun cterm_fun f (Cterm {sign, t, ...}) = cterm_of sign (f t);
+
-(*dest_implies for cterms. Note T=prop below*)
-fun dest_cimplies (Cterm{sign, T, maxidx, t=Const("==>",_) $ A $ B}) =
+(*dest_implies for cterms. Note T=prop below*)
+fun dest_cimplies (Cterm{sign, T, maxidx, t=Const("==>", _) $ A $ B}) =
(Cterm{sign=sign, T=T, maxidx=maxidx, t=A},
- Cterm{sign=sign, T=T, maxidx=maxidx, t=B})
- | dest_cimplies ct = raise TERM("dest_cimplies", [term_of ct]);
+ Cterm{sign=sign, T=T, maxidx=maxidx, t=B})
+ | dest_cimplies ct = raise TERM ("dest_cimplies", [term_of ct]);
-(** Reading of cterms -- needed twice below! **)
+
-(*Lexing, parsing, polymorphic typechecking of a term.*)
-fun read_def_cterm (sign, types, sorts) (a,T) =
- let val {tsig, const_tab, syn,...} = Sign.rep_sg sign
- val showtyp = Sign.string_of_typ sign
- and showterm = Sign.string_of_term sign
- fun termerr [] = ""
- | termerr [t] = "\nInvolving this term:\n" ^ showterm t ^ "\n"
- | termerr ts = "\nInvolving these terms:\n" ^
- cat_lines (map showterm ts)
- val t = Syntax.read syn T a;
- val (t',tye) = Type.infer_types (tsig, const_tab, types,
- sorts, showtyp, T, t)
- handle TYPE (msg, Ts, ts) =>
- error ("Type checking error: " ^ msg ^ "\n" ^
- cat_lines (map showtyp Ts) ^ termerr ts)
- in (cterm_of sign t', tye)
- end
- handle TERM (msg, _) => error ("Error: " ^ msg);
+(** read cterms **)
+
+(*read term, infer types, certify term*)
+
+fun read_def_cterm (sign, types, sorts) (a, T) =
+ let
+ val {tsig, const_tab, syn, ...} = Sign.rep_sg sign;
+ val showtyp = Sign.string_of_typ sign;
+ val showterm = Sign.string_of_term sign;
+
+ fun termerr [] = ""
+ | termerr [t] = "\nInvolving this term:\n" ^ showterm t
+ | termerr ts = "\nInvolving these terms:\n" ^ cat_lines (map showterm ts);
+
+ val T' = Sign.certify_typ sign T
+ handle TYPE (msg, _, _) => error msg;
+ val t = Syntax.read syn T' a;
+ val (t', tye) = Type.infer_types (tsig, const_tab, types, sorts, T', t)
+ handle TYPE (msg, Ts, ts) => error ("Type checking error: " ^ msg ^ "\n"
+ ^ cat_lines (map showtyp Ts) ^ termerr ts);
+ val ct = cterm_of sign t' handle TERM (msg, _) => error msg;
+ in (ct, tye) end;
fun read_cterm sign = #1 o (read_def_cterm (sign, K None, K None));
+
+
(**** META-THEOREMS ****)
datatype thm = Thm of
- {sign: Sign.sg, maxidx: int, hyps: term list, prop: term};
+ {sign: Sign.sg, maxidx: int, hyps: term list, prop: term};
-fun rep_thm (Thm x) = x;
+fun rep_thm (Thm args) = args;
(*Errors involving theorems*)
exception THM of string * int * thm list;
@@ -200,8 +212,8 @@
fun concl_of (Thm{prop,...}) = Logic.strip_imp_concl prop;
(*The statement of any Thm is a Cterm*)
-fun cprop_of (Thm{sign,maxidx,hyps,prop}) =
- Cterm{sign=sign, maxidx=maxidx, T=propT, t=prop};
+fun cprop_of (Thm{sign,maxidx,hyps,prop}) =
+ Cterm{sign=sign, maxidx=maxidx, T=propT, t=prop};
(*Stamps associated with a signature*)
val stamps_of_thm = #stamps o Sign.rep_sg o #sign o rep_thm;
@@ -224,8 +236,9 @@
(*return the axioms of a theory and its ancestors*)
fun axioms_of (Pure _) = []
- | axioms_of (Extend{axioms,thy,...}) = Symtab.alist_of axioms
- | axioms_of (Merge{thy1,thy2,...}) = axioms_of thy1 @ axioms_of thy2;
+ | axioms_of (Extend {axioms, thy, ...}) =
+ axioms_of thy @ Symtab.alist_of axioms
+ | axioms_of (Merge {thy1, thy2, ...}) = axioms_of thy1 @ axioms_of thy2;
(*return the immediate ancestors -- also distinguishes the kinds of theories*)
fun parents_of (Pure _) = []
@@ -250,49 +263,49 @@
val disch = gen_rem (op aconv);
(*The assumption rule A|-A in a theory *)
-fun assume ct : thm =
+fun assume ct : thm =
let val {sign, t=prop, T, maxidx} = rep_cterm ct
- in if T<>propT then
- raise THM("assume: assumptions must have type prop", 0, [])
+ in if T<>propT then
+ raise THM("assume: assumptions must have type prop", 0, [])
else if maxidx <> ~1 then
- raise THM("assume: assumptions may not contain scheme variables",
- maxidx, [])
+ raise THM("assume: assumptions may not contain scheme variables",
+ maxidx, [])
else Thm{sign = sign, maxidx = ~1, hyps = [prop], prop = prop}
end;
-(* Implication introduction
- A |- B
- -------
- A ==> B *)
+(* Implication introduction
+ A |- B
+ -------
+ A ==> B *)
fun implies_intr cA (thB as Thm{sign,maxidx,hyps,prop}) : thm =
let val {sign=signA, t=A, T, maxidx=maxidxA} = rep_cterm cA
in if T<>propT then
- raise THM("implies_intr: assumptions must have type prop", 0, [thB])
- else Thm{sign= Sign.merge (sign,signA), maxidx= max[maxidxA, maxidx],
- hyps= disch(hyps,A), prop= implies$A$prop}
+ raise THM("implies_intr: assumptions must have type prop", 0, [thB])
+ else Thm{sign= Sign.merge (sign,signA), maxidx= max[maxidxA, maxidx],
+ hyps= disch(hyps,A), prop= implies$A$prop}
handle TERM _ =>
raise THM("implies_intr: incompatible signatures", 0, [thB])
end;
(* Implication elimination
- A ==> B A
- ---------------
- B *)
+ A ==> B A
+ ---------------
+ B *)
fun implies_elim thAB thA : thm =
let val Thm{maxidx=maxA, hyps=hypsA, prop=propA,...} = thA
- and Thm{sign, maxidx, hyps, prop,...} = thAB;
- fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
+ and Thm{sign, maxidx, hyps, prop,...} = thAB;
+ fun err(a) = raise THM("implies_elim: "^a, 0, [thAB,thA])
in case prop of
- imp$A$B =>
- if imp=implies andalso A aconv propA
- then Thm{sign= merge_theories(thAB,thA),
- maxidx= max[maxA,maxidx],
- hyps= hypsA union hyps, (*dups suppressed*)
- prop= B}
- else err("major premise")
- | _ => err("major premise")
+ imp$A$B =>
+ if imp=implies andalso A aconv propA
+ then Thm{sign= merge_theories(thAB,thA),
+ maxidx= max[maxA,maxidx],
+ hyps= hypsA union hyps, (*dups suppressed*)
+ prop= B}
+ else err("major premise")
+ | _ => err("major premise")
end;
-
+
(* Forall introduction. The Free or Var x must not be free in the hypotheses.
A
------
@@ -300,46 +313,46 @@
fun forall_intr cx (th as Thm{sign,maxidx,hyps,prop}) =
let val x = term_of cx;
fun result(a,T) = Thm{sign= sign, maxidx= maxidx, hyps= hyps,
- prop= all(T) $ Abs(a, T, abstract_over (x,prop))}
+ prop= all(T) $ Abs(a, T, abstract_over (x,prop))}
in case x of
- Free(a,T) =>
- if exists (apl(x, Logic.occs)) hyps
- then raise THM("forall_intr: variable free in assumptions", 0, [th])
- else result(a,T)
+ Free(a,T) =>
+ if exists (apl(x, Logic.occs)) hyps
+ then raise THM("forall_intr: variable free in assumptions", 0, [th])
+ else result(a,T)
| Var((a,_),T) => result(a,T)
| _ => raise THM("forall_intr: not a variable", 0, [th])
end;
(* Forall elimination
- !!x.A
- --------
- A[t/x] *)
+ !!x.A
+ --------
+ A[t/x] *)
fun forall_elim ct (th as Thm{sign,maxidx,hyps,prop}) : thm =
let val {sign=signt, t, T, maxidx=maxt} = rep_cterm ct
in case prop of
- Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
- if T<>qary then
- raise THM("forall_elim: type mismatch", 0, [th])
- else Thm{sign= Sign.merge(sign,signt),
- maxidx= max[maxidx, maxt],
- hyps= hyps, prop= betapply(A,t)}
- | _ => raise THM("forall_elim: not quantified", 0, [th])
+ Const("all",Type("fun",[Type("fun",[qary,_]),_])) $ A =>
+ if T<>qary then
+ raise THM("forall_elim: type mismatch", 0, [th])
+ else Thm{sign= Sign.merge(sign,signt),
+ maxidx= max[maxidx, maxt],
+ hyps= hyps, prop= betapply(A,t)}
+ | _ => raise THM("forall_elim: not quantified", 0, [th])
end
handle TERM _ =>
- raise THM("forall_elim: incompatible signatures", 0, [th]);
+ raise THM("forall_elim: incompatible signatures", 0, [th]);
(*** Equality ***)
(*Definition of the relation =?= *)
val flexpair_def =
- Thm{sign= Sign.pure, hyps= [], maxidx= 0,
- prop= term_of
- (read_cterm Sign.pure
- ("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))};
+ Thm{sign= Sign.pure, hyps= [], maxidx= 0,
+ prop= term_of
+ (read_cterm Sign.pure
+ ("(?t =?= ?u) == (?t == ?u::?'a::{})", propT))};
(*The reflexivity rule: maps t to the theorem t==t *)
-fun reflexive ct =
+fun reflexive ct =
let val {sign, t, T, maxidx} = rep_cterm ct
in Thm{sign= sign, hyps= [], maxidx= maxidx, prop= Logic.mk_equals(t,t)}
end;
@@ -351,7 +364,7 @@
fun symmetric (th as Thm{sign,hyps,prop,maxidx}) =
case prop of
(eq as Const("==",_)) $ t $ u =>
- Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop= eq$u$t}
+ Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop= eq$u$t}
| _ => raise THM("symmetric", 0, [th]);
(*The transitive rule
@@ -364,21 +377,21 @@
fun err(msg) = raise THM("transitive: "^msg, 0, [th1,th2])
in case (prop1,prop2) of
((eq as Const("==",_)) $ t1 $ u, Const("==",_) $ u' $ t2) =>
- if not (u aconv u') then err"middle term" else
- Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
- maxidx= max[max1,max2], prop= eq$t1$t2}
+ if not (u aconv u') then err"middle term" else
+ Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
+ maxidx= max[max1,max2], prop= eq$t1$t2}
| _ => err"premises"
end;
(*Beta-conversion: maps (%(x)t)(u) to the theorem (%(x)t)(u) == t[u/x] *)
-fun beta_conversion ct =
+fun beta_conversion ct =
let val {sign, t, T, maxidx} = rep_cterm ct
in case t of
- Abs(_,_,bodt) $ u =>
- Thm{sign= sign, hyps= [],
- maxidx= maxidx_of_term t,
- prop= Logic.mk_equals(t, subst_bounds([u],bodt))}
- | _ => raise THM("beta_conversion: not a redex", 0, [])
+ Abs(_,_,bodt) $ u =>
+ Thm{sign= sign, hyps= [],
+ maxidx= maxidx_of_term t,
+ prop= Logic.mk_equals(t, subst_bounds([u],bodt))}
+ | _ => raise THM("beta_conversion: not a redex", 0, [])
end;
(*The extensionality rule (proviso: x not free in f, g, or hypotheses)
@@ -388,18 +401,18 @@
fun extensional (th as Thm{sign,maxidx,hyps,prop}) =
case prop of
(Const("==",_)) $ (f$x) $ (g$y) =>
- let fun err(msg) = raise THM("extensional: "^msg, 0, [th])
+ let fun err(msg) = raise THM("extensional: "^msg, 0, [th])
in (if x<>y then err"different variables" else
case y of
- Free _ =>
- if exists (apl(y, Logic.occs)) (f::g::hyps)
- then err"variable free in hyps or functions" else ()
- | Var _ =>
- if Logic.occs(y,f) orelse Logic.occs(y,g)
- then err"variable free in functions" else ()
- | _ => err"not a variable");
- Thm{sign=sign, hyps=hyps, maxidx=maxidx,
- prop= Logic.mk_equals(f,g)}
+ Free _ =>
+ if exists (apl(y, Logic.occs)) (f::g::hyps)
+ then err"variable free in hyps or functions" else ()
+ | Var _ =>
+ if Logic.occs(y,f) orelse Logic.occs(y,g)
+ then err"variable free in functions" else ()
+ | _ => err"not a variable");
+ Thm{sign=sign, hyps=hyps, maxidx=maxidx,
+ prop= Logic.mk_equals(f,g)}
end
| _ => raise THM("extensional: premise", 0, [th]);
@@ -410,18 +423,18 @@
%(x)t == %(x)u *)
fun abstract_rule a cx (th as Thm{sign,maxidx,hyps,prop}) =
let val x = term_of cx;
- val (t,u) = Logic.dest_equals prop
- handle TERM _ =>
- raise THM("abstract_rule: premise not an equality", 0, [th])
+ val (t,u) = Logic.dest_equals prop
+ handle TERM _ =>
+ raise THM("abstract_rule: premise not an equality", 0, [th])
fun result T =
Thm{sign= sign, maxidx= maxidx, hyps= hyps,
- prop= Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
- Abs(a, T, abstract_over (x,u)))}
+ prop= Logic.mk_equals(Abs(a, T, abstract_over (x,t)),
+ Abs(a, T, abstract_over (x,u)))}
in case x of
- Free(_,T) =>
- if exists (apl(x, Logic.occs)) hyps
- then raise THM("abstract_rule: variable free in assumptions", 0, [th])
- else result T
+ Free(_,T) =>
+ if exists (apl(x, Logic.occs)) hyps
+ then raise THM("abstract_rule: variable free in assumptions", 0, [th])
+ else result T
| Var(_,T) => result T
| _ => raise THM("abstract_rule: not a variable", 0, [th])
end;
@@ -435,8 +448,8 @@
and Thm{maxidx=max2, hyps=hyps2, prop=prop2,...} = th2
in case (prop1,prop2) of
(Const("==",_) $ f $ g, Const("==",_) $ t $ u) =>
- Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
- maxidx= max[max1,max2], prop= Logic.mk_equals(f$t, g$u)}
+ Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
+ maxidx= max[max1,max2], prop= Logic.mk_equals(f$t, g$u)}
| _ => raise THM("combination: premises", 0, [th1,th2])
end;
@@ -451,9 +464,9 @@
fun err(msg) = raise THM("equal_elim: "^msg, 0, [th1,th2])
in case prop1 of
Const("==",_) $ A $ B =>
- if not (prop2 aconv A) then err"not equal" else
- Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
- maxidx= max[max1,max2], prop= B}
+ if not (prop2 aconv A) then err"not equal" else
+ Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
+ maxidx= max[max1,max2], prop= B}
| _ => err"major premise"
end;
@@ -468,10 +481,10 @@
fun err(msg) = raise THM("equal_intr: "^msg, 0, [th1,th2])
in case (prop1,prop2) of
(Const("==>",_) $ A $ B, Const("==>",_) $ B' $ A') =>
- if A aconv A' andalso B aconv B'
- then Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
- maxidx= max[max1,max2], prop= Logic.mk_equals(A,B)}
- else err"not equal"
+ if A aconv A' andalso B aconv B'
+ then Thm{sign= merge_theories(th1,th2), hyps= hyps1 union hyps2,
+ maxidx= max[max1,max2], prop= Logic.mk_equals(A,B)}
+ else err"not equal"
| _ => err"premises"
end;
@@ -481,33 +494,33 @@
Repeated hypotheses are discharged only once; fold cannot do this*)
fun implies_intr_hyps (Thm{sign, maxidx, hyps=A::As, prop}) =
implies_intr_hyps
- (Thm{sign=sign, maxidx=maxidx,
- hyps= disch(As,A), prop= implies$A$prop})
+ (Thm{sign=sign, maxidx=maxidx,
+ hyps= disch(As,A), prop= implies$A$prop})
| implies_intr_hyps th = th;
(*Smash" unifies the list of term pairs leaving no flex-flex pairs.
- Instantiates the theorem and deletes trivial tpairs.
+ Instantiates the theorem and deletes trivial tpairs.
Resulting sequence may contain multiple elements if the tpairs are
not all flex-flex. *)
fun flexflex_rule (Thm{sign,maxidx,hyps,prop}) =
- let fun newthm env =
- let val (tpairs,horn) =
- Logic.strip_flexpairs (Envir.norm_term env prop)
- (*Remove trivial tpairs, of the form t=t*)
- val distpairs = filter (not o op aconv) tpairs
- val newprop = Logic.list_flexpairs(distpairs, horn)
- in Thm{sign= sign, hyps= hyps,
- maxidx= maxidx_of_term newprop, prop= newprop}
- end;
+ let fun newthm env =
+ let val (tpairs,horn) =
+ Logic.strip_flexpairs (Envir.norm_term env prop)
+ (*Remove trivial tpairs, of the form t=t*)
+ val distpairs = filter (not o op aconv) tpairs
+ val newprop = Logic.list_flexpairs(distpairs, horn)
+ in Thm{sign= sign, hyps= hyps,
+ maxidx= maxidx_of_term newprop, prop= newprop}
+ end;
val (tpairs,_) = Logic.strip_flexpairs prop
in Sequence.maps newthm
- (Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs))
+ (Unify.smash_unifiers(sign, Envir.empty maxidx, tpairs))
end;
(*Instantiation of Vars
- A
- --------------------
- A[t1/v1,....,tn/vn] *)
+ A
+ --------------------
+ A[t1/v1,....,tn/vn] *)
(*Check that all the terms are Vars and are distinct*)
fun instl_ok ts = forall is_Var ts andalso null(findrep ts);
@@ -527,40 +540,40 @@
(*Left-to-right replacements: ctpairs = [...,(vi,ti),...].
Instantiates distinct Vars by terms of same type.
Normalizes the new theorem! *)
-fun instantiate (vcTs,ctpairs) (th as Thm{sign,maxidx,hyps,prop}) =
+fun instantiate (vcTs,ctpairs) (th as Thm{sign,maxidx,hyps,prop}) =
let val (newsign,tpairs) = foldr add_ctpair (ctpairs, (sign,[]));
val (newsign,vTs) = foldr add_ctyp (vcTs, (newsign,[]));
- val newprop =
- Envir.norm_term (Envir.empty 0)
- (subst_atomic tpairs
- (Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop))
+ val newprop =
+ Envir.norm_term (Envir.empty 0)
+ (subst_atomic tpairs
+ (Type.inst_term_tvars(#tsig(Sign.rep_sg newsign),vTs) prop))
val newth = Thm{sign= newsign, hyps= hyps,
- maxidx= maxidx_of_term newprop, prop= newprop}
- in if not(instl_ok(map #1 tpairs))
+ maxidx= maxidx_of_term newprop, prop= newprop}
+ in if not(instl_ok(map #1 tpairs))
then raise THM("instantiate: variables not distinct", 0, [th])
else if not(null(findrep(map #1 vTs)))
then raise THM("instantiate: type variables not distinct", 0, [th])
else (*Check types of Vars for agreement*)
case findrep (map (#1 o dest_Var) (term_vars newprop)) of
- ix::_ => raise THM("instantiate: conflicting types for variable " ^
- Syntax.string_of_vname ix ^ "\n", 0, [newth])
- | [] =>
- case findrep (map #1 (term_tvars newprop)) of
- ix::_ => raise THM
- ("instantiate: conflicting sorts for type variable " ^
- Syntax.string_of_vname ix ^ "\n", 0, [newth])
+ ix::_ => raise THM("instantiate: conflicting types for variable " ^
+ Syntax.string_of_vname ix ^ "\n", 0, [newth])
+ | [] =>
+ case findrep (map #1 (term_tvars newprop)) of
+ ix::_ => raise THM
+ ("instantiate: conflicting sorts for type variable " ^
+ Syntax.string_of_vname ix ^ "\n", 0, [newth])
| [] => newth
end
- handle TERM _ =>
+ handle TERM _ =>
raise THM("instantiate: incompatible signatures",0,[th])
| TYPE _ => raise THM("instantiate: type conflict", 0, [th]);
(*The trivial implication A==>A, justified by assume and forall rules.
A can contain Vars, not so for assume! *)
-fun trivial ct : thm =
+fun trivial ct : thm =
let val {sign, t=A, T, maxidx} = rep_cterm ct
- in if T<>propT then
- raise THM("trivial: the term must have type prop", 0, [])
+ in if T<>propT then
+ raise THM("trivial: the term must have type prop", 0, [])
else Thm{sign= sign, maxidx= maxidx, hyps= [], prop= implies$A$A}
end;
@@ -568,7 +581,7 @@
fun varifyT(Thm{sign,maxidx,hyps,prop}) =
let val tfrees = foldr add_term_tfree_names (hyps,[])
in Thm{sign=sign, maxidx=max[0,maxidx], hyps=hyps,
- prop= Type.varify(prop,tfrees)}
+ prop= Type.varify(prop,tfrees)}
end;
(* Replace all TVars by new TFrees *)
@@ -593,42 +606,41 @@
fun lift_rule (state, i) orule =
let val Thm{prop=sprop,maxidx=smax,...} = state;
val (Bi::_, _) = Logic.strip_prems(i, [], Logic.skip_flexpairs sprop)
- handle TERM _ => raise THM("lift_rule", i, [orule,state]);
+ handle TERM _ => raise THM("lift_rule", i, [orule,state]);
val (lift_abs,lift_all) = Logic.lift_fns(Bi,smax+1);
val (Thm{sign,maxidx,hyps,prop}) = orule
val (tpairs,As,B) = Logic.strip_horn prop
in Thm{hyps=hyps, sign= merge_theories(state,orule),
- maxidx= maxidx+smax+1,
- prop= Logic.rule_of(map (pairself lift_abs) tpairs,
- map lift_all As, lift_all B)}
+ maxidx= maxidx+smax+1,
+ prop= Logic.rule_of(map (pairself lift_abs) tpairs,
+ map lift_all As, lift_all B)}
end;
(*Solve subgoal Bi of proof state B1...Bn/C by assumption. *)
fun assumption i state =
let val Thm{sign,maxidx,hyps,prop} = state;
val (tpairs, Bs, Bi, C) = dest_state(state,i)
- fun newth (env as Envir.Envir{maxidx,asol,iTs}, tpairs) =
- Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
- case (Envir.alist_of_olist asol, iTs) of
- (*avoid wasted normalizations*)
- ([],[]) => Logic.rule_of(tpairs, Bs, C)
- | _ => (*normalize the new rule fully*)
- Envir.norm_term env (Logic.rule_of(tpairs, Bs, C))};
+ fun newth (env as Envir.Envir{maxidx, ...}, tpairs) =
+ Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
+ if Envir.is_empty env then (*avoid wasted normalizations*)
+ Logic.rule_of (tpairs, Bs, C)
+ else (*normalize the new rule fully*)
+ Envir.norm_term env (Logic.rule_of (tpairs, Bs, C))};
fun addprfs [] = Sequence.null
| addprfs ((t,u)::apairs) = Sequence.seqof (fn()=> Sequence.pull
(Sequence.mapp newth
- (Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs))
- (addprfs apairs)))
+ (Unify.unifiers(sign,Envir.empty maxidx, (t,u)::tpairs))
+ (addprfs apairs)))
in addprfs (Logic.assum_pairs Bi) end;
-(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
+(*Solve subgoal Bi of proof state B1...Bn/C by assumption.
Checks if Bi's conclusion is alpha-convertible to one of its assumptions*)
fun eq_assumption i state =
let val Thm{sign,maxidx,hyps,prop} = state;
val (tpairs, Bs, Bi, C) = dest_state(state,i)
in if exists (op aconv) (Logic.assum_pairs Bi)
- then Thm{sign=sign, hyps=hyps, maxidx=maxidx,
- prop=Logic.rule_of(tpairs, Bs, C)}
+ then Thm{sign=sign, hyps=hyps, maxidx=maxidx,
+ prop=Logic.rule_of(tpairs, Bs, C)}
else raise THM("eq_assumption", 0, [state])
end;
@@ -644,23 +656,23 @@
val (tpairs, Bs, Bi, C) = dest_state(state,i)
val iparams = map #1 (Logic.strip_params Bi)
val short = length iparams - length cs
- val newnames =
- if short<0 then error"More names than abstractions!"
- else variantlist(take (short,iparams), cs) @ cs
+ val newnames =
+ if short<0 then error"More names than abstractions!"
+ else variantlist(take (short,iparams), cs) @ cs
val freenames = map (#1 o dest_Free) (term_frees prop)
val newBi = Logic.list_rename_params (newnames, Bi)
- in
+ in
case findrep cs of
c::_ => error ("Bound variables not distinct: " ^ c)
| [] => (case cs inter freenames of
a::_ => error ("Bound/Free variable clash: " ^ a)
| [] => Thm{sign=sign, hyps=hyps, maxidx=maxidx, prop=
- Logic.rule_of(tpairs, Bs@[newBi], C)})
+ Logic.rule_of(tpairs, Bs@[newBi], C)})
end;
(*** Preservation of bound variable names ***)
-(*Scan a pair of terms; while they are similar,
+(*Scan a pair of terms; while they are similar,
accumulate corresponding bound vars in "al"*)
fun match_bvs(Abs(x,_,s),Abs(y,_,t), al) = match_bvs(s,t,(x,y)::al)
| match_bvs(f$s, g$t, al) = match_bvs(f,g,match_bvs(s,t,al))
@@ -670,14 +682,14 @@
fun match_bvars((s,t),al) = match_bvs(strip_abs_body s, strip_abs_body t, al);
-(* strip_apply f A(,B) strips off all assumptions/parameters from A
+(* strip_apply f A(,B) strips off all assumptions/parameters from A
introduced by lifting over B, and applies f to remaining part of A*)
fun strip_apply f =
let fun strip(Const("==>",_)$ A1 $ B1,
- Const("==>",_)$ _ $ B2) = implies $ A1 $ strip(B1,B2)
- | strip((c as Const("all",_)) $ Abs(a,T,t1),
- Const("all",_) $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
- | strip(A,_) = f A
+ Const("==>",_)$ _ $ B2) = implies $ A1 $ strip(B1,B2)
+ | strip((c as Const("all",_)) $ Abs(a,T,t1),
+ Const("all",_) $ Abs(_,_,t2)) = c$Abs(a,T,strip(t1,t2))
+ | strip(A,_) = f A
in strip end;
(*Use the alist to rename all bound variables and some unknowns in a term
@@ -685,74 +697,72 @@
Preserves unknowns in tpairs and on lhs of dpairs. *)
fun rename_bvs([],_,_,_) = I
| rename_bvs(al,dpairs,tpairs,B) =
- let val vars = foldr add_term_vars
- (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
- (*unknowns appearing elsewhere be preserved!*)
- val vids = map (#1 o #1 o dest_Var) vars;
- fun rename(t as Var((x,i),T)) =
- (case assoc(al,x) of
- Some(y) => if x mem vids orelse y mem vids then t
- else Var((y,i),T)
- | None=> t)
+ let val vars = foldr add_term_vars
+ (map fst dpairs @ map fst tpairs @ map snd tpairs, [])
+ (*unknowns appearing elsewhere be preserved!*)
+ val vids = map (#1 o #1 o dest_Var) vars;
+ fun rename(t as Var((x,i),T)) =
+ (case assoc(al,x) of
+ Some(y) => if x mem vids orelse y mem vids then t
+ else Var((y,i),T)
+ | None=> t)
| rename(Abs(x,T,t)) =
- Abs(case assoc(al,x) of Some(y) => y | None => x,
- T, rename t)
+ Abs(case assoc(al,x) of Some(y) => y | None => x,
+ T, rename t)
| rename(f$t) = rename f $ rename t
| rename(t) = t;
- fun strip_ren Ai = strip_apply rename (Ai,B)
+ fun strip_ren Ai = strip_apply rename (Ai,B)
in strip_ren end;
(*Function to rename bounds/unknowns in the argument, lifted over B*)
fun rename_bvars(dpairs, tpairs, B) =
- rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
+ rename_bvs(foldr match_bvars (dpairs,[]), dpairs, tpairs, B);
(*** RESOLUTION ***)
(*strip off pairs of assumptions/parameters in parallel -- they are
identical because of lifting*)
-fun strip_assums2 (Const("==>", _) $ _ $ B1,
- Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
+fun strip_assums2 (Const("==>", _) $ _ $ B1,
+ Const("==>", _) $ _ $ B2) = strip_assums2 (B1,B2)
| strip_assums2 (Const("all",_)$Abs(a,T,t1),
- Const("all",_)$Abs(_,_,t2)) =
+ Const("all",_)$Abs(_,_,t2)) =
let val (B1,B2) = strip_assums2 (t1,t2)
in (Abs(a,T,B1), Abs(a,T,B2)) end
| strip_assums2 BB = BB;
(*Composition of object rule r=(A1...Am/B) with proof state s=(B1...Bn/C)
- Unifies B with Bi, replacing subgoal i (1 <= i <= n)
+ Unifies B with Bi, replacing subgoal i (1 <= i <= n)
If match then forbid instantiations in proof state
If lifted then shorten the dpair using strip_assums2.
If eres_flg then simultaneously proves A1 by assumption.
- nsubgoal is the number of new subgoals (written m above).
+ nsubgoal is the number of new subgoals (written m above).
Curried so that resolution calls dest_state only once.
*)
local open Sequence; exception Bicompose
in
-fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
+fun bicompose_aux match (state, (stpairs, Bs, Bi, C), lifted)
(eres_flg, orule, nsubgoal) =
let val Thm{maxidx=smax, hyps=shyps, ...} = state
and Thm{maxidx=rmax, hyps=rhyps, prop=rprop,...} = orule;
val sign = merge_theories(state,orule);
(** Add new theorem with prop = '[| Bs; As |] ==> C' to thq **)
- fun addth As ((env as Envir.Envir{maxidx,asol,iTs}, tpairs), thq) =
- let val minenv = case Envir.alist_of_olist asol of
- [] => ~1 | ((_,i),_) :: _ => i;
- val minx = min (minenv :: map (fn ((_,i),_) => i) iTs);
- val normt = Envir.norm_term env;
- (*Perform minimal copying here by examining env*)
- val normp = if minx = ~1 then (tpairs, Bs@As, C)
- else
- let val ntps = map (pairself normt) tpairs
- in if minx>smax then (*no assignments in state*)
- (ntps, Bs @ map normt As, C)
- else if match then raise Bicompose
- else (*normalize the new rule fully*)
- (ntps, map normt (Bs @ As), normt C)
- end
- val th = Thm{sign=sign, hyps=rhyps union shyps, maxidx=maxidx,
- prop= Logic.rule_of normp}
+ fun addth As ((env as Envir.Envir {maxidx, ...}, tpairs), thq) =
+ let val normt = Envir.norm_term env;
+ (*perform minimal copying here by examining env*)
+ val normp =
+ if Envir.is_empty env then (tpairs, Bs @ As, C)
+ else
+ let val ntps = map (pairself normt) tpairs
+ in if the (Envir.minidx env) > smax then (*no assignments in state*)
+ (ntps, Bs @ map normt As, C)
+ else if match then raise Bicompose
+ else (*normalize the new rule fully*)
+ (ntps, map normt (Bs @ As), normt C)
+ end
+ val th = Thm{sign=sign, hyps=rhyps union shyps, maxidx=maxidx,
+ prop= Logic.rule_of normp}
in cons(th, thq) end handle Bicompose => thq
val (rtpairs,rhorn) = Logic.strip_flexpairs(rprop);
val (rAs,B) = Logic.strip_prems(nsubgoal, [], rhorn)
@@ -760,10 +770,10 @@
(*Modify assumptions, deleting n-th if n>0 for e-resolution*)
fun newAs(As0, n, dpairs, tpairs) =
let val As1 = if !Logic.auto_rename orelse not lifted then As0
- else map (rename_bvars(dpairs,tpairs,B)) As0
+ else map (rename_bvars(dpairs,tpairs,B)) As0
in (map (Logic.flatten_params n) As1)
- handle TERM _ =>
- raise THM("bicompose: 1st premise", 0, [orule])
+ handle TERM _ =>
+ raise THM("bicompose: 1st premise", 0, [orule])
end;
val env = Envir.empty(max[rmax,smax]);
val BBi = if lifted then strip_assums2(B,Bi) else (B,Bi);
@@ -771,19 +781,19 @@
(*elim-resolution: try each assumption in turn. Initially n=1*)
fun tryasms (_, _, []) = null
| tryasms (As, n, (t,u)::apairs) =
- (case pull(Unify.unifiers(sign, env, (t,u)::dpairs)) of
- None => tryasms (As, n+1, apairs)
- | cell as Some((_,tpairs),_) =>
- its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs)))
- (seqof (fn()=> cell),
- seqof (fn()=> pull (tryasms (As, n+1, apairs)))));
+ (case pull(Unify.unifiers(sign, env, (t,u)::dpairs)) of
+ None => tryasms (As, n+1, apairs)
+ | cell as Some((_,tpairs),_) =>
+ its_right (addth (newAs(As, n, [BBi,(u,t)], tpairs)))
+ (seqof (fn()=> cell),
+ seqof (fn()=> pull (tryasms (As, n+1, apairs)))));
fun eres [] = raise THM("bicompose: no premises", 0, [orule,state])
| eres (A1::As) = tryasms (As, 1, Logic.assum_pairs A1);
(*ordinary resolution*)
fun res(None) = null
- | res(cell as Some((_,tpairs),_)) =
- its_right (addth(newAs(rev rAs, 0, [BBi], tpairs)))
- (seqof (fn()=> cell), null)
+ | res(cell as Some((_,tpairs),_)) =
+ its_right (addth(newAs(rev rAs, 0, [BBi], tpairs)))
+ (seqof (fn()=> cell), null)
in if eres_flg then eres(rev rAs)
else res(pull(Unify.unifiers(sign, env, dpairs)))
end;
@@ -797,26 +807,26 @@
and conclusion B. If eres_flg then checks 1st premise of rule also*)
fun could_bires (Hs, B, eres_flg, rule) =
let fun could_reshyp (A1::_) = exists (apl(A1,could_unify)) Hs
- | could_reshyp [] = false; (*no premise -- illegal*)
- in could_unify(concl_of rule, B) andalso
- (not eres_flg orelse could_reshyp (prems_of rule))
+ | could_reshyp [] = false; (*no premise -- illegal*)
+ in could_unify(concl_of rule, B) andalso
+ (not eres_flg orelse could_reshyp (prems_of rule))
end;
(*Bi-resolution of a state with a list of (flag,rule) pairs.
Puts the rule above: rule/state. Renames vars in the rules. *)
-fun biresolution match brules i state =
+fun biresolution match brules i state =
let val lift = lift_rule(state, i);
- val (stpairs, Bs, Bi, C) = dest_state(state,i)
- val B = Logic.strip_assums_concl Bi;
- val Hs = Logic.strip_assums_hyp Bi;
- val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
- fun res [] = Sequence.null
- | res ((eres_flg, rule)::brules) =
- if could_bires (Hs, B, eres_flg, rule)
- then Sequence.seqof (*delay processing remainder til needed*)
- (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
- res brules))
- else res brules
+ val (stpairs, Bs, Bi, C) = dest_state(state,i)
+ val B = Logic.strip_assums_concl Bi;
+ val Hs = Logic.strip_assums_hyp Bi;
+ val comp = bicompose_aux match (state, (stpairs, Bs, Bi, C), true);
+ fun res [] = Sequence.null
+ | res ((eres_flg, rule)::brules) =
+ if could_bires (Hs, B, eres_flg, rule)
+ then Sequence.seqof (*delay processing remainder til needed*)
+ (fn()=> Some(comp (eres_flg, lift rule, nprems_of rule),
+ res brules))
+ else res brules
in Sequence.flats (res brules) end;
@@ -827,14 +837,14 @@
(*Look up the named axiom in the theory*)
fun get_axiom thy axname =
let fun get (Pure _) = raise Match
- | get (Extend{axioms,thy,...}) =
- (case Symtab.lookup(axioms,axname) of
- Some th => th
- | None => get thy)
- | get (Merge{thy1,thy2,...}) =
- get thy1 handle Match => get thy2
+ | get (Extend{axioms,thy,...}) =
+ (case Symtab.lookup(axioms,axname) of
+ Some th => th
+ | None => get thy)
+ | get (Merge{thy1,thy2,...}) =
+ get thy1 handle Match => get thy2
in get thy
- handle Match => raise THEORY("get_axiom: No axiom "^axname, [thy])
+ handle Match => raise THEORY("get_axiom: No axiom "^axname, [thy])
end;
(*Converts Frees to Vars: axioms can be written without question marks*)
@@ -844,14 +854,14 @@
(*Read an axiom for a new theory*)
fun read_ax sign (a, sP) : string*thm =
let val prop = prepare_axiom sign sP
- in (a, Thm{sign=sign, hyps=[], maxidx= maxidx_of_term prop, prop= prop})
+ in (a, Thm{sign=sign, hyps=[], maxidx= maxidx_of_term prop, prop= prop})
end
handle ERROR =>
- error("extend_theory: The error above occurred in axiom " ^ a);
+ error("extend_theory: The error above occurred in axiom " ^ a);
fun mk_axioms sign axpairs =
- Symtab.st_of_alist(map (read_ax sign) axpairs, Symtab.null)
- handle Symtab.DUPLICATE(a) => error("Two axioms named " ^ a);
+ Symtab.st_of_alist(map (read_ax sign) axpairs, Symtab.null)
+ handle Symtab.DUPLICATE(a) => error("Two axioms named " ^ a);
(*Extension of a theory with given classes, types, constants and syntax.
Reads the axioms from strings: axpairs have the form (axname, axiom). *)
@@ -861,9 +871,9 @@
in Extend{sign=sign, axioms= axioms, thy = thy} end;
(*The union of two theories*)
-fun merge_theories (thy1,thy2) =
- Merge{sign = Sign.merge(sign_of thy1, sign_of thy2),
- thy1 = thy1, thy2 = thy2};
+fun merge_theories (thy1, thy2) =
+ Merge {sign = Sign.merge (sign_of thy1, sign_of thy2),
+ thy1 = thy1, thy2 = thy2} handle TERM (msg, _) => error msg;
(*** Meta simp sets ***)
@@ -966,10 +976,10 @@
fun mk_rews_of_mss(Mss{mk_rews,...}) = mk_rews;
-(*** Meta-level rewriting
+(*** Meta-level rewriting
uses conversions, omitting proofs for efficiency. See
- L C Paulson, A higher-order implementation of rewriting,
- Science of Computer Programming 3 (1983), pages 119-149. ***)
+ L C Paulson, A higher-order implementation of rewriting,
+ Science of Computer Programming 3 (1983), pages 119-149. ***)
type prover = meta_simpset -> thm -> thm option;
type termrec = (Sign.sg * term list) * term;
@@ -991,7 +1001,7 @@
fun rewritec (prover,signt) (mss as Mss{net,...}) (hypst,t) =
let val t = Pattern.eta_contract t;
fun rew {thm as Thm{sign,hyps,maxidx,prop,...}, lhs} =
- let val unit = if Sign.subsig(sign,signt) then ()
+ let val unit = if Sign.subsig(sign,signt) then ()
else (writeln"Warning: rewrite rule from different theory";
raise Pattern.MATCH)
val insts = Pattern.match (#tsig(Sign.rep_sg signt)) (lhs,t)
@@ -1086,7 +1096,7 @@
(*** Meta-rewriting: rewrites t to u and returns the theorem t==u ***)
(* Parameters:
- mode = (simplify A, use A in simplifying B) when simplifying A ==> B
+ mode = (simplify A, use A in simplifying B) when simplifying A ==> B
mss: contains equality theorems of the form [|p1,...|] ==> t==u
prover: how to solve premises in conditional rewrites and congruences
*)
@@ -1100,3 +1110,4 @@
end
end;
+