File: Version.2.02

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hol88 2.02.19940316-35
  • links: PTS
  • area: main
  • in suites: bullseye, buster, sid
  • size: 65,988 kB
  • ctags: 21,623
  • sloc: ml: 199,939; ansic: 9,666; sh: 7,118; makefile: 6,095; lisp: 2,747; yacc: 894; sed: 201; cpp: 87; awk: 5
file content (2457 lines) | stat: -rw-r--r-- 110,499 bytes parent folder | download | duplicates (7)
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******************************************************************************
******************************** Version 2.02 ********************************
******************************************************************************



+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix for Common Lisp                                      |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/f-parsml.l                                             |
|----------------------------------------------------------------------------|
| DATE:          5 December 1992.                                            |
+----------------------------------------------------------------------------+

Preterm handlers were not working in Common Lisp. Fixed by forcing
some atoms to be lower case.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (sets libraries).                                    |
|----------------------------------------------------------------------------|
| CHANGED BY:    TFM                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/{sets,finite_sets,pred_sets}                        |
|----------------------------------------------------------------------------|
| DATE:          4 January 1993.                                             |
+----------------------------------------------------------------------------+

Konrad Slind noticed that the insert function was sometimes used as a prefix
"INSERT x s" rather than an infix "x INSERT s" in the sources for the set
theory libraries.  To avoid confusing people who may be reading the sources,
the infix form has been universally adopted.  Users should not notice the
change.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (X_SKOLEM_CONV / SKOLEM_CONV)                        |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/conv.ml                                                  |
|----------------------------------------------------------------------------|
| DATE:          5 February 1993.                                            |
+----------------------------------------------------------------------------+

Formerly, SKOLEM_CONV would succeed (with no effect) on simply existential
terms like "?x. x = 1". This was considered undesirable because it makes it
inconvenient to achieve multiple skolemizations by REDEPTH_CONV etc. Now
X_SKOLEM_CONV has been changed so if given a term "!x1..xn. ?y. ..." it will
fail unless there is at least one variable x1..xn. There is a consequent effect
on SKOLEM_CONV.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement/Bug-fix.                                        |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/latex-hol                                           |
|----------------------------------------------------------------------------|
| DATE:          5 February 1993.                                            |
+----------------------------------------------------------------------------+

This library is enhanced to handle restricted quatifiers. They are formatted
in the syntax similar to that pretty printed by the system when the
flag print_restict is true. And bugs in the LaTeX macros are fixed.

File: holmacs.tex
 1) Fix bug in macro definitions for symbols.
    Adding \relax in front of \ifmmode to prevent it to be expand before
    alignment. This fixes the problem where these symbols are the first
    thing in a line within an eqnarray environment.
 2) Adding the macro definition for double colons. Required by restricted
    quantifiers.

File: latex_term.pp

 Adding the rule for restricted quatifiers.

File: precedence.ml

 Adding precedence for restriced quatifiers. They have equal
 precedence as binders.

File: filters.ml

 Add translation from HOL constants to LaTeX symbols for restricted
 quantifiers.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Bug-fix (theory loading)                                    |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml                                               |
|----------------------------------------------------------------------------|
| DATE:          8 February 1993.                                            |
+----------------------------------------------------------------------------+

The loading of theories was slow due to the repeatedly activating binders
of the ancestors theories in the function activate_all_binders.
This function is called by the theory loading functions load_theory,
extend_theory and new_parent.

The function activate_all_binders is reimplemented as a local
function. It first finds out all the ancestors, then activates the
binders in each of them. It then remember the theories it has visited
so when ask to activate binders next time, it will not visit those
theories again.

The REFERENCE entry of activate_all_binders is deleted.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Bug-fix (parsing HOL lists)                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/parslist.l                                             |
|----------------------------------------------------------------------------|
| DATE:          9 February 1993.                                            |
+----------------------------------------------------------------------------+


Recently introduced bug that prevented nested lists like "[[1];[2]]"
from parsing has been fixed.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (library loading)                                    |
|----------------------------------------------------------------------------|
| CHANGED BY:    PC                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/more_lists/more_lists.ml,                           |
|                Library/more_lists/call_load_auxiliary.ml                   |
|----------------------------------------------------------------------------|
| DATE:          16 February 1993.                                           |
+----------------------------------------------------------------------------+

A bug that prevented the more_lists library from loading  when in draft mode
has been fixed.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Support for recording proofs                                |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml                                               |
|                ml/hol-rule.ml                                              |
|                ml/hol-drule.ml                                             |
|                ml/drul.ml                                                  |
|                ml/numconv.ml                                               |
|                ml/proof_rec.ml (new file)                                  |
|----------------------------------------------------------------------------|
| DATE:          03 March 1993                                               |
+----------------------------------------------------------------------------+

This change is based on the same changed made by MJCG. A separate version of
HOL was created for experiment this new feature. I now incorporate
this feature into the regular version of the system.

Those functions that generate theorems directly (i.e. call mk_thm)
have been modified to record a trace of their application in an ML
local assignable variable called steplist.

A step is a new ML concrete type defined by:

   type step = AssumeStep of term
             | ReflStep of term
             | SubstStep of (thm#term)list # term # thm
             | BetaConvStep of term
             | AbsStep of term # thm
             | InstTypeStep of (type#type)list # thm
             | DischStep of term # thm
             | MpStep of thm # thm
             | MkCombStep of thm # thm
             | MkAbsStep of thm
             | AlphaStep of term # term
             | AddAssumStep of term # thm
             | SymStep of thm
             | TransStep of thm # thm
             | ImpTransStep of thm # thm
             | ApTermStep of term # thm
             | ApThmStep of thm # term
             | EqMpStep of thm # thm
             | EqImpRuleStep of thm
             | SpecStep of term # thm
             | EqtIntroStep of thm
             | GenStep of term # thm
             | EtaConvStep of term
             | ExtStep of thm
             | ExistsStep of (term # term) # thm
             | ChooseStep of (term # thm) # thm
             | ImpAntisymRuleStep of thm # thm
             | MkExistsStep of thm
             | SubsStep of thm list # thm
             | SubsOccsStep of (int list # thm) list # thm
             | SubstConvStep of (thm # term) list # term # term
             | ConjStep of thm # thm
             | Conjunct1Step of thm
             | Conjunct2Step of thm
             | Disj1Step of thm # term
             | Disj2Step of term # thm
             | DisjCasesStep of thm # thm # thm
             | NotIntroStep of thm
             | NotElimStep of thm
             | ContrStep of term # thm
             | CcontrStep of term # thm
             | InstStep of (term # term) list # thm
             | StoreDefinitionStep of string # term
             | DefinitionStep of string # string
             | DefExistsRuleStep of term
             | NewAxiomStep of string # term
             | AxiomStep of string # string
             | TheoremStep of string # string
             | NewConstantStep of string # type
             | NewTypeStep of int # string
             | NumConvStep of term

The recording of steps is controlled by a flag `record_proof_flag`, which
is a local variable, and it is initially false. After setting it to
true, any step that is performed is added to the front of steplist.

The function

   record_proof : bool -> void

sets the flag `record_proof_flag` to its argument. If this is true, it
clears the list steplist. The function

   is_recording_proof : void -> void

returns the current setting of the flag `record_proof_flag`.
The function

   last_proof : void -> step list

returns the current value of the step list without modifying it. The
actual recording is done by the function

   RecordStep : step -> void

which adds its argument, a step, to the front of the step list only if
the `record_proof_flag` is true, otherwise it does nothing.

The function

   MakeProof : step list -> line list

converts a list of steps into a Hilbert style formal proof,
represented by a list of lines, where a line is defined by:

   type line = Line of (int # thm list # justification)

Where  a line

   Line(m, [th1;...;thn], j)

is the mth step in a proof; proves th1,...,thn and is
justified by j, where justifications are defined by:

   type justification =
      Hypothesis
    | Assume of term
    | Refl of term
    | Subst of (int#term)list # term # int
    | BetaConv of term
    | Abs of term # int
    | InstType of (type#type)list # int
    | Disch of term # int
    | Mp of int # int
    | MkComb of int # int
    | MkAbs of int
    | Alpha of term # term
    | AddAssum of term # int
    | Sym of int
    | Trans of int # int
    | ImpTrans of int # int
    | ApTerm of term # int
    | ApThm of int # term
    | EqMp of int # int
    | EqImpRule of int
    | Spec of term # int
    | EqtIntro of int
    | Gen of term # int
    | EtaConv of term
    | Ext of int
    | Exists of (term # term) # int
    | Choose of (term # int) # int
    | ImpAntisymRule of int # int
    | MkExists of int
    | Subs of int list # int
    | SubsOccs of (int list # int) list # int
    | SubstConv of (int # term) list # term # term
    | Conj of int # int
    | Conjunct1 of int
    | Conjunct2 of int
    | Disj1 of int # term
    | Disj2 of term # int
    | DisjCases of int # int # int
    | NotIntro of int
    | NotElim of int
    | Contr of term # int
    | Ccontr of term # int
    | Inst of (term # term) list # int
    | StoreDefinition of string # term
    | Definition of string # string
    | DefExistsRule of term
    | NewAxiom of string # term
    | Axiom of string # string
    | Theorem of string # string
    | NewConstant of string # type
    | NewType of int # string
    | NumConv of term

Justifications are like steps, but have the line number establishing a
theorem replacing the explicit theorem in a step.

Hypotheses (the first kind of justification) are theorems occurring in
steps that are not proved by the proof. They are given negative line
numbers.

Example:

#record_proof true;;
() : void

#last_proof();;
[] : step list

#g "A ==> (A \/ B)";;
"A ==> A \/ B"

() : void

#e(STRIP_TAC THEN ASM_REWRITE_TAC[]);;
OK..
goal proved
|- A ==> A \/ B

Previous subproof:
goal proved
() : void

#top_print print_all_thm;; % causes assumptions of theorems to be printed %
- : (thm -> void)

#rev (last_proof());;
[AssumeStep"A";
 AssumeStep"A";
 EqtIntroStepA |- A;
 ApTermStep("$\/", A |- A = T);
 ApThmStep(A |- $\/ A = $\/ T, "B");
 InstStep([("B", "GEN%VAR%266")], |- T \/ GEN%VAR%266 = T);
 TransStep(A |- A \/ B = T \/ B, |- T \/ B = T);
 SymStepA |- A \/ B = T;
 EqMpStep(A |- T = A \/ B, |- T);
 DischStep("A", A |- A \/ B);
 MpStep(|- A ==> A \/ B, A |- A);
 DischStep("A", A |- A \/ B);
 SymStepA |- A \/ B = T;
 EqMpStep(A |- T = A \/ B, |- T);
 DischStep("A", A |- A \/ B);
 MpStep(|- A ==> A \/ B, A |- A);
 DischStep("A", A |- A \/ B)]
: step list

#ShowProof ();;
[Line(-2, [|- T], Hypothesis);
 Line(-1, [|- T \/ GEN%VAR%266 = T], Hypothesis);
 Line(1, [A |- A], Assume"A");
 Line(2, [A |- A], Assume"A");
 Line(3, [A |- A = T], EqtIntro 2);
 Line(4, [A |- $\/ A = $\/ T], ApTerm("$\/", 3));
 Line(5, [A |- A \/ B = T \/ B], ApThm(4, "B"));
 Line(6, [|- T \/ B = T], Inst([("B", "GEN%VAR%266")], -1));
 Line(7, [A |- A \/ B = T], Trans(5, 6));
 Line(8, [A |- T = A \/ B], Sym 7);
 Line(9, [A |- A \/ B], EqMp(8, -2));
 Line(10, [|- A ==> A \/ B], Disch("A", 9));
 Line(11, [A |- A \/ B], Mp(10, 2));
 Line(12, [|- A ==> A \/ B], Disch("A", 11));
 Line(13, [A |- T = A \/ B], Sym 7);
 Line(14, [A |- A \/ B], EqMp(13, -2));
 Line(15, [|- A ==> A \/ B], Disch("A", 14));
 Line(16, [A |- A \/ B], Mp(15, 2));
 Line(17, [|- A ==> A \/ B], Disch("A", 16))]
: line list

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (wellorder library)                             |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/wellorder/mk_wellorder.ml                           |
|----------------------------------------------------------------------------|
| DATE:          31 March 1993.                                              |
+----------------------------------------------------------------------------+

Some theorems about induction and recursion over wellordered sets have been
added; in particular a theorem justifying quite general forms of transfinite
recursion.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   new library.                                                |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/Makefile                                            |
|                Library/res_quan                                            |
|----------------------------------------------------------------------------|
| DATE:          16 April 1993.                                              |
+----------------------------------------------------------------------------+

A new library res_quan containing tools for manipulating restricted
quantifications and conditional rewriting is added to the system.
See the manual or a summary of facicities in the directory Manual for
more details.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (mk_thm)                                        |
|----------------------------------------------------------------------------|
| CHANGED BY:    JVT                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml                                               |
|----------------------------------------------------------------------------|
| DATE:          21 April 1993.                                              |
+----------------------------------------------------------------------------+

The definition of mk_thm has been changed to remove occurrences of "o"
and "#".  These created additional embedded calls to "%ap" when expanded
by the ML -> lisp translator.  See the comments in ml/hol-syn.ml for the
before and after versions of the function.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Bugfix (num_EQ_CONV)                                        |
|----------------------------------------------------------------------------|
| CHANGED BY:    TFM                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/num.ml                                                   |
|----------------------------------------------------------------------------|
| DATE:          5 May 1993.                                                 |
+----------------------------------------------------------------------------+

The built-in conversion num_EQ_CONV had a bug (spotted by Konrad Slind)
that manifested itself in failure to prove certain inequalities:


   #num_EQ_CONV "3 = SUC(SUC(SUC 1))";;
   evaluation failed     num_EQ_CONV

This has now been fixed.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (adding theorem)                                |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: theory/mk_list_thms.ml                                      |
|                ml/load_thms.ml                                             |
|----------------------------------------------------------------------------|
| DATE:          7 May 1993.                                                 |
+----------------------------------------------------------------------------+

The following theorem is added to the list theory:
  LENGTH_MAP2
        |- !l1 l2. (LENGTH l1 = LENGTH l2) ==>
           (!f:*->**->***.
             (LENGTH(MAP2 f l1 l2) = LENGTH l1) /\
             (LENGTH(MAP2 f l1 l2) = LENGTH l2))
It is set up to be auto-loaded.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (recording proof)                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml, ml/proof_rec.ml                              |
|----------------------------------------------------------------------------|
| DATE:          11 May 1993.                                                |
+----------------------------------------------------------------------------+

Several functions are added to the suite of utitlies for recording proofs.
The first two are:

        suspend_recording : void -> void
        resume_recording : void -> void

By using these functions, one can temporarily suspend the recording of
a proof.  This allows one to do some auxiliary proofs whish are not
recorded in the midst of the main proof.

The functions
        write_last_proof : string -> void
        write_last_proof_add_to : string -> string -> void
output the proof steps since last time record_proof is called into a
text file. The first arguament of these functions is the name of the
file. The difference between the functions is that the second one
appends the proof to the named file. The second argument to this
function specifies the name  of the proof.

The syntax of the proof file is simple LISP-like expresseions. A file
may contain one or more proofs. The syntax of a proof is given below:

proof ::= `(` `PROOF` string proof_line_list `)` ;;

proof_line ::= `(` `LINE` num justification thm_list `)` ;;

justification ::= `(` just_name just_arg `)` ;;

thm ::= `(` `THM` term_list term `)` ;;

term ::= `(` term_atom `)` ;;

term_atom ::= `V` string type | `C` string type
        | `A` term term | `L` term term ;;

type ::= `(` type_atom `) ;;

type_atom ::= `TV` string | `TO` string type_list ;;

The terminal tokens are enclosed in backquote(`). The non-terminal
tokens which end with the suffix _list represent a list of tokens of
the same kind. For example, term_list is a list of terms. Every list
if enclosed in brackets, e.g. [(A (...)(...)) (C ...(...))] is a list
of two terms.

The token string represents a string of non-blank characters. Strings
are interpreted as names or identifiers, so they should follow the
rules of HOL identifiers, i.e., they can be either alphnumeric or
symbolic. The string following `TV` should begin with `*` since it is
type variable.

Space between items are optional except were the absence of it will
cause ambiguity. The general rules are
 1) two alphanumeric tokens must separated by space, and
 2) two symbolic tokens must separated by space.
The TAB, NEWLINE, LINEFEED and FORMFEED are treated as space
characters.

The token just_name is a string representing the name of
justification. The token just_arg is the argument of the justification
which varies according to the kind of justification. (See previous
comment on the type justification.)



+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement                                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    PC                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/more_arithmetic/                                    |
|----------------------------------------------------------------------------|
| DATE:          12 May 1993.                                                |
+----------------------------------------------------------------------------+

Several new theorems by Wai Wong have been added. These include many theorems
about DIV and MOD for which a new theory div_mod has been created. The new
theorems are given below. The theory heirarchy has been modified.

The theory pre:
Theorems --
  LESS_IMP_LESS_EQ_PRE    |- !m n. 0 < n ==> (m < n = m <= (PRE n))

The theory mult:
Theorems --
  NOT_MULT_LESS_0     |- !m n. 0 < m /\ 0 < n ==> 0 < (m * n)
  EXP1                |- !n. n EXP 1 = n
  ZERO_LESS_TWO_EXP   |- !n. 0 < (2 EXP n)
  ONE_LESS_EQ_TWO_EXP |- !n. 1 <= (2 EXP n)

The theory div_mod:
Theorems --
  SUC_MOD          |- !n m. (SUC n) < m ==> ((SUC n) MOD m = SUC(n MOD m))
  MULT_DIV         |- !n q. 0 < n ==> ((q * n) DIV n = q)
  LESS_DIV_EQ_ZERO |- !r n. r < n ==> (r DIV n = 0)
  MOD_MULT_MOD
    |- !m n. 0 < n /\ 0 < m ==> (!x. (x MOD (n * m)) MOD n = x MOD n)
  DIV_ONE          |- !q. q DIV (SUC 0) = q
  ADD_DIV_SUC_DIV  |- !n. 0 < n ==> (!r. (n + r) DIV n = SUC(r DIV n))
  SUC_MOD_SELF     |- !n. (SUC n) MOD (SUC n) = 0
  SUC_DIV_SELF     |- !n. (SUC n) DIV (SUC n) = 1
  ADD_DIV_ADD_DIV  |- !n. 0 < n ==> (!x r. ((x * n) + r) DIV n = x + (r DIV n))
  SUC_DIV_CASES
    |- !n. 0 < n ==>
            (!x. ((SUC x) DIV n = x DIV n) \/ ((SUC x) DIV n = SUC(x DIV n)))
  DIV_DIV_DIV_MULT
    |- !m n. 0 < m /\ 0 < n ==> (!x. (x DIV m) DIV n = x DIV (m * n))
  LESS_EQ_MONO_DIV |- !n. 0 < n ==> (!p q. p <= q ==> (p DIV n) <= (q DIV n))


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement                                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    PC                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/more_lists/                                         |
|----------------------------------------------------------------------------|
| DATE:          12 May 1993.                                                |
+----------------------------------------------------------------------------+

Several new theorems, conversions and tactics by Wai Wong have been added.
ELL which extracts elements indexed from the end of a list has been defined,
and a new theory ell created. The theory heirarchy has been modified.
The theorems EL_MAP and MAP_EL1_SUC_CONS have been moved to the theory el.

The following tactics have been added:
  EQ_LENGTH_INDUCT_TAC
  EQ_LENGTH_SNOC_INDUCT_TAC
  LENGTH_LIST_INDUCT_TAC

The following conversions have been added:
  BUTLAST_CONV
  EL_CONV
  LAST_CONV
  MAP2_CONV
  NBUTLAST_CONV
  SPLIT_CONV
  ELL_CONV
  LASTN_CONV
  SNOC_CONV

The following theorems have been added:
Theory snoc:
Theorems --
  SAME_LENGTH_SNOC
    |- !l a b. (LENGTH l = LENGTH(SNOC a b)) =
            (?a' b'. (LENGTH b' = LENGTH b) /\ (l = SNOC a' b'))

Theory append:
Theorems --
  APPEND_LENGTH_EQ
   |- !l1 l1'.
        (LENGTH l1 = LENGTH l1') ==>
          (!l2 l2'.
             (LENGTH l2 = LENGTH l2') ==>
             ((APPEND l1 l2 = APPEND l1' l2') = (l1 = l1') /\ (l2 = l2')))

Theory map:
Theorems --
  NULL_MAP   |- !f l. NULL(MAP f l) = NULL l
  TAIL_MAP   |- !f l. TAIL(MAP f l) = MAP f(TAIL l)
  MAP2_SNOC
    |- !f h1 h2 l1 l2.
      (LENGTH l1 = LENGTH l2) ==>
      (MAP2 f(SNOC h1 l1)(SNOC h2 l2) = SNOC(f h1 h2)(MAP2 f l1 l2))

Theory el:
Theorems --
  EL_BUTLAST
    |- !l x. ~NULL l ==> (SUC x) < (LENGTH l) ==> (EL x(BUTLAST l) = EL x l)
  MAP_EL  |- !f l n. n < (LENGTH l) ==> (MAP f[EL n l] = [f(EL n l)])
  EL_MAP2
    |- !f l l' n.
      (LENGTH l = LENGTH l') ==>
      n < (LENGTH l) \/ n < (LENGTH l') ==>
      (EL n(MAP2 f l l') = f(EL n l)(EL n l'))
  MAP2_EL
    |- !f l l' n.
      (LENGTH l = LENGTH l') ==>
      n < (LENGTH l) \/ n < (LENGTH l') ==>
      (MAP2 f[EL n l][EL n l'] = [f(EL n l)(EL n l')])

Theory ell:
Definitions --
  ELL
    |- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))

Theorems --
  ELL_LAST  |- !l. ~NULL l ==> (ELL 0 l = LAST l)
  ELL_LENGTH_APPEND
    |- !l1 l2. ~NULL l1 ==> (ELL(LENGTH l2)(APPEND l1 l2) = LAST l1)
  ELL_SNOC0  |- !l x. ELL 0(SNOC x l) = x
  ELL_SNOC  |- !l x k. 0 < k ==> (ELL k(SNOC x l) = ELL(PRE k)l)
  ELL_SUC_SNOC  |- !k x l. ELL(SUC k)(SNOC x l) = ELL k l
  ELL_CONS  |- !l x k. k < (LENGTH l) ==> (ELL k(CONS x l) = ELL k l)
  HD_ELL_LENGTH_SNOC
    |- !l x. ELL(LENGTH l)(SNOC x l) = (NULL l => x | HD l)
  HD_ELL_LENGTH_CONS  |- !l x. ELL(LENGTH l)(CONS x l) = x
  ELL_APPEND_1
    |- !l1 l2 k. k < (LENGTH l2) ==> (ELL k(APPEND l1 l2) = ELL k l2)
  ELL_APPEND_2
    |- !l1 l2 k.
        (LENGTH l2) <= k ==>
        (ELL k(APPEND l1 l2) = ELL(k - (LENGTH l2))l1)
  HD_ELL_PRE_LENGTH  |- !l. ~NULL l ==> (ELL(PRE(LENGTH l))l = HD l)
  EL_ELL
    |- !l k. k < (LENGTH l) ==> (EL k l = ELL(PRE((LENGTH l) - k))l)
  ELL_EL
    |- !l k. k < (LENGTH l) ==> (ELL k l = EL(PRE((LENGTH l) - k))l)
  ELL_MAP  |- !f l n. n < (LENGTH l) ==> (ELL n(MAP f l) = f(ELL n l))
  MAP_ELL  |- !f l n. n < (LENGTH l) ==> (MAP f[ELL n l] = [f(ELL n l)])
  ELL_MAP2
    |- !f l l' n.
        (LENGTH l = LENGTH l') ==>
        n < (LENGTH l) \/ n < (LENGTH l') ==>
        (ELL n(MAP2 f l l') = f(ELL n l)(ELL n l'))
  MAP2_ELL
    |- !f l l' n.
        (LENGTH l = LENGTH l') ==>
        n < (LENGTH l) \/ n < (LENGTH l') ==>
        (MAP2 f[ELL n l][ELL n l'] = [f(ELL n l)(ELL n l')])

Theory last_subseq:
Theorems --
  LASTN_LENGTH_APPEND  |- !l1 l2. LASTN(LENGTH l2)(APPEND l1 l2) = l2
  NBUTLAST_CONS
    |- !h l2 n.
        n <= (LENGTH l2) ==>
        (NBUTLAST n(CONS h l2) = CONS h(NBUTLAST n l2))
  NBUTLAST_LENGTH_CONS  |- !l h. NBUTLAST(LENGTH l)(CONS h l) = [h]
  NOT_NULL_NBUTLAST  |- !k l. k < (LENGTH l) ==> ~NULL(NBUTLAST k l)
  LAST_NBUTLAST_EL
    |- !k l.
        k < (LENGTH l) ==>
        (LAST(NBUTLAST k l) = EL(PRE((LENGTH l) - k))l)
  EL_NBUTLAST
    |- !l x k.
        k < (LENGTH l) /\ x < ((LENGTH l) - k) ==>
        (EL x(NBUTLAST k l) = EL x l)
  NBUTLAST_SUC_SNOC  |- !l x i. NBUTLAST(SUC i)(SNOC x l) = NBUTLAST i l
  LASTN_SUC_SNOC  |- !l x i. LASTN(SUC i)(SNOC x l) = SNOC x(LASTN i l)
  LAST_LASTN
    |- !l m. m <= (LENGTH l) ==> 0 < m ==> (LAST(LASTN m l) = LAST l)
  NBUTLAST_LASTN_NIL
    |- !l i. i <= (LENGTH l) ==> (NBUTLAST i(LASTN i l) = [])
  LASTN_NBUTLAST
    |- !l i k.
        (i + k) < (LENGTH l) ==>
        (LASTN k(NBUTLAST i l) = NBUTLAST i(LASTN(i + k)l))
  NBUTLAST_LASTN
    |- !l i k.
        i <= k /\ k <= (LENGTH l) ==>
        (NBUTLAST i(LASTN k l) = LASTN(k - i)(NBUTLAST i l))
  APPEND_LASTN_LASTN
    |- !l m1 m2.
        (m1 + m2) <= (LENGTH l) ==>
        (APPEND(LASTN m2(NBUTLAST m1 l))(LASTN m1 l) = LASTN(m1 + m2)l)
  LAST_TO_LASTN  |- !l. ~NULL l ==> ([LAST l] = LASTN 1 l)
  BUTLAST_TO_NBUTLAST  |- !l. ~NULL l ==> (BUTLAST l = NBUTLAST 1 l)
  LASTN_NBUTLAST_TL_SPLIT
    |- !l m k.
        0 < m /\ (k + m) < (LENGTH l) ==>
        (LASTN m(NBUTLAST k l) =
         APPEND(LASTN(m - 1)(NBUTLAST(k + 1)l))(LASTN 1(NBUTLAST k l)))
  NBUTLAST_APPEND1
    |- !l1 l2 k.
        (LENGTH l2) <= k ==>
        (NBUTLAST k(APPEND l1 l2) = NBUTLAST(k - (LENGTH l2))l1)
  LASTN_APPEND
    |- !l1 l2 n.
        n <= (LENGTH l2) ==> (LASTN n(APPEND l1 l2) = LASTN n l2)
  LASTN_APPEND2
    |- !l1 l2 n.
        (LENGTH l2) <= n ==>
        (LASTN n(APPEND l1 l2) = APPEND(LASTN(n - (LENGTH l2))l1)l2)
  LASTN_MAP
    |- !f l n. n <= (LENGTH l) ==> (LASTN n(MAP f l) = MAP f(LASTN n l))
  NBUTLAST_MAP
    |- !f l n.
        n <= (LENGTH l) ==> (NBUTLAST n(MAP f l) = MAP f(NBUTLAST n l))
  LASTN_MAP2
    |- !f l1 l2 n.
        (LENGTH l1 = LENGTH l2) ==>
        n <= (LENGTH l1) ==>
        (LASTN n(MAP2 f l1 l2) = MAP2 f(LASTN n l1)(LASTN n l2))
  NBUTLAST_MAP2
    |- !f l1 l2 n.
        (LENGTH l1 = LENGTH l2) ==>
        n <= (LENGTH l1) ==>
        (NBUTLAST n(MAP2 f l1 l2) =
         MAP2 f(NBUTLAST n l1)(NBUTLAST n l2))
  LAST_NBUTLAST_ELL
    |- !k l. k < (LENGTH l) ==> (LAST(NBUTLAST k l) = ELL k l)
  ELL_NBUTLAST
    |- !l k j.
        (j + k) <= (LENGTH l) ==> (ELL j(NBUTLAST k l) = ELL(j + k)l)
  ELL_LASTN
    |- !l m j.
        m <= (LENGTH l) ==> j < m ==> (ELL j(LASTN m l) = ELL j l)
  LASTN_NBUTLAST_APPEND
    |- !l1 l2 m k.
        (m + k) <= ((LENGTH l1) + (LENGTH l2)) /\
        k < (LENGTH l2) /\
        (LENGTH l2) <= (m + k) ==>
        (LASTN m(NBUTLAST k(APPEND l1 l2)) =
         APPEND
         (LASTN((m + k) - (LENGTH l2))l1)
         (LASTN((LENGTH l2) - k)(NBUTLAST k l2)))

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Optimization                                                |
|----------------------------------------------------------------------------|
| CHANGED BY:    JVT                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/conv.ml ml/hol-syn.ml ml/rewrite.ml ml/tacticals.ml      |
|----------------------------------------------------------------------------|
| DATE:          13 May 1993.                                                |
+----------------------------------------------------------------------------+

Recent profiling has shown that function composition in ML ("o") creates extra
calls to %ap (the ML application function).  The primitive rewrites, as well
as other core functions, have been rewritten to take advantage of this fact.
See the comments in the above-mentioned files to see exactly what was done
to each function.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (adding theorems)                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/more_lists/map.ml                                   |
|                Library/more_lists/lastn.ml                                 |
|----------------------------------------------------------------------------|
| DATE:          13 May 1993.                                                |
+----------------------------------------------------------------------------+

The following two theorems have been added to the library more_lists
in the theory as indicated:

 EVERY_SNOC snoc
        |- !P h l. EVERY P(SNOC h l) = EVERY P l /\ P

 EVERY_LASTN last_subseq
        |- !P l. EVERY P l ==> (!m. m <= (LENGTH l) ==> EVERY P(LASTN m l))

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (library loading)                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Makefile                                                    |
|                ml/lis.ml                                                   |
|                ml/lib_loader.ml (new file)                                 |
|----------------------------------------------------------------------------|
| DATE:          19 May 1993.                                                |
+----------------------------------------------------------------------------+

A generic library loader which carries out the standard library loading
procedures is provided for library authors. The library loading file
can be written much more concisely. The following three functions are added
to the system:

   library_loader --- a generic library loader
   define_load_lib_function --- defines load library function dynamically
   splitp --- general list function

Manual entries of these functions are added as well.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (new library)                                   |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/Makefile                                            |
|                Library/word (new directory)                                |
|----------------------------------------------------------------------------|
| DATE:          19 May 1993.                                                |
+----------------------------------------------------------------------------+

A new library `word' for modelling bit vectors is added to the system.
See manual for details.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Optimization (SELECT_RULE)                                  |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-drule.ml                                             |
|----------------------------------------------------------------------------|
| DATE:          29 June 1993.                                               |
+----------------------------------------------------------------------------+

A new version of SELECT_RULE has been introduced. It avoids a lot of run-time
computation, and is about twice as fast. It has the additional (potential)
advantage of not relying of CHOOSE.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Update (makeindex sources).                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    TFM                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: Manual/LaTeX/makeindex.src                                  |
|----------------------------------------------------------------------------|
| DATE:          3 July 1993.                                                |
+----------------------------------------------------------------------------+

The makeindex sources distribued with the system have been updated
from version 2.4 [20-Mar-88] to version 2.11 [19-Oct-1991].

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Optimization (ancestors)                                    |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-thyfn.ml                                             |
|                ml/hol-syn.ml                                               |
|----------------------------------------------------------------------------|
| DATE:          5 July 1993.                                                |
+----------------------------------------------------------------------------+

The ML function ancestors is very slow du to unnecessary recursive
search up the theory hierarchy. The new implementation uses a local
function which takes auxiliary list as extra arugment for storing the
search results to avoid repeated search. The order of the theories in
the resulting list is different from the original slow version.

This function is moved to the file hol-syn.ml since it is needed
in activate_binders (See change log entry dated 8 February 1993.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Support for proof recording                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml                                               |
|----------------------------------------------------------------------------|
| DATE:          5 July 1993.                                                |
+----------------------------------------------------------------------------+

The function new_infix was defined by dml so, unlike constants, when a
new infix constant is defined it won't be recorded. Define this
function in ML and call RecordStep.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Optimization.                                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    TFM/slind                                                   |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/conv.ml                                                  |
|----------------------------------------------------------------------------|
| DATE:          22 July 1993.                                               |
+----------------------------------------------------------------------------+

Konrad Slind noticed that in SUB_QCONV we have

     if (is_abs tm) then
        (let (bv,body) = dest_abs tm
        in  let bodyth = conv body
        in  MK_ABS (GEN bv bodyth))

It seems to me that the

    MK_ABS (GEN bv bodyth)

bit could be replaced with

    ABS bv bodyth

which might save on a bit of computation. This change has therefore
been made.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Bug fix.                                                    |
|----------------------------------------------------------------------------|
| CHANGED BY:    TFM                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/tactics.ml                                               |
|----------------------------------------------------------------------------|
| DATE:          22 July 1993.                                               |
+----------------------------------------------------------------------------+

ACCEPT_TAC has been fixed so that the justification it returns proves a
theorem syntactically identical to the goal and not just alpha-equivalent.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Support for proof recording                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml                                               |
|                Makefile, Library/Makefile                                  |
|                ml/prim_rec.ml, ml/lis.ml                                   |
| FILE DELETED:  ml/proof_rec.ml                                             |
| NEW LIBRARY:   record_proof                                                |
|----------------------------------------------------------------------------|
| DATE:          24 July 1993.                                               |
+----------------------------------------------------------------------------+

A new library record_proof for recording proof is added to the system.
See the manual in the library for more information.

Some functions in the library were implemented in the system in the file
`ml/proof_rec.ml`. As they are now in the library, the file
proof_rec.ml is deleted, and its entry in the Makefile is also deleted.

The function last_proof in ml/hol-syn.ml has been renamed to
get_steps.

Document pages for proof recording functions implemented in the system
are added to the help directory.

The function remove in the file ml/prim_rec.ml is moved to the file
ml/lis.ml because ml/hol-syn.ml need it but ml/prim_rec is compiled after
ml/hol-syn.ml

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Bug fix / Generalisation                                    |
|----------------------------------------------------------------------------|
| CHANGED BY:    JG                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/conv.ml                                                  |
|----------------------------------------------------------------------------|
| DATE:          19 October 1993.                                            |
+----------------------------------------------------------------------------+

SELECT_CONV will now work with alpha-equivalnce.
That is it works with terms like: "!z. (@e. !x. e + x = x) + z = z",
where previously this would have to be: "!x. (@e. !x. e + x = x) + x = x".


+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix                                                      |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/hol-pars.l                                             |
|----------------------------------------------------------------------------|
| DATE:          17 November 1993.                                           |
+----------------------------------------------------------------------------+

An obscure problem with parsing using defined constants named `::` has
been fixed.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix                                                      |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-syn.ml ml/hol-thyfn.ml                               |
|----------------------------------------------------------------------------|
| DATE:          6 December 1993.                                            |
+----------------------------------------------------------------------------+

The name `definition' has been bound to two functions at top level.
Once in the file ml/hol-syn.ml and once in the file ml/hol-thyfn.ml. The
function in hol-syn.ml has been masked out by the function in hol-thyfn.ml.

The binding and the function in hol-syn.ml are deleted. The
functionality, namely recording proof step, is incorporated in to the
function in hol-thyfn.ml.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix                                                      |
|----------------------------------------------------------------------------|
| CHANGED BY:    JG                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/window/basic_close.ml                               |
|----------------------------------------------------------------------------|
| DATE:          7 December 1993.                                            |
+----------------------------------------------------------------------------+

Fixed a bug in LET_CLOSE which filtered out the assumption it was supposed to
add.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement                                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    JG                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/window/hol_ext.ml                                   |
|----------------------------------------------------------------------------|
| DATE:          7 December 1993.                                            |
+----------------------------------------------------------------------------+

Added the new functions IMP_PMI_CONV and PMI_PMI_CONV.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix                                                      |
|----------------------------------------------------------------------------|
| CHANGED BY:    JG                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/window/inter.ml                                     |
|----------------------------------------------------------------------------|
| DATE:          7 December 1993.                                            |
+----------------------------------------------------------------------------+

Fixed bug where you could not end a stack if there was a current stack.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement                                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    JG                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/window/win.ml                                       |
|----------------------------------------------------------------------------|
| DATE:          7 December 1993.                                            |
+----------------------------------------------------------------------------+

Now when you open a window to establish a conjecture,
the conjecture (and the lemmas that depend on it) dissapear from the
context.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   new library (numeral)                                       |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/Makefile                                            |
|                Library/numeral                                             |
|----------------------------------------------------------------------------|
| DATE:          13 December 1993                                            |
+----------------------------------------------------------------------------+

A new library `numeral', written by Tim Leonard,  has been added. It provides
facilities for the manipulation of positionally-represented numbers and fast
arithmetic on them. Full standard documentation is provided.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   New built-in theory fun                                     |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| NEW FILE:      theories/mk_fun.ml                                          |
|----------------------------------------------------------------------------|
| DATE:          5 January 1994                                              |
+----------------------------------------------------------------------------+

This new thoery contains definitions of several predicates on functions
and some theorems about them. They are used in the new list theory. They
are also generally useful. So this new theory is created for them.
The output of "print_theory`fun`" is as below:

The Theory fun
Parents --  BASIC-HOL
Constants --
  ASSOC ":(* -> (* -> *)) -> bool"
  COMM ":(* -> (* -> **)) -> bool"
  FCOMM ":(* -> (* -> *)) -> ((* -> (* -> *)) -> bool)"
  RIGHT_ID ":(* -> (** -> *)) -> (** -> bool)"
  LEFT_ID ":(** -> (* -> *)) -> (** -> bool)"
  MONOID ":(* -> (* -> *)) -> (* -> bool)"
Definitions --
  ASSOC_DEF  |- !f. ASSOC f = (!x y z. f x(f y z) = f(f x y)z)
  COMM_DEF  |- !f. COMM f = (!x y. f x y = f y x)
  FCOMM_DEF  |- !f g. FCOMM f g = (!x y z. g x(f y z) = f(g x y)z)
  RIGHT_ID_DEF  |- !f e. RIGHT_ID f e = (!x. f x e = x)
  LEFT_ID_DEF  |- !f e. LEFT_ID f e = (!x. f e x = x)
  MONOID_DEF
    |- !f e. MONOID f e = ASSOC f /\ RIGHT_ID f e /\ LEFT_ID f e

Theorems --
  ASSOC_CONJ  |- ASSOC $/\
  ASSOC_DISJ  |- ASSOC $\/
  FCOMM_ASSOC  |- !f. FCOMM f f = ASSOC f
  MONOID_CONJ_T  |- MONOID $/\ T
  MONOID_DISJ_F  |- MONOID $\/ F

******************** fun ********************

() : void


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Revision of the theory list                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: theories/mk_list_thms.ml                                    |
| NEW FILE:      theories/mk_list_defs.ml theories/mk_list_thm2.ml           |
|----------------------------------------------------------------------------|
| DATE:          5 January 1994                                              |
+----------------------------------------------------------------------------+

The built-in theory list has been extensively revised and extended.

All definitions and theorem in the old list theory are kept unchanged
except the constant EVERY.  It has been changed to ALL_EL. The name of
its definition is changed from EVERY_DEF to ALL_EL, and two theorems,
EVERY_CONJ and EVERY_EL are changed to ALL_EL_CONJ and ALL_EL_EL,
respectively.

The files creating the list theory:
   theories/mk_list.ml --- list type definition (old, unchanged)
   theories/mk_list_defs.ml --- all constant definitions (new)
   theories/mk_list_thms.ml --- old theorems (old, changed)
   theories/mk_list_thm2.ml --- new theorems (new)

The list theory now looks like below:

The Theory list
Parents --  BASIC-HOL     arithmetic     combin
Types --  ":(*)list"
Constants --
  IS_list_REP ":(num -> *) # num -> bool"
  REP_list ":(*)list -> (num -> *) # num"
  ABS_list ":(num -> *) # num -> (*)list"     NIL ":(*)list"
  CONS ":* -> ((*)list -> (*)list)"     NULL ":(*)list -> bool"
  HD ":(*)list -> *"     TL ":(*)list -> (*)list"
  SNOC ":* -> ((*)list -> (*)list)"
  FOLDR ":(* -> (** -> **)) -> (** -> ((*)list -> **))"
  FOLDL ":(** -> (* -> **)) -> (** -> ((*)list -> **))"
  FILTER ":(* -> bool) -> ((*)list -> (*)list)"
  SCANL ":(** -> (* -> **)) -> (** -> ((*)list -> (**)list))"
  SCANR ":(* -> (** -> **)) -> (** -> ((*)list -> (**)list))"
  REVERSE ":(*)list -> (*)list"
  APPEND ":(*)list -> ((*)list -> (*)list)"
  FLAT ":((*)list)list -> (*)list"     LENGTH ":(*)list -> num"
  MAP ":(* -> **) -> ((*)list -> (**)list)"
  MAP2 ":(* -> (** -> ***)) -> ((*)list -> ((**)list -> (***)list))"
  ALL_EL ":(* -> bool) -> ((*)list -> bool)"
  SOME_EL ":(* -> bool) -> ((*)list -> bool)"
  IS_EL ":* -> ((*)list -> bool)"
  FIRSTN ":num -> ((*)list -> (*)list)"
  BUTFIRSTN ":num -> ((*)list -> (*)list)"
  SEG ":num -> (num -> ((*)list -> (*)list))"
  LAST ":(*)list -> *"     BUTLAST ":(*)list -> (*)list"
  LASTN ":num -> ((*)list -> (*)list)"
  BUTLASTN ":num -> ((*)list -> (*)list)"
  EL ":num -> ((*)list -> *)"     ELL ":num -> ((*)list -> *)"
  IS_PREFIX ":(*)list -> ((*)list -> bool)"
  IS_SUFFIX ":(*)list -> ((*)list -> bool)"
  IS_SUBLIST ":(*)list -> ((*)list -> bool)"
  SPLITP ":(* -> bool) -> ((*)list -> (*)list # (*)list)"
  PREFIX ":(* -> bool) -> ((*)list -> (*)list)"
  SUFFIX ":(* -> bool) -> ((*)list -> (*)list)"
  ZIP ":(*)list # (*)list -> (* # *)list"
  UNZIP ":(* # **)list -> (*)list # (**)list"
  UNZIP_FST ":(* # **)list -> (*)list"
  UNZIP_SND ":(* # **)list -> (**)list"     SUM ":(num)list -> num"
Definitions --
  IS_list_REP
    |- !r. IS_list_REP r = (?f n. r = (\m. (m < n => f m | (@x. T))),n)
  list_TY_DEF  |- ?rep. TYPE_DEFINITION IS_list_REP rep
  list_ISO_DEF
    |- (!a. ABS_list(REP_list a) = a) /\
       (!r. IS_list_REP r = (REP_list(ABS_list r) = r))
  NIL_DEF  |- [] = ABS_list((\n. @e. T),0)
  CONS_DEF
    |- !h t.
        CONS h t =
        ABS_list
        ((\m. ((m = 0) => h | FST(REP_list t)(PRE m))),
         SUC(SND(REP_list t)))
  NULL_DEF  |- (NULL[] = T) /\ (!h t. NULL(CONS h t) = F)
  HD  |- !h t. HD(CONS h t) = h
  TL  |- !h t. TL(CONS h t) = t
  SNOC
    |- (!x. SNOC x[] = [x]) /\
       (!x x' l. SNOC x(CONS x' l) = CONS x'(SNOC x l))
  FOLDR
    |- (!f e. FOLDR f e[] = e) /\
       (!f e x l. FOLDR f e(CONS x l) = f x(FOLDR f e l))
  FOLDL
    |- (!f e. FOLDL f e[] = e) /\
       (!f e x l. FOLDL f e(CONS x l) = FOLDL f(f e x)l)
  FILTER
    |- (!P. FILTER P[] = []) /\
       (!P x l.
         FILTER P(CONS x l) = (P x => CONS x(FILTER P l) | FILTER P l))
  SCANL
    |- (!f e. SCANL f e[] = [e]) /\
       (!f e x l. SCANL f e(CONS x l) = CONS e(SCANL f(f e x)l))
  SCANR
    |- (!f e. SCANR f e[] = [e]) /\
       (!f e x l.
         SCANR f e(CONS x l) = CONS(f x(HD(SCANR f e l)))(SCANR f e l))
  REVERSE
    |- (REVERSE[] = []) /\ (!x l. REVERSE(CONS x l) = SNOC x(REVERSE l))
  APPEND
    |- (!l. APPEND[]l = l) /\
       (!l1 l2 h. APPEND(CONS h l1)l2 = CONS h(APPEND l1 l2))
  FLAT  |- (FLAT[] = []) /\ (!h t. FLAT(CONS h t) = APPEND h(FLAT t))
  LENGTH  |- (LENGTH[] = 0) /\ (!h t. LENGTH(CONS h t) = SUC(LENGTH t))
  MAP
    |- (!f. MAP f[] = []) /\
       (!f h t. MAP f(CONS h t) = CONS(f h)(MAP f t))
  MAP2
    |- (!f. MAP2 f[][] = []) /\
       (!f h1 t1 h2 t2.
         MAP2 f(CONS h1 t1)(CONS h2 t2) = CONS(f h1 h2)(MAP2 f t1 t2))
  ALL_EL
    |- (!P. ALL_EL P[] = T) /\
       (!P x l. ALL_EL P(CONS x l) = P x /\ ALL_EL P l)
  SOME_EL
    |- (!P. SOME_EL P[] = F) /\
       (!P x l. SOME_EL P(CONS x l) = P x \/ SOME_EL P l)
  IS_EL_DEF  |- !x l. IS_EL x l = SOME_EL(\y. x = y)l
  FIRSTN
    |- (!l. FIRSTN 0 l = []) /\
       (!n x l. FIRSTN(SUC n)(CONS x l) = CONS x(FIRSTN n l))
  BUTFIRSTN
    |- (!l. BUTFIRSTN 0 l = l) /\
       (!n x l. BUTFIRSTN(SUC n)(CONS x l) = BUTFIRSTN n l)
  SEG
    |- (!k l. SEG 0 k l = []) /\
       (!m x l. SEG(SUC m)0(CONS x l) = CONS x(SEG m 0 l)) /\
       (!m k x l. SEG(SUC m)(SUC k)(CONS x l) = SEG(SUC m)k l)
  LAST_DEF  |- !l. LAST l = HD(SEG 1(PRE(LENGTH l))l)
  BUTLAST_DEF  |- !l. BUTLAST l = SEG(PRE(LENGTH l))0 l
  LASTN
    |- (!l. LASTN 0 l = []) /\
       (!n x l. LASTN(SUC n)(SNOC x l) = SNOC x(LASTN n l))
  BUTLASTN
    |- (!l. BUTLASTN 0 l = l) /\
       (!n x l. BUTLASTN(SUC n)(SNOC x l) = BUTLASTN n l)
  EL  |- (!l. EL 0 l = HD l) /\ (!l n. EL(SUC n)l = EL n(TL l))
  ELL
    |- (!l. ELL 0 l = LAST l) /\ (!n l. ELL(SUC n)l = ELL n(BUTLAST l))
  IS_PREFIX
    |- (!l. IS_PREFIX l[] = T) /\
       (!x l. IS_PREFIX[](CONS x l) = F) /\
       (!x1 l1 x2 l2.
         IS_PREFIX(CONS x1 l1)(CONS x2 l2) =
         (x1 = x2) /\ IS_PREFIX l1 l2)
  IS_SUFFIX
    |- (!l. IS_SUFFIX l[] = T) /\
       (!x l. IS_SUFFIX[](SNOC x l) = F) /\
       (!x1 l1 x2 l2.
         IS_SUFFIX(SNOC x1 l1)(SNOC x2 l2) =
         (x1 = x2) /\ IS_SUFFIX l1 l2)
  IS_SUBLIST
    |- (!l. IS_SUBLIST l[] = T) /\
       (!x l. IS_SUBLIST[](CONS x l) = F) /\
       (!x1 l1 x2 l2.
         IS_SUBLIST(CONS x1 l1)(CONS x2 l2) =
         (x1 = x2) /\ IS_PREFIX l1 l2 \/ IS_SUBLIST l1(CONS x2 l2))
  SPLITP
    |- (!P. SPLITP P[] = [],[]) /\
       (!P x l.
         SPLITP P(CONS x l) =
         (P x =>
          ([],CONS x l) |
          (CONS x(FST(SPLITP P l)),SND(SPLITP P l))))
  PREFIX_DEF  |- !P l. PREFIX P l = FST(SPLITP($~ o P)l)
  SUFFIX_DEF
    |- !P l. SUFFIX P l = FOLDL(\l' x. (P x => SNOC x l' | []))[]l
  ZIP
    |- (ZIP([],[]) = []) /\
       (!x1 l1 x2 l2.
         ZIP(CONS x1 l1,CONS x2 l2) = CONS(x1,x2)(ZIP(l1,l2)))
  UNZIP
    |- (UNZIP[] = [],[]) /\
       (!x l.
         UNZIP(CONS x l) =
         CONS(FST x)(FST(UNZIP l)),CONS(SND x)(SND(UNZIP l)))
  UNZIP_FST_DEF  |- !l. UNZIP_FST l = FST(UNZIP l)
  UNZIP_SND_DEF  |- !l. UNZIP_SND l = SND(UNZIP l)
  SUM  |- (SUM[] = 0) /\ (!h t. SUM(CONS h t) = h + (SUM t))

Theorems --
  list_Axiom
    |- !x f. ?! fn. (fn[] = x) /\ (!h t. fn(CONS h t) = f(fn t)h t)
  NULL  |- NULL[] /\ (!h t. ~NULL(CONS h t))
  list_INDUCT
    |- !P. P[] /\ (!t. P t ==> (!h. P(CONS h t))) ==> (!l. P l)
  list_CASES  |- !l. (l = []) \/ (?t h. l = CONS h t)
  CONS_11  |- !h t h' t'. (CONS h t = CONS h' t') = (h = h') /\ (t = t')
  NOT_NIL_CONS  |- !h t. ~([] = CONS h t)
  NOT_CONS_NIL  |- !h t. ~(CONS h t = [])
  LIST_NOT_EQ
    |- !l1 l2. ~(l1 = l2) ==> (!h1 h2. ~(CONS h1 l1 = CONS h2 l2))
  NOT_EQ_LIST
    |- !h1 h2. ~(h1 = h2) ==> (!l1 l2. ~(CONS h1 l1 = CONS h2 l2))
  EQ_LIST
    |- !h1 h2.
        (h1 = h2) ==> (!l1 l2. (l1 = l2) ==> (CONS h1 l1 = CONS h2 l2))
  CONS  |- !l. ~NULL l ==> (CONS(HD l)(TL l) = l)
  APPEND_ASSOC
    |- !l1 l2 l3. APPEND l1(APPEND l2 l3) = APPEND(APPEND l1 l2)l3
  LENGTH_APPEND
    |- !l1 l2. LENGTH(APPEND l1 l2) = (LENGTH l1) + (LENGTH l2)
  MAP_APPEND
    |- !f l1 l2. MAP f(APPEND l1 l2) = APPEND(MAP f l1)(MAP f l2)
  LENGTH_MAP  |- !l f. LENGTH(MAP f l) = LENGTH l
  LENGTH_NIL  |- !l. (LENGTH l = 0) = (l = [])
  LENGTH_CONS
    |- !l n.
        (LENGTH l = SUC n) = (?h l'. (LENGTH l' = n) /\ (l = CONS h l'))
  LENGTH_EQ_CONS
    |- !P n.
        (!l. (LENGTH l = SUC n) ==> P l) =
        (!l. (LENGTH l = n) ==> (\l. !x. P(CONS x l))l)
  LENGTH_EQ_NIL  |- !P. (!l. (LENGTH l = 0) ==> P l) = P[]
  LENGTH_MAP2
    |- !l1 l2.
        (LENGTH l1 = LENGTH l2) ==>
        (!f.
          (LENGTH(MAP2 f l1 l2) = LENGTH l1) /\
          (LENGTH(MAP2 f l1 l2) = LENGTH l2))
  NULL_EQ_EMPTY  |- !l. NULL l = (l = [])
  LENGTH_EQ  |- !x y. (x = y) ==> (LENGTH x = LENGTH y)
  LENGTH_NOT_NULL  |- !l. 0 < (LENGTH l) = ~NULL l
  REVERSE_SNOC  |- !x l. REVERSE(SNOC x l) = CONS x(REVERSE l)
  REVERSE_REVERSE  |- !l. REVERSE(REVERSE l) = l
  SNOC_Axiom
    |- !e f. ?! fn. (fn[] = e) /\ (!x l. fn(SNOC x l) = f(fn l)x l)
  SNOC_INDUCT
    |- !P. P[] /\ (!l. P l ==> (!x. P(SNOC x l))) ==> (!l. P l)
  SNOC_CASES  |- !l. (l = []) \/ (?l' x. l = SNOC x l')
  LENGTH_SNOC  |- !x l. LENGTH(SNOC x l) = SUC(LENGTH l)
  NOT_NULL_SNOC  |- !x l. ~NULL(SNOC x l)
  NOT_NIL_SNOC  |- !x l. ~([] = SNOC x l)
  NOT_SNOC_NIL  |- !x l. ~(SNOC x l = [])
  SNOC_11  |- !x l x' l'. (SNOC x l = SNOC x' l') = (x = x') /\ (l = l')
  SNOC_EQ_LENGTH_EQ
    |- !x1 l1 x2 l2.
        (SNOC x1 l1 = SNOC x2 l2) ==> (LENGTH l1 = LENGTH l2)
  SNOC_REVERSE_CONS  |- !x l. SNOC x l = REVERSE(CONS x(REVERSE l))
  SNOC_APPEND  |- !x l. SNOC x l = APPEND l[x]
  MAP_SNOC  |- !f x l. MAP f(SNOC x l) = SNOC(f x)(MAP f l)
  FOLDR_SNOC  |- !f e x l. FOLDR f e(SNOC x l) = FOLDR f(f x e)l
  FOLDL_SNOC  |- !f e x l. FOLDL f e(SNOC x l) = f(FOLDL f e l)x
  FOLDR_FOLDL  |- !f e. MONOID f e ==> (!l. FOLDR f e l = FOLDL f e l)
  LENGTH_FOLDR  |- !l. LENGTH l = FOLDR(\x l'. SUC l')0 l
  LENGTH_FOLDL  |- !l. LENGTH l = FOLDL(\l' x. SUC l')0 l
  MAP_FOLDR  |- !f l. MAP f l = FOLDR(\x l'. CONS(f x)l')[]l
  MAP_FOLDL  |- !f l. MAP f l = FOLDL(\l' x. SNOC(f x)l')[]l
  MAP_o  |- !f g. MAP(f o g) = (MAP f) o (MAP g)
  MAP_MAP_o  |- !f g l. MAP f(MAP g l) = MAP(f o g)l
  FILTER_FOLDR
    |- !P l. FILTER P l = FOLDR(\x l'. (P x => CONS x l' | l'))[]l
  FILTER_SNOC
    |- !P x l.
        FILTER P(SNOC x l) = (P x => SNOC x(FILTER P l) | FILTER P l)
  FILTER_FOLDL
    |- !P l. FILTER P l = FOLDL(\l' x. (P x => SNOC x l' | l'))[]l
  FILTER_COMM
    |- !f1 f2 l. FILTER f1(FILTER f2 l) = FILTER f2(FILTER f1 l)
  FILTER_IDEM  |- !f l. FILTER f(FILTER f l) = FILTER f l
  FILTER_MAP
    |- !f1 f2 l. FILTER f1(MAP f2 l) = MAP f2(FILTER(f1 o f2)l)
  LENGTH_SEG
    |- !n k l. (n + k) <= (LENGTH l) ==> (LENGTH(SEG n k l) = n)
  APPEND_NIL  |- (!l. APPEND l[] = l) /\ (!l. APPEND[]l = l)
  APPEND_SNOC  |- !l1 x l2. APPEND l1(SNOC x l2) = SNOC x(APPEND l1 l2)
  REVERSE_APPEND
    |- !l1 l2. REVERSE(APPEND l1 l2) = APPEND(REVERSE l2)(REVERSE l1)
  APPEND_FOLDR  |- !l1 l2. APPEND l1 l2 = FOLDR CONS l2 l1
  APPEND_FOLDL  |- !l1 l2. APPEND l1 l2 = FOLDL(\l' x. SNOC x l')l1 l2
  FOLDR_APPEND
    |- !f e l1 l2. FOLDR f e(APPEND l1 l2) = FOLDR f(FOLDR f e l2)l1
  FOLDL_APPEND
    |- !f e l1 l2. FOLDL f e(APPEND l1 l2) = FOLDL f(FOLDL f e l1)l2
  CONS_APPEND  |- !x l. CONS x l = APPEND[x]l
  ASSOC_APPEND  |- ASSOC APPEND
  FCOMM_APPEND_CONS  |- !f. FCOMM APPEND(\x l'. CONS(f x)l')
  FCOMM_SNOC_APPEND  |- !f. FCOMM(\l' x. SNOC(f x)l')APPEND
  RIGHT_ID_APPEND_NIL  |- RIGHT_ID APPEND[]
  LEFT_ID_APPEND_NIL  |- LEFT_ID APPEND[]
  MONOID_APPEND_NIL  |- MONOID APPEND[]
  APPEND_LENGTH_EQ
    |- !l1 l1'.
        (LENGTH l1 = LENGTH l1') ==>
        (!l2 l2'.
          (LENGTH l2 = LENGTH l2') ==>
          ((APPEND l1 l2 = APPEND l1' l2') = (l1 = l1') /\ (l2 = l2')))
  FILTER_APPEND
    |- !f l1 l2.
        FILTER f(APPEND l1 l2) = APPEND(FILTER f l1)(FILTER f l2)
  FLAT_SNOC  |- !x l. FLAT(SNOC x l) = APPEND(FLAT l)x
  FLAT_FOLDR  |- !l. FLAT l = FOLDR APPEND[]l
  FLAT_FOLDL  |- !l. FLAT l = FOLDL APPEND[]l
  LENGTH_FLAT  |- !l. LENGTH(FLAT l) = SUM(MAP LENGTH l)
  REVERSE_FOLDR  |- !l. REVERSE l = FOLDR SNOC[]l
  REVERSE_FOLDL  |- !l. REVERSE l = FOLDL(\l' x. CONS x l')[]l
  LENGTH_REVERSE  |- !l. LENGTH(REVERSE l) = LENGTH l
  REVERSE_EQ_NIL  |- !l. (REVERSE l = []) = (l = [])
  ALL_EL_SNOC  |- !P x l. ALL_EL P(SNOC x l) = ALL_EL P l /\ P x
  ALL_EL_CONJ
    |- !P Q l. ALL_EL(\x. P x /\ Q x)l = ALL_EL P l /\ ALL_EL Q l
  ALL_EL_MAP  |- !P f l. ALL_EL P(MAP f l) = ALL_EL(P o f)l
  ALL_EL_APPEND
    |- !P l1 l2. ALL_EL P(APPEND l1 l2) = ALL_EL P l1 /\ ALL_EL P l2
  SOME_EL_SNOC  |- !P x l. SOME_EL P(SNOC x l) = P x \/ SOME_EL P l
  NOT_ALL_EL_SOME_EL  |- !P l. ~ALL_EL P l = SOME_EL($~ o P)l
  NOT_SOME_EL_ALL_EL  |- !P l. ~SOME_EL P l = ALL_EL($~ o P)l
  IS_EL
    |- (!x. IS_EL x[] = F) /\
       (!y x l. IS_EL y(CONS x l) = (y = x) \/ IS_EL y l)
  IS_EL_SNOC  |- !y x l. IS_EL y(SNOC x l) = (y = x) \/ IS_EL y l
  SUM_SNOC  |- !x l. SUM(SNOC x l) = (SUM l) + x
  SUM_FOLDR  |- !l. SUM l = FOLDR $+ 0 l
  SUM_FOLDL  |- !l. SUM l = FOLDL $+ 0 l
  IS_PREFIX_APPEND  |- !l1 l2. IS_PREFIX l1 l2 = (?l. l1 = APPEND l2 l)
  IS_SUFFIX_APPEND  |- !l1 l2. IS_SUFFIX l1 l2 = (?l. l1 = APPEND l l2)
  IS_SUBLIST_APPEND
    |- !l1 l2. IS_SUBLIST l1 l2 = (?l l'. l1 = APPEND l(APPEND l2 l'))
  IS_PREFIX_IS_SUBLIST  |- !l1 l2. IS_PREFIX l1 l2 ==> IS_SUBLIST l1 l2
  IS_SUFFIX_IS_SUBLIST  |- !l1 l2. IS_SUFFIX l1 l2 ==> IS_SUBLIST l1 l2
  IS_PREFIX_REVERSE
    |- !l1 l2. IS_PREFIX(REVERSE l1)(REVERSE l2) = IS_SUFFIX l1 l2
  IS_SUFFIX_REVERSE
    |- !l1 l2. IS_SUFFIX(REVERSE l1)(REVERSE l2) = IS_PREFIX l1 l2
  IS_SUBLIST_REVERSE
    |- !l1 l2. IS_SUBLIST(REVERSE l1)(REVERSE l2) = IS_SUBLIST l1 l2
  PREFIX_FOLDR
    |- !P l. PREFIX P l = FOLDR(\x l'. (P x => CONS x l' | []))[]l
  PREFIX
    |- (!P. PREFIX P[] = []) /\
       (!P x l. PREFIX P(CONS x l) = (P x => CONS x(PREFIX P l) | []))
  IS_PREFIX_PREFIX  |- !P l. IS_PREFIX l(PREFIX P l)
  LENGTH_SCANL  |- !f e l. LENGTH(SCANL f e l) = SUC(LENGTH l)
  LENGTH_SCANR  |- !f e l. LENGTH(SCANR f e l) = SUC(LENGTH l)
  FOLDL_IDENT
    |- !f.
        COMM f ==>
        (!unt.
          MONOID f unt ==> (!e l. FOLDL f e l = f e(FOLDL f unt l)))
  FOLDR_IDENT
    |- !f.
        COMM f ==>
        (!unt.
          MONOID f unt ==> (!e l. FOLDR f e l = f e(FOLDR f unt l)))
  FOLDR_APPEND_FOLDR
    |- !f g.
        FCOMM g f ==>
        (!e.
          LEFT_ID g e ==>
          (!l1 l2.
            FOLDR f e(APPEND l1 l2) = g(FOLDR f e l1)(FOLDR f e l2)))
  FOLDL_APPEND_FOLDL
    |- !g f.
        FCOMM f g ==>
        (!e.
          RIGHT_ID g e ==>
          (!l1 l2.
            FOLDL f e(APPEND l1 l2) = g(FOLDL f e l1)(FOLDL f e l2)))
  MONOID_FOLDR_APPEND_FOLDR
    |- !f e.
        MONOID f e ==>
        (!l1 l2.
          FOLDR f e(APPEND l1 l2) = f(FOLDR f e l1)(FOLDR f e l2))
  MONOID_FOLDL_APPEND_FOLDL
    |- !f e.
        MONOID f e ==>
        (!l1 l2.
          FOLDL f e(APPEND l1 l2) = f(FOLDL f e l1)(FOLDL f e l2))
  FOLDL_SINGLE  |- !f e x. FOLDL f e[x] = f e x
  FOLDR_SINGLE  |- !f e x. FOLDR f e[x] = f x e
  FOLDR_CONS_NIL  |- !l. FOLDR CONS[]l = l
  FOLDL_SNOC_NIL  |- !l. FOLDL(\xs x. SNOC x xs)[]l = l
  FOLDR_FOLDL_REVERSE
    |- !f e l. FOLDR f e l = FOLDL(\x y. f y x)e(REVERSE l)
  FOLDL_FOLDR_REVERSE
    |- !f e l. FOLDL f e l = FOLDR(\x y. f y x)e(REVERSE l)
  FOLDR_REVERSE  |- !f e l. FOLDR f e(REVERSE l) = FOLDL(\x y. f y x)e l
  FOLDL_REVERSE  |- !f e l. FOLDL f e(REVERSE l) = FOLDR(\x y. f y x)e l
  FOLDR_MAP  |- !f e g l. FOLDR f e(MAP g l) = FOLDR(\x y. f(g x)y)e l
  FOLDL_MAP  |- !f e g l. FOLDL f e(MAP g l) = FOLDL(\x y. f x(g y))e l
  ALL_EL_FOLDR  |- !P l. ALL_EL P l = FOLDR(\x l'. P x /\ l')T l
  ALL_EL_FOLDL  |- !P l. ALL_EL P l = FOLDL(\l' x. l' /\ P x)T l
  SOME_EL_FOLDR  |- !P l. SOME_EL P l = FOLDR(\x l'. P x \/ l')F l
  SOME_EL_FOLDL  |- !P l. SOME_EL P l = FOLDL(\l' x. l' \/ P x)F l
  ALL_EL_FOLDR_MAP  |- !P l. ALL_EL P l = FOLDR $/\ T(MAP P l)
  ALL_EL_FOLDL_MAP  |- !P l. ALL_EL P l = FOLDL $/\ T(MAP P l)
  SOME_EL_FOLDR_MAP  |- !P l. SOME_EL P l = FOLDR $\/ F(MAP P l)
  SOME_EL_FOLDL_MAP  |- !P l. SOME_EL P l = FOLDL $\/ F(MAP P l)
  FOLDR_FILTER
    |- !f e P l.
        FOLDR f e(FILTER P l) = FOLDR(\x y. (P x => f x y | y))e l
  FOLDL_FILTER
    |- !f e P l.
        FOLDL f e(FILTER P l) = FOLDL(\x y. (P y => f x y | x))e l
  FOLDR_FLAT
    |- !f.
        ASSOC f ==>
        (!e.
          LEFT_ID f e ==>
          (!l. FOLDR f e(FLAT l) = FOLDR f e(MAP(FOLDR f e)l)))
  MONOID_FOLDR_FLAT
    |- !f e.
        MONOID f e ==>
        (!l. FOLDR f e(FLAT l) = FOLDR f e(MAP(FOLDR f e)l))
  FOLDL_FLAT
    |- !f.
        ASSOC f ==>
        (!e.
          RIGHT_ID f e ==>
          (!l. FOLDL f e(FLAT l) = FOLDL f e(MAP(FOLDL f e)l)))
  MONOID_FOLDL_FLAT
    |- !f e.
        MONOID f e ==>
        (!l. FOLDL f e(FLAT l) = FOLDL f e(MAP(FOLDL f e)l))
  FCOMM_FOLDR_FLAT
    |- !f.
        FCOMM APPEND f ==>
        (!l. FOLDR f[](FLAT l) = FLAT(MAP(FOLDR f[])l))
  FCOMM_FOLDL_FLAT
    |- !f.
        FCOMM f APPEND ==>
        (!l. FOLDL f[](FLAT l) = FLAT(MAP(FOLDL f[])l))
  MAP_FLAT  |- !f l. MAP f(FLAT l) = FLAT(MAP(MAP f)l)
  FILTER_FLAT  |- !P l. FILTER P(FLAT l) = FLAT(MAP(FILTER P)l)
  SOME_EL_MAP  |- !P f l. SOME_EL P(MAP f l) = SOME_EL(P o f)l
  SOME_EL_APPEND
    |- !P l1 l2. SOME_EL P(APPEND l1 l2) = SOME_EL P l1 \/ SOME_EL P l2
  SOME_EL_DISJ
    |- !P Q l. SOME_EL(\x. P x \/ Q x)l = SOME_EL P l \/ SOME_EL Q l
  IS_EL_APPEND
    |- !l1 l2 x. IS_EL x(APPEND l1 l2) = IS_EL x l1 \/ IS_EL x l2
  IS_EL_FOLDR  |- !y l. IS_EL y l = FOLDR(\x l'. (y = x) \/ l')F l
  IS_EL_FOLDL  |- !y l. IS_EL y l = FOLDL(\l' x. l' \/ (y = x))F l
  NULL_FOLDR  |- !l. NULL l = FOLDR(\x l'. F)T l
  NULL_FOLDL  |- !l. NULL l = FOLDL(\x l'. F)T l
  MAP_REVERSE  |- !f l. MAP f(REVERSE l) = REVERSE(MAP f l)
  FILTER_REVERSE  |- !P l. FILTER P(REVERSE l) = REVERSE(FILTER P l)
  LAST  |- !x l. LAST(SNOC x l) = x
  BUTLAST  |- !x l. BUTLAST(SNOC x l) = l
  SEG_LENGTH_ID  |- !l. SEG(LENGTH l)0 l = l
  SEG_SUC_CONS  |- !m n l x. SEG m(SUC n)(CONS x l) = SEG m n l
  SEG_SNOC0
    |- !m l x. m <= (LENGTH l) ==> (SEG m 0(SNOC x l) = SEG m 0 l)
  BUTLASTN_SEG
    |- !n l. n <= (LENGTH l) ==> (BUTLASTN n l = SEG((LENGTH l) - n)0 l)
  LASTN_CONS
    |- !n l. n <= (LENGTH l) ==> (!x. LASTN n(CONS x l) = LASTN n l)
  LENGTH_LASTN  |- !n l. n <= (LENGTH l) ==> (LENGTH(LASTN n l) = n)
  LASTN_LENGTH_ID  |- !l. LASTN(LENGTH l)l = l
  LASTN_LASTN
    |- !l n m.
        m <= (LENGTH l) ==> n <= m ==> (LASTN n(LASTN m l) = LASTN n l)
  FIRSTN_LENGTH_ID  |- !l. FIRSTN(LENGTH l)l = l
  FIRSTN_SNOC
    |- !n l. n <= (LENGTH l) ==> (!x. FIRSTN n(SNOC x l) = FIRSTN n l)
  BUTLASTN_LENGTH_NIL  |- !l. BUTLASTN(LENGTH l)l = []
  BUTLASTN_SUC_BUTLAST
    |- !n l.
        n < (LENGTH l) ==> (BUTLASTN(SUC n)l = BUTLASTN n(BUTLAST l))
  BUTLASTN_BUTLAST_SYM
    |- !n l.
        n < (LENGTH l) ==>
        (BUTLASTN n(BUTLAST l) = BUTLAST(BUTLASTN n l))
  LENGTH_BUTLASTN
    |- !n l. n <= (LENGTH l) ==> (LENGTH(BUTLASTN n l) = (LENGTH l) - n)
  BUTLASTN_BUTLASTN
    |- !m n l.
        (n + m) <= (LENGTH l) ==>
        (BUTLASTN n(BUTLASTN m l) = BUTLASTN(n + m)l)
  APPEND_BUTLASTN_LASTN
    |- !n l. n <= (LENGTH l) ==> (APPEND(BUTLASTN n l)(LASTN n l) = l)
  APPEND_FIRSTN_LASTN
    |- !m n l.
        (m + n = LENGTH l) ==> (APPEND(FIRSTN n l)(LASTN m l) = l)
  BUTLASTN_APPEND2
    |- !n l1 l2.
        n <= (LENGTH l2) ==>
        (BUTLASTN n(APPEND l1 l2) = APPEND l1(BUTLASTN n l2))
  BUTLASTN_LENGTH_APPEND
    |- !l2 l1. BUTLASTN(LENGTH l2)(APPEND l1 l2) = l1
  LASTN_LENGTH_APPEND  |- !l1 l2. LASTN(LENGTH l2)(APPEND l1 l2) = l2
  BUTLASTN_CONS
    |- !n l.
        n <= (LENGTH l) ==>
        (!x. BUTLASTN n(CONS x l) = CONS x(BUTLASTN n l))
  BUTLASTN_LENGTH_CONS  |- !l x. BUTLASTN(LENGTH l)(CONS x l) = [x]
  LAST_LASTN_LAST
    |- !n l. n <= (LENGTH l) ==> 0 < n ==> (LAST(LASTN n l) = LAST l)
  BUTLASTN_LASTN_NIL
    |- !n l. n <= (LENGTH l) ==> (BUTLASTN n(LASTN n l) = [])
  LASTN_BUTLASTN
    |- !m n l.
        (m + n) < (LENGTH l) ==>
        (LASTN n(BUTLASTN m l) = BUTLASTN m(LASTN(m + n)l))
  BUTLASTN_LASTN
    |- !m n l.
        m <= n /\ n <= (LENGTH l) ==>
        (BUTLASTN m(LASTN n l) = LASTN(n - m)(BUTLASTN m l))
  LAST_LASTN  |- !l. ~NULL l ==> ([LAST l] = LASTN 1 l)
  BUTLAST_BUTLASTN  |- !l. ~NULL l ==> (BUTLAST l = BUTLASTN 1 l)
  BUTLASTN_APPEND1
    |- !l2 n.
        (LENGTH l2) <= n ==>
        (!l1. BUTLASTN n(APPEND l1 l2) = BUTLASTN(n - (LENGTH l2))l1)
  LASTN_APPEND2
    |- !n l2.
        n <= (LENGTH l2) ==> (!l1. LASTN n(APPEND l1 l2) = LASTN n l2)
  LASTN_APPEND1
    |- !l2 n.
        (LENGTH l2) <= n ==>
        (!l1.
          LASTN n(APPEND l1 l2) = APPEND(LASTN(n - (LENGTH l2))l1)l2)
  LASTN_MAP
    |- !n l.
        n <= (LENGTH l) ==> (!f. LASTN n(MAP f l) = MAP f(LASTN n l))
  BUTLASTN_MAP
    |- !n l.
        n <= (LENGTH l) ==>
        (!f. BUTLASTN n(MAP f l) = MAP f(BUTLASTN n l))
  ALL_EL_LASTN
    |- !P l.
        ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(LASTN m l))
  ALL_EL_BUTLASTN
    |- !P l.
        ALL_EL P l ==> (!m. m <= (LENGTH l) ==> ALL_EL P(BUTLASTN m l))
  LENGTH_FIRSTN  |- !n l. n <= (LENGTH l) ==> (LENGTH(FIRSTN n l) = n)
  FIRSTN_FIRSTN
    |- !m l.
        m <= (LENGTH l) ==>
        (!n. n <= m ==> (FIRSTN n(FIRSTN m l) = FIRSTN n l))
  LENGTH_BUTFIRSTN
    |- !n l.
        n <= (LENGTH l) ==> (LENGTH(BUTFIRSTN n l) = (LENGTH l) - n)
  BUTFIRSTN_LENGTH_NIL  |- !l. BUTFIRSTN(LENGTH l)l = []
  BUTFIRSTN_APPEND1
    |- !n l1.
        n <= (LENGTH l1) ==>
        (!l2. BUTFIRSTN n(APPEND l1 l2) = APPEND(BUTFIRSTN n l1)l2)
  BUTFIRSTN_APPEND2
    |- !l1 n.
        (LENGTH l1) <= n ==>
        (!l2. BUTFIRSTN n(APPEND l1 l2) = BUTFIRSTN(n - (LENGTH l1))l2)
  BUTFIRSTN_BUTFIRSTN
    |- !n m l.
        (n + m) <= (LENGTH l) ==>
        (BUTFIRSTN n(BUTFIRSTN m l) = BUTFIRSTN(n + m)l)
  APPEND_FIRSTN_BUTFIRSTN
    |- !n l. n <= (LENGTH l) ==> (APPEND(FIRSTN n l)(BUTFIRSTN n l) = l)
  LASTN_SEG
    |- !n l. n <= (LENGTH l) ==> (LASTN n l = SEG n((LENGTH l) - n)l)
  FIRSTN_SEG  |- !n l. n <= (LENGTH l) ==> (FIRSTN n l = SEG n 0 l)
  BUTFIRSTN_SEG
    |- !n l.
        n <= (LENGTH l) ==> (BUTFIRSTN n l = SEG((LENGTH l) - n)n l)
  APPEND_BUTLAST_LAST
    |- !l. ~(l = []) ==> (APPEND(BUTLAST l)[LAST l] = l)
  BUTFIRSTN_SNOC
    |- !n l.
        n <= (LENGTH l) ==>
        (!x. BUTFIRSTN n(SNOC x l) = SNOC x(BUTFIRSTN n l))
  APPEND_BUTLASTN_BUTFIRSTN
    |- !m n l.
        (m + n = LENGTH l) ==> (APPEND(BUTLASTN m l)(BUTFIRSTN n l) = l)
  SEG_SEG
    |- !n1 m1 n2 m2 l.
        (n1 + m1) <= (LENGTH l) /\ (n2 + m2) <= n1 ==>
        (SEG n2 m2(SEG n1 m1 l) = SEG n2(m1 + m2)l)
  SEG_APPEND1
    |- !n m l1.
        (n + m) <= (LENGTH l1) ==>
        (!l2. SEG n m(APPEND l1 l2) = SEG n m l1)
  SEG_APPEND2
    |- !l1 m n l2.
        (LENGTH l1) <= m /\ n <= (LENGTH l2) ==>
        (SEG n m(APPEND l1 l2) = SEG n(m - (LENGTH l1))l2)
  SEG_BUTFISTN_FIRSTN
    |- !n m l.
        (n + m) <= (LENGTH l) ==> (SEG n m l = FIRSTN n(BUTFIRSTN m l))
  SEG_APPEND
    |- !m l1 n l2.
        m < (LENGTH l1) /\
        (LENGTH l1) <= (n + m) /\
        (n + m) <= ((LENGTH l1) + (LENGTH l2)) ==>
        (SEG n m(APPEND l1 l2) =
         APPEND
         (SEG((LENGTH l1) - m)m l1)
         (SEG((n + m) - (LENGTH l1))0 l2))
  SEG_LENGTH_SNOC  |- !l x. SEG 1(LENGTH l)(SNOC x l) = [x]
  SEG_SNOC
    |- !n m l.
        (n + m) <= (LENGTH l) ==> (!x. SEG n m(SNOC x l) = SEG n m l)
  ELL_SEG
    |- !n l.
        n < (LENGTH l) ==> (ELL n l = HD(SEG 1(PRE((LENGTH l) - n))l))

******************** list ********************

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (better error message)                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/f-simpl.l                                              |
|----------------------------------------------------------------------------|
| DATE:          1 January 1994                                              |
+----------------------------------------------------------------------------+

The error message produced by the LISP function |ml-term_match| has been
changed from TERM-MATCH to MATCH.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (CHOOSE rule)                                        |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/hol-drule.ml                                             |
|                help/ENTRIES/CHOOSE.doc                                     |
|----------------------------------------------------------------------------|
| DATE:          12 January 1994                                             |
+----------------------------------------------------------------------------+
The derived rule CHOOSE was specified as

    A1 |- ?x. s[x]    A2 u {{s[v/x]}} |- t
   ---------------------------------------  CHOOSE ("v",(A1 |- ?x. s[x]))
                A1 u A2 |- t
where {v} is not free in {A1}, {A2} or {t}.

There are two changes made to the rule CHOOSE:

1) The implementation and the document of the derived rule CHOOSE are
   inconsistent.  When applied to a theorem not of the correct form,
   namely, the term s[v/x] does not occur in the assumptions of the second
   theorem,  CHOOSE does not fail as described in the document, but return the
   input theorem. Although, this bug should not lead to unsoundedness, it
   is undesirable that such behaviour may be used in other proof procedure.

A check for the occurrence of an assumption in the second input theorem which
matches the body of the existentially quantified theorem in the first
theorem is added. Also, the failure message is made clearer.

2) The old implementation requires that the variable v is free in A1.
   This is too restrictive. It is relaxed by removing the check on this.
   The document (on line help entry) is modified to reflect the change.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (MP rule)                                            |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| NEW FILE:  help/ENTRIES/dest_neg_imp.doc                                   |
| FILES CHANGED: ml/hol-syn.ml  help/ENTRIES/dest_imp.doc                    |
|                ml/hol-rule.ml ml/drul.ml ml/resovle.ml ml/conv.ml          |
|                ml/hol-drule.ml ml/tydefs.ml ml/tyfns.ml ml/tacont.ml       |
|                ml/tactics.ml                                               |
|----------------------------------------------------------------------------|
| DATE:          24 January 1994                                             |
+----------------------------------------------------------------------------+
The primitive inference rule MP performs extra inferences in addition
to strict  Modus Ponens. It treats negation as an implication with F
as its conclusion.  For example,
   MP (A1 |- ~t) (A2 |- t) = (A1,A2 |- F)
This was discovered in the course of testing a proof checker.

This special behaviour is due to some historical decisions made on the
implementation of dest_imp. This function is renamed to dest_neg_imp.
dest_imp is re-implemented as a strict implication destructor.
Document of old dest_imp is also renemed. New document is added for
new dest_imp.

The new implementation of MP performs a strict primitive Modus Ponens. The
behaviour of the old MP function is implemented by NOT_MP. Users are
not recommended to use NOT_MP. It may disappear in future version of
the system. Document of MP need not be changed as it is a correct
description of primitive Modus Ponens.

As dest_imp and MP are used in many places in the system. The above
changes may affect many functions. These may be classified
into three cases and the solutions of each cases are detailed below.

1) Functions which should use only the documented behaviour of dest_imp
and/or MP. They are documented as such, e.g., they fails when the
argument is not strictly an implication.  No changes need to be made
to such functions since the changes in dest_imp and MP will enforce this.

2) Functions which are known to depend on ONLY the special behaviour of either
dest_imp or MP, e.g., NOT_EQ_SYM. These functions are modified to
reflect this fact. dest_neg and extra inference, such as NOT_ELIM,
will be used instead of dest_imp or MP.

3) Functions which depend both on the special behaviours
of dest_imp and/or MP, i.e., they may work on both implication and
negation. To preserve the behaviour of such functions,
the calls to dest_imp and MP are changed to calls to dest_neg_imp and
NOT_MP.

Below is a list of functions to whom changes have been made. The
number after the function name indicates which of the above groups it
belongs to. The number "3.2" means that the function should be in
group 2, but group 3 fix has been done. All these functions should
behave as before.

hol-drule.ml:
        UNDISCH 3
        NOT_EQ_SYM 2
drul.ml:
        IMP_CANON 3
resolve.ml:
        RES_CANON 3
        MATCH_MP (local version) 3
        MATCH_MP_TAC 3
conv.ml:
        NOT_FORALL_CONV 3.2
        NOT_EXISTS_CONV 3.2
        FORALL_OR_CONV 3.2
        LEFT_OR_FORALL_CONV 3.2
        RIGHT_OR_FORALL_CONV 3.2
        EXISTS_IMP_CONV 3.2
        CONTRAPOS_CONV 2
tydefs.ml:
        prove_existence 3
tyfns.ml:
        prove_cases_thm 3
tacont.ml:
        DISCH_THEN 3
tactics.ml:
        FILTER_DISCH_THEN 3

Below is a list od group 1 functions. No change has been made to their
source code. As the result of changes in dest_imp and MP, these
function will fail if the input term or theorem are no implicative.
This failure condition has already been documented in their reference pages.

abs-rep.ml:
        define_new_type_bijection
conv.ml:
        ANTE_CONJ_CONV
        EXISTS_IMP_CONV
        EXISTS_UNIQUE_CONV
        EXISTENCE
        FORALL_IMP_CONV
        LEFT_AND_EXISTS_CONV
        LEFT_IMP_EXISTS_CONV
        LEFT_IMP_FORALL_CONV
        MATCH_MP
        RIGHT_AND_EXISTS_CONV
        RIGHT_IMP_EXISTS_CONV
        RIGHT_IMP_FORALL_CONV
drul.ml:
        IMP_CONJ
        IMP_ELIM
        LIST_MP
        PROVE_HYP
hol-drule.ml:
        CONJ_DISCH
        IMP_TRANS
        SELECT_ELIM
        SELECT_INTRO
ind.ml:
        INDUCT_THEN
        TACF (local)
list.ml:
        LIST_INDUCT
num.ml:
        INDUCT
        num_EQ_CONV
tactics.ml:
        MP_TAC
tydefs.ml:
        EQN_ELIM_CONV (local)
        FORALL_IN_CONV (local)
        LENGTH_MAP_CONV (local)
        OR_IMP_CONV (local)
        define_type
tyfns.ml:
        ANTE_ALL_CONV (local)
        DISJ_CHAIN (local)
        STEP_CONV (local)
        UNIQUENESS (local)
        prove_constructors_distinct


+----------------------------------------------------------------------------+
| CHANGE TYPE:   Bugfix (INST_TYPE)                                          |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/f-inst.l                                               |
|----------------------------------------------------------------------------|
| DATE:          25 January 1994.                                            |
+----------------------------------------------------------------------------+

The following proof of |- F is due to Richard Boulton, exploiting a bug
in INST_TYPE discovered by Joakim Von Wright.

   #let th1 = REFL (mk_abs("x:*","x:bool"));;
   th1 = |- (\x. x) = (\x. x)

   #let th2 =
   # prove
   #  (mk_eq(mk_abs("x:*","x':bool"),mk_abs("y:*","x':bool")),
   #   CONV_TAC FUN_EQ_CONV THEN GEN_TAC THEN BETA_TAC THEN REFL_TAC);;
   th2 = |- (\x. x') = (\y. x')

   #let th3 = CONJ th1 th2;;
   th3 = |- ((\x. x) = (\x. x)) /\ ((\x. x') = (\y. x'))

   #let th4 = INST_TYPE[":bool",":*"] th3;;
   th4 = |- ((\x'. x) = (\x'. x)) /\ ((\x'. x') = (\y. x'))

   #let th5 = CONJUNCT2 th4;;
   th5 = |- (\x'. x') = (\y. x')

   #let th6 = AP_THM th5 "F";;
   th6 = |- (\x'. x')F = (\y. x')F

   #let th7 = BETA_RULE th6;;
   th7 = |- F = x'

   #let th8 = EQT_ELIM (SPEC "T" (GEN "x':bool" th7));;
   th8 = |- F

INST_TYPE has now been fixed to block this.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   fixes                                                       |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: libraries (see below)                                       |
|----------------------------------------------------------------------------|
| DATE:          26 January 1994.                                            |
+----------------------------------------------------------------------------+

Due to changes described in the previous two entries, a small number
of proofs in the libraries do not work. Changes are necessary in order
to rebuild them.

Library pair:
    File conv.ml:
        Changes were made in the proofs NOT_FORALL_THM,
        NOT_EXISTS_THM, LEFT_FORALL_OR_THM, RIGHT_FORALL_OR_THM,
        LEFT_EXISTS_IMP_THM. These fixes are of class 2 described in
        the above entry about MP.

Library prog_logic88:
    File mk_dijkstra.ml:
        A change was made in the proof T_SPEC_WP. The tactic to solve
        the first subgoal was
         IMP_RES_TAC WP_WEAKEST THEN IMP_RES_TAC WEAKER
        The second resolution failed to solve the subgoal because a
        variable was instantiated and did not match the supplied
        theorem. The new tactic now is:
         IMP_RES_THEN MP_TAC WP_WEAKEST THEN
         PURE_ONCE_REWRITE_TAC[WEAKER] THEN DISCH_TAC THEN RES_TAC;

Library group:
    File mk_more_gp:
        Changes were made in the proof LEFT_COSET_DISJOINT_UNION.
        Two calls to REPEAT STRIP_TAC were eliminated. Instead, less
        powerful tactics are used.

Library integer:
    File mk_integer:
        A change was make in the proof DISCRETE because a call to
        RES_TAC did not solve the subgoal.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   enhancement                                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/gen.ml                                                   |
|----------------------------------------------------------------------------|
| DATE:          29 January 1994.                                            |
+----------------------------------------------------------------------------+

The application |funpow f n x| will now return |x| if |n| is negative.
Previously it failed to terminate.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   enhancement (numeral library)                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/numeral/numeral_theory.ml                           |
|                Library/numeral/numeral_rules.ml                            |
|----------------------------------------------------------------------------|
| DATE:          30 January 1994.                                            |
+----------------------------------------------------------------------------+

The numeral library has been tidied in various minor ways, including removing
dependence on all other libraries. An asymptotically faster version of the
multiplication operation has been added.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix (PCHOOSE rule)                                       |
|----------------------------------------------------------------------------|
| CHANGED BY:    JG                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: Library/pair/exi.ml                                         |
|----------------------------------------------------------------------------|
| DATE:          31 January 1994                                             |
+----------------------------------------------------------------------------+

Updated the functionality of the paired choose rule in line with the change
made by WW to the basic CHOOSE rule.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Change to printing of subgoals (print_hyps)                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: ml/goals.ml                                                 |
|----------------------------------------------------------------------------|
| DATE:          31 January 1994.                                            |
|                08 February 1994.                                           |
+----------------------------------------------------------------------------+

Assumptions of goals printed by the subgoal package are now
numbered. This can be disabled by setting the flag `number_subgoals`
to false.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Enhancement (infix_variable)                                |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/f-parsol.l                                             |
|                lisp/hol-writ.l                                             |
|                lisp/f-dml.l                                                |
|                help/ENTRIES/infix_variable.doc                             |
|----------------------------------------------------------------------------|
| DATE:          01 February 1994.                                           |
+----------------------------------------------------------------------------+

An example:

   #new_special_symbol `<<`;;
   () : void

   #infix_variable `<<`;;
   () : void

   #"!$<<. TRANSITIVE $<< = !(x y z:*). x << y /\ y << z ==> x << z";;
   "TRANSITIVE $<< = (!x y z. x << y /\ y << z ==> x << z)" : term

See help/ENTRIES/infix_variable.doc for full details.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Revision of the theory list                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILES CHANGED: theories/mk_list_thms.ml                                    |
|                theories/mk_list_defs.ml theories/mk_list_thm2.ml           |
|                ml/list.ml ml/load_thms.ml                                  |
|----------------------------------------------------------------------------|
| DATE:          2 February 1994                                             |
+----------------------------------------------------------------------------+

More definitions, theorems, conversions and tactics are added. All
definitions and theorems in the list theorey, except a few theorem used
only for low level type definition, add set up to autoload.

New conversions added are:

 FOLDR_CONV, FOLDL_CONV, list_FOLD_CONV,
 SUM_CONV, FILTER_CONV, SNOC_CONV, REVERSE_CONV, FLAT_CONV,
 EL_CONV, ELL_CONV,  MAP2_CONV, ALL_EL_CONV,  SOME_EL_CONV,
 IS_EL_CONV,  LAST_CONV, BUTLAST_CONV, SEG_CONV, LASTN_CONV,
 BUTLASTN_CONV, BUTFIRSTN_CONV, FIRSTN_CONV, SCANL_CONV, SCANR_CONV,
 REPLICATE_CONV, GENLIST_CONV

New tactics added are:

  SNOC_INDUCT_TAC, EQ_LENGTH_INDUCT_TAC, EQ_LENGTH_SNOC_INDUCT_TAC

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Correction of documentation                                 |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: Manual/Description/system.tex                               |
|                Manual/Description/version2.tex                             |
|----------------------------------------------------------------------------|
| DATE:          7 February 1994                                             |
+----------------------------------------------------------------------------+

In DESCRIPTION (and page 250 of "Introduction to HOL") the description
of define_finite_set_syntax has a small typo:

  "c1 t1 (c1 t2 ... (c1 tn c2) ... ))"

should be:

  "c2 t1 (c2 t2 ... (c2 tn c1) ... ))"

However, the online documentation is correct.


+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix in Lisp                                              |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/hol-pars.l                                             |
|----------------------------------------------------------------------------|
| DATE:          8 February 1994.                                            |
+----------------------------------------------------------------------------+

"#*" used to crash the system. This was due to an uninitialized
variable (zeros-count) in the Lisp code to support the parsing of
constants "#..." of ":word<n>" type. This code is probably obsolete
and its deletion is under consideration.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Updating the library word                                   |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| DATE:          8 February 1994                                             |
+----------------------------------------------------------------------------+
The library word has been updated. It used to depend on the more_lists
library. Since the list theory in the core system has been expanded,
the word library does no longer need to use more_lists. The dependence
is removed.

The constant SEG in the word library is changed to WSEG to avoid name
crash with the list theory.

The predicate EXISTSABIT is now defined in terms of SOME_EL.
The function NVAL is now defined in terms of FOLDL.

A number of proofs are changed to use new theorems in the list theory.

The conversions PWORDLEN_CONV and PWORDLEN_bitop_CONV now return an
equational theorem whose right-hand side is T.

The Manual is revised to refect these changes.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Deletion of more_list library                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| DATE:          9 February 1994                                             |
+----------------------------------------------------------------------------+
Since the list theory in the core system has been revised and
expanded, the more_list library should not been needed. It is deleted
from the system. However, the library is kept in the contrib directory
in case some is despair for it.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Automated doc file generation                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILE CHANGED: Manual/Reference/Makefile                                    |
|----------------------------------------------------------------------------|
| DATE:          9 February 1994                                             |
+----------------------------------------------------------------------------+

An entry is added to the Makefile in Manual/Reference. This entry
specifies how to create .doc files for the definitions and
theorems in the theories which are descentants of BASIC-HOL.
Type "make thmdoc" to activate this entry. This is necessary if one of
the theory has been changed. This automatic recreation of doc file
keeps the document up-to-date with the system.

Note: doc files of the definitions and theorems in the theories ind
and bool, and of theorems which are not saved in any theory are not
recreated by this make entry because they are not grouped according to
theory.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   New functions                                               |
|----------------------------------------------------------------------------|
| CHANGED BY:    WW                                                          |
|----------------------------------------------------------------------------|
| FILE CHANGED:  ml/num.ml                                                   |
|----------------------------------------------------------------------------|
| NEW FILES:     help/ENTRIES/int_of_term.doc help/ENTRIES/term_of_int.doc   |
|----------------------------------------------------------------------------|
| DATE:          10 February 1994                                            |
+----------------------------------------------------------------------------+

Two new functions, int_of_term and term_of_int, for converting between
ML integers and numeric terms are added to the core system. They were
defined in several libraries.

For example:

#int_of_term "2";;
2 : int

#term_of_int 2;;
"2" : term

#term_of_int (-2);;
evaluation failed     mk_const: -2 not a constant

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Modification to rewriting (with two new functions)          |
|----------------------------------------------------------------------------|
| CHANGED BY:    RJB                                                         |
|----------------------------------------------------------------------------|
| FILE CHANGED:  ml/conv.ml ml/rewrite.ml                                    |
|                help/ENTRIES/TOP_DEPTH_CONV.doc                             |
|                help/ENTRIES/ONCE_DEPTH_CONV.doc                            |
|----------------------------------------------------------------------------|
| NEW FILES:     help/ENTRIES/REW_DEPTH_CONV.doc                             |
|                help/ENTRIES/ONCE_REW_DEPTH_CONV.doc                        |
|----------------------------------------------------------------------------|
| DATE:          15 February 1994                                            |
+----------------------------------------------------------------------------+

The rewriting conversions, rules, and tactics have been modified to fix the
following bug (reported by John Harrison):

   Consider the sequence below. The assumption "Q x" disables the possible
   rewrite "!x. P x". What seems to go wrong is that when recursively going
   through the term, both assumptions seem valid rewrites. But then when we
   come to perform the ABS it cannot be done since "x" is free in the
   assumptions -- this throws away *both* rewrites.

   #g "!(P:*->bool) Q. Q x /\ (!x. P x) ==> (!x. Q x ==> P x)";;
   "!P Q. Q x /\ (!x. P x) ==> (!x. Q x ==> P x)"

   () : void

   #e(REPEAT GEN_TAC THEN STRIP_TAC);;
   OK..
   "!x. Q x ==> P x"
       [ "Q x" ]
       [ "!x. P x" ]

   () : void

   #e(ASM_REWRITE_TAC[]);;
   OK..
   "!x. Q x ==> P x"
       [ "Q x" ]
       [ "!x. P x" ]

   () : void

   #e(UNDISCH_TAC "(Q:*->bool) x" THEN DISCH_THEN(K ALL_TAC));;
   OK..
   "!x. Q x ==> P x"
       [ "!x. P x" ]

   () : void

   #e(ASM_REWRITE_TAC[]);;
   OK..
   goal proved
   . |- !x. Q x ==> P x
   .. |- !x. Q x ==> P x
   .. |- !x. Q x ==> P x
   |- !P Q. Q x /\ (!x. P x) ==> (!x. Q x ==> P x)

   Previous subproof:
   goal proved
   () : void

This has been fixed by using a special version of SUB_CONV. If failure occurs
when ABS is applied to the result of rewriting the body, the abstraction is
alpha converted so that the bound variable is a genvar, and the conversion is
reapplied.

The rewriting functions formerly used SUB_CONV via TOP_DEPTH_CONV and
ONCE_DEPTH_CONV. They now use new functions called REW_DEPTH_CONV and
ONCE_REW_DEPTH_CONV respectively. The original behaviour of TOP_DEPTH_CONV
and ONCE_DEPTH_CONV is retained, so any conversions written using them should
not be affected.

The proofs of the following theorems required fixes:

   Library/reals/theories/hreal.ml   HREAL_MUL_LINV
   Library/group/mk_more_gp.ml       QUOTIENT_IM_LEMMA

Compatibility files can be found in: contrib/pre-v2.02-rewr/

+----------------------------------------------------------------------------+
| CHANGE TYPE:   bugfix                                                      |
|----------------------------------------------------------------------------|
| CHANGED BY:    MJCG                                                        |
|----------------------------------------------------------------------------|
| FILES CHANGED: lisp/parslet.l                                              |
|----------------------------------------------------------------------------|
| DATE:          28 February 1994.                                           |
|                04 March 1994.                                              |
+----------------------------------------------------------------------------+

Malcolm Newey reported the bug illustrated below:

-------------------------------------------------------------------------------

===============================================================================
         HOL88 Version 2.02 (SUN4/AKCL), built on 24/2/94
===============================================================================

#new_theory `bugs`;;
() : void

#let In_Def = new_infix_definition (`In_Def`, "in (x:*) f = (f x):bool");;
In_Def = |- !x f. x in f = f x

#"0 in f";;
"0 in f" : term

#"T in g";;
"T in g" : term

#"0 in f)";;
cannot find end of quotation
skipping: f ) " ;; parse failed

#"0 in f";;
Badly typed application of:  "0"
   which has type:           ":num"
to the argument term:        "$in"
   which has type:           ":?1 -> ((?1 -> bool) -> bool)"

evaluation failed     mk_comb in quotation

#"0 in f";;
Badly typed application of:  "0"
   which has type:           ":num"
to the argument term:        "$in"
   which has type:           ":?1 -> ((?1 -> bool) -> bool)"

evaluation failed     mk_comb in quotation

#quit();;
Bye.


%------------------------------------------------------------------------

   File:        infix_bug.ml
   Description:
                Exhibits a bug that manifests itself in error recovery.
                The infix defined must be "in".

   Author:      M. C. Newey
   Date:        December, 1989

-------------------------------------------------------------------------------

This is due to the ollp of a user defined infix "in" being clobbered
on error recovery (by the Lisp function hol-insetup). This clobbering
has been suppressed. A similar bug with "and" predicted and also fixed.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Libraries moved to contrib                                  |
|----------------------------------------------------------------------------|
| CHANGED BY:    RJB                                                         |
|----------------------------------------------------------------------------|
| FILE CHANGED:  Library/UNITY/                                              |
|                Library/auxiliary/                                          |
|                Library/bags/                                               |
|                Library/convert/                                            |
|                Library/eval/                                               |
|                Library/fixpoints/                                          |
|                Library/group/                                              |
|                Library/int_mod/                                            |
|                Library/integer/                                            |
|                Library/prog_logic88/                                       |
|                Library/quotient/                                           |
|----------------------------------------------------------------------------|
| DATE:          1 March 1994                                                |
+----------------------------------------------------------------------------+

The libraries UNITY, auxiliary, bags, convert, eval, fixpoints, group,
int_mod, integer, prog_logic88, and quotient have been moved to the contrib
directory because they do not have proper documentation.

+----------------------------------------------------------------------------+
| CHANGE TYPE:   Library reorganization (wellorder)                          |
|----------------------------------------------------------------------------|
| CHANGED BY:    JRH                                                         |
|----------------------------------------------------------------------------|
| FILE CHANGED:  Library/wellorder/mk_wellorder.ml                           |
|                Library/wellorder/wellorder.ml                              |
|----------------------------------------------------------------------------|
| DATE:          3 March 1994                                                |
+----------------------------------------------------------------------------+

The internal organization of the wellorder library has been changed somewhat.
This entails the introduction of a few new theorems and constants, but few
users should notice any change in the external behaviour.