changes for new manual.bib
Tue, 11 May 1999 10:32:10 +0200
changeset 6631 ccae8c659762
parent 6630 5f810292c030
child 6632 3f807540e939
changes for new manual.bib
--- a/doc-src/Inductive/ind-defs.bbl	Mon May 10 17:45:16 1999 +0200
+++ /dev/null	Thu Jan 01 00:00:00 1970 +0000
@@ -1,214 +0,0 @@
-Abramsky, S.,
-\newblock The lazy lambda calculus,
-\newblock In {\em Research Topics in Functional Programming}, D.~A. Turner, Ed.
-  Addison-Wesley, 1977, pp.~65--116
-Aczel, P.,
-\newblock An introduction to inductive definitions,
-\newblock In {\em Handbook of Mathematical Logic}, J.~Barwise, Ed.
-  North-Holland, 1977, pp.~739--782
-Aczel, P.,
-\newblock {\em Non-Well-Founded Sets},
-\newblock CSLI, 1988
-Boyer, R.~S., Moore, J.~S.,
-\newblock {\em A Computational Logic},
-\newblock Academic Press, 1979
-Camilleri, J., Melham, T.~F.,
-\newblock Reasoning with inductively defined relations in the {HOL} theorem
-  prover,
-\newblock Tech. Rep. 265, Comp. Lab., Univ. Cambridge, Aug. 1992
-Davey, B.~A., Priestley, H.~A.,
-\newblock {\em Introduction to Lattices and Order},
-\newblock Cambridge Univ. Press, 1990
-Dybjer, P.,
-\newblock Inductive sets and families in {Martin-L\"of's} type theory and their
-  set-theoretic semantics,
-\newblock In {\em Logical Frameworks}, G.~Huet G.~Plotkin, Eds. Cambridge Univ.
-  Press, 1991, pp.~280--306
-Dybjer, P., Nordstr{\"om}, B., Smith, J., Eds.,
-\newblock {\em Types for Proofs and Programs: International Workshop {TYPES
-  '94}},
-\newblock LNCS 996. Springer, 1995
-Farmer, W.~M., Guttman, J.~D., Thayer, F.~J.,
-\newblock {IMPS}: An interactive mathematical proof system,
-\newblock {\em J. Auto. Reas. {\bf 11}}, 2 (1993), 213--248
-Frost, J.,
-\newblock A case study of co-induction in {Isabelle},
-\newblock Tech. Rep. 359, Comp. Lab., Univ. Cambridge, Feb. 1995
-Gim{\'e}nez, E.,
-\newblock Codifying guarded definitions with recursive schemes,
-\newblock In Dybjer et~al. \cite{types94}, pp.~39--59
-Gunter, E.~L.,
-\newblock A broader class of trees for recursive type definitions for {HOL},
-\newblock In {\em Higher Order Logic Theorem Proving and Its Applications: HUG
-  '93\/} (Published 1994), J.~Joyce C.~Seger, Eds., LNCS 780, Springer,
-  pp.~141--154
-Hennessy, M.,
-\newblock {\em The Semantics of Programming Languages: An Elementary
-  Introduction Using Structural Operational Semantics},
-\newblock Wiley, 1990
-Huet, G.,
-\newblock Induction principles formalized in the {Calculus of Constructions},
-\newblock In {\em Programming of Future Generation Computers\/} (1988),
-  K.~Fuchi M.~Nivat, Eds., Elsevier, pp.~205--216
-Melham, T.~F.,
-\newblock Automating recursive type definitions in higher order logic,
-\newblock In {\em Current Trends in Hardware Verification and Automated Theorem
-  Proving}, G.~Birtwistle P.~A. Subrahmanyam, Eds. Springer, 1989, pp.~341--386
-Milner, R.,
-\newblock How to derive inductions in {LCF},
-\newblock note, Dept. Comp. Sci., Univ. Edinburgh, 1980
-Milner, R.,
-\newblock {\em Communication and Concurrency},
-\newblock Prentice-Hall, 1989
-Milner, R., Tofte, M.,
-\newblock Co-induction in relational semantics,
-\newblock {\em Theoretical Comput. Sci. {\bf 87}\/} (1991), 209--220
-Monahan, B.~Q.,
-\newblock {\em Data Type Proofs using Edinburgh {LCF}},
-\newblock PhD thesis, University of Edinburgh, 1984
-Nipkow, T.,
-\newblock More {Church-Rosser} proofs (in {Isabelle/HOL}),
-\newblock In {\em Automated Deduction --- {CADE}-13 International Conference\/}
-  (1996), M.~McRobbie J.~K. Slaney, Eds., LNAI 1104, Springer, pp.~733--747
-Owre, S., Shankar, N., Rushby, J.~M.,
-\newblock {\em The {PVS} specification language},
-\newblock Computer Science Laboratory, SRI International, Menlo Park, CA, Apr.
-  1993,
-\newblock Beta release
-Paulin-Mohring, C.,
-\newblock Inductive definitions in the system {Coq}: Rules and properties,
-\newblock In {\em Typed Lambda Calculi and Applications\/} (1993), M.~Bezem
-  J.~Groote, Eds., LNCS 664, Springer, pp.~328--345
-Paulson, L.~C.,
-\newblock {\em Logic and Computation: Interactive proof with Cambridge LCF},
-\newblock Cambridge Univ. Press, 1987
-Paulson, L.~C.,
-\newblock Set theory for verification: {I}. {From} foundations to functions,
-\newblock {\em J. Auto. Reas. {\bf 11}}, 3 (1993), 353--389
-Paulson, L.~C.,
-\newblock {\em Isabelle: A Generic Theorem Prover},
-\newblock Springer, 1994,
-\newblock LNCS 828
-Paulson, L.~C.,
-\newblock A concrete final coalgebra theorem for {ZF} set theory,
-\newblock In Dybjer et~al. \cite{types94}, pp.~120--139
-Paulson, L.~C.,
-\newblock Set theory for verification: {II}. {Induction} and recursion,
-\newblock {\em J. Auto. Reas. {\bf 15}}, 2 (1995), 167--215
-Paulson, L.~C.,
-\newblock Mechanizing coinduction and corecursion in higher-order logic,
-\newblock {\em J. Logic and Comput. {\bf 7}}, 2 (Mar. 1997), 175--204
-Paulson, L.~C.,
-\newblock Tool support for logics of programs,
-\newblock In {\em Mathematical Methods in Program Development: Summer School
-  Marktoberdorf 1996}, M.~Broy, Ed., NATO ASI Series F. Springer, Published
-  1997, pp.~461--498
-Paulson, L.~C., Gr\c{a}bczewski, K.,
-\newblock Mechanizing set theory: Cardinal arithmetic and the axiom of choice,
-\newblock {\em J. Auto. Reas. {\bf 17}}, 3 (Dec. 1996), 291--323
-Pitts, A.~M.,
-\newblock A co-induction principle for recursively defined domains,
-\newblock {\em Theoretical Comput. Sci. {\bf 124}\/} (1994), 195--219
-Rasmussen, O.,
-\newblock The {Church-Rosser} theorem in {Isabelle}: A proof porting
-  experiment,
-\newblock Tech. Rep. 364, Computer Laboratory, University of Cambridge, May
-  1995
-Saaltink, M., Kromodimoeljo, S., Pase, B., Craigen, D., Meisels, I.,
-\newblock An {EVES} data abstraction example,
-\newblock In {\em FME '93: Industrial-Strength Formal Methods\/} (1993),
-  J.~C.~P. Woodcock P.~G. Larsen, Eds., LNCS 670, Springer, pp.~578--596
-Slind, K.,
-\newblock Function definition in higher-order logic,
-\newblock In {\em Theorem Proving in Higher Order Logics: {TPHOLs} '96\/}
-  (1996), J.~von Wright, J.~Grundy, J.~Harrison, Eds., LNCS 1125
-Szasz, N.,
-\newblock A machine checked proof that {Ackermann's} function is not primitive
-  recursive,
-\newblock In {\em Logical Environments}, G.~Huet G.~Plotkin, Eds. Cambridge
-  Univ. Press, 1993, pp.~317--338
-V\"olker, N.,
-\newblock On the representation of datatypes in {Isabelle/HOL},
-\newblock In {\em Proceedings of the First Isabelle Users Workshop\/} (Sept.
-  1995), L.~C. Paulson, Ed., Technical Report 379, Comp. Lab., Univ. Cambridge,
-  pp.~206--218
-Winskel, G.,
-\newblock {\em The Formal Semantics of Programming Languages},
-\newblock MIT Press, 1993
--- a/doc-src/Inductive/ind-defs.tex	Mon May 10 17:45:16 1999 +0200
+++ b/doc-src/Inductive/ind-defs.tex	Tue May 11 10:32:10 1999 +0200
@@ -582,7 +582,7 @@
   domains   "listn(A)" <= "nat*list(A)"
     NilI  "<0,Nil>: listn(A)"
-    ConsI "[| a: A;  <n,l>: listn(A) |] ==> <succ(n), Cons(a,l)>: listn(A)"
+    ConsI "[| a:A; <n,l>:listn(A) |] ==> <succ(n), Cons(a,l)>: listn(A)"
   type_intrs "nat_typechecks @ list.intrs"
@@ -696,15 +696,17 @@
 To make this coinductive definition, the theory file includes (after the
 declaration of $\llist(A)$) the following lines:
 consts    lleq :: i=>i
   domains "lleq(A)" <= "llist(A) * llist(A)"
     LNil  "<LNil,LNil> : lleq(A)"
-    LCons "[| a:A; <l,l'>: lleq(A) |] ==> <LCons(a,l),LCons(a,l')>: lleq(A)"
+    LCons "[| a:A; <l,l'>:lleq(A) |] ==> <LCons(a,l),LCons(a,l')>: lleq(A)"
   type_intrs  "llist.intrs"
 The domain of $\lleq(A)$ is $\llist(A)\times\llist(A)$.  The type-checking
 rules include the introduction rules for $\llist(A)$, whose 
 declaration is discussed below (\S\ref{lists-sec}).
@@ -830,27 +832,29 @@
-Primrec = List +
-  primrec :: i
-  SC      :: i
-  \(\vdots\)
+Primrec_defs = Main +
+consts SC :: i
+ \(\vdots\)
-  SC_def    "SC == lam l:list(nat).list_case(0, \%x xs.succ(x), l)"
-  \(\vdots\)
+ SC_def    "SC == lam l:list(nat).list_case(0, \%x xs.succ(x), l)"
+ \(\vdots\)
+Primrec = Primrec_defs +
+consts prim_rec :: i
-  domains "primrec" <= "list(nat)->nat"
-  intrs
-    SC       "SC : primrec"
-    CONST    "k: nat ==> CONST(k) : primrec"
-    PROJ     "i: nat ==> PROJ(i) : primrec"
-    COMP     "[| g: primrec; fs: list(primrec) |] ==> COMP(g,fs): primrec"
-    PREC     "[| f: primrec; g: primrec |] ==> PREC(f,g): primrec"
-  monos       list_mono
-  con_defs    SC_def, CONST_def, PROJ_def, COMP_def, PREC_def
-  type_intrs "nat_typechecks @ list.intrs @                      
-              [lam_type, list_case_type, drop_type, map_type,    
-               apply_type, rec_type]"
+ domains "primrec" <= "list(nat)->nat"
+ intrs
+   SC     "SC : primrec"
+   CONST  "k: nat ==> CONST(k) : primrec"
+   PROJ   "i: nat ==> PROJ(i) : primrec"
+   COMP   "[| g: primrec; fs: list(primrec) |] ==> COMP(g,fs): primrec"
+   PREC   "[| f: primrec; g: primrec |] ==> PREC(f,g): primrec"
+ monos       list_mono
+ con_defs    SC_def, CONST_def, PROJ_def, COMP_def, PREC_def
+ type_intrs "nat_typechecks @ list.intrs @                      
+             [lam_type, list_case_type, drop_type, map_type,    
+              apply_type, rec_type]"
@@ -937,7 +941,7 @@
 $\QInl(a)$ and $\QInr(b)$ for $a$, $b\in\quniv(A)$.  In a typical codatatype
 definition with set parameters $A_1$, \ldots, $A_k$, a suitable domain is
 $\quniv(A_1\un\cdots\un A_k)$.  Details are published
 \subsection{The case analysis operator}
 The (co)datatype package automatically defines a case analysis operator,
@@ -1000,7 +1004,7 @@
 Now $\lst(A)$ is a datatype and enjoys the usual induction rule.
-Since $\lst(A)$ is a datatype, it enjoys a structural induction rule, {\tt
+Since $\lst(A)$ is a datatype, it has a structural induction rule, {\tt
 \[ \infer{P(x)}{x\in\lst(A) & P(\Nil)
         & \infer*{P(\Cons(a,l))}{[a\in A & l\in\lst(A) & P(l)]_{a,l}} }
@@ -1079,7 +1083,7 @@
          \right]_{t,f}} }
 This rule establishes a single predicate for $\TF(A)$, the union of the
-recursive sets.  Although such reasoning is sometimes useful
+recursive sets.  Although such reasoning can be useful
 \cite[\S4.5]{paulson-set-II}, a proper mutual induction rule should establish
 separate predicates for $\tree(A)$ and $\forest(A)$.  The package calls this
 rule {\tt tree\\_induct}.  Observe the usage of $P$ and $Q$ in
@@ -1292,7 +1296,7 @@
 Isabelle/\textsc{zf} instead uses a variant notion of ordered pairing, which
 can be generalized to a variant notion of function.  Elsewhere I have
 proved that this simple approach works (yielding final coalgebras) for a broad
-class of definitions~\cite{paulson-final}.
+class of definitions~\cite{paulson-mscs}.
 Several large studies make heavy use of inductive definitions.  L\"otzbeyer
 and Sandner have formalized two chapters of a semantics book~\cite{winskel93},
@@ -1318,15 +1322,12 @@
 The approach is not restricted to set theory.  It should be suitable for any
 logic that has some notion of set and the Knaster-Tarski theorem.  I have
 ported the (co)inductive definition package from Isabelle/\textsc{zf} to
-Isabelle/\textsc{hol} (higher-order logic).  V\"olker~\cite{voelker95}
-is investigating how to port the (co)datatype package.  \textsc{hol}
-represents sets by unary predicates; defining the corresponding types may
-cause complications.
+Isabelle/\textsc{hol} (higher-order logic).