\DOC set_list_thm_database
\TYPE {set_list_thm_database: {{Aux_thms: thm list, Fold_thms: thm list}}
-> unit}
\SYNOPSIS
Modifies the database of theorems known by {LIST_CONV} and {X_LIST_CONV}.
\DESCRIBE The conversions {LIST_CONV} and {X_LIST_CONV} use a database of
theorems relating to system list constants. These theorems fall into two
categories: definitions of list operators in terms of {FOLDR} and
{FOLDL}; and
auxiliary theorems about the base elements and step functions in those
definitions. The database can be modified using {set_list_thm_database}.
A call {set_list_thm_database{{Fold_thms=fold_thms,Aux_thms=aux_thms}}}
replaces the existing database with the theorems given as the arguments.
The
{Fold_thms} field of the record contains the new fold definitions. The
{Aux_thms} field contains the new auxiliary theorems. Theorems which do
not
have an appropriate form will be ignored.
The following is an example of a fold definition in the database:
{
|- !l. SUM l = FOLDR $+ 0 l
}
Here {$+} is the step function and 0 is the base element of the
definition. Definitions are initially held for the following system
operators:
{APPEND}, {FLAT}, {LENGTH}, {NULL}, {REVERSE}, {MAP}, {FILTER}, {ALL_EL},
{SUM}, {SOME_EL}, {IS_EL}, {AND_EL}, {OR_EL}, {PREFIX}, {SUFFIX}, {SNOC}
and
{FLAT} combined with {REVERSE}.
The following is an example of an auxiliary theorem:
{
|- MONOID $+ 0
}
Auxiliary theorems stored include monoid, commutativity,
associativity, binary function commutativity, left identity and right
identity
theorems.
\USES
The conversion {LIST_CONV} uses the theorems in the database to prove
theorems about list operators. Users are encouraged to define list
operators
in terms of either {FOLDR} or {FOLDL} rather than recursively. Then if
the
definition is passed to {LIST_CONV}, it will be able to prove the
recursive
clauses for the definition. If auxilary properties are proved about the
step
function and base element, and they are passed to {LIST_CONV} then it may
be
able to prove other useful theorems. Theorems can be passed either as
arguments to {LIST_CONV} or they can be added to the database using
{set_list_thm_database}.
\EXAMPLE
After the following call, {LIST_CONV} will only be able to prove a few
theorems about {SUM}.
{
set_list_thm_database
{{Fold_thms = [theorem "list" "SUM_FOLDR"],
Aux_thms = [theorem "arithmetic" "MONOID_ADD_0"]}};
}
The following shows a new definition being added which multiplies
the elements of a list. {LIST_CONV} is then called to prove the recursive
clause.
{
- val MULTL = new_definition("MULTL",(--`MULTL l = FOLDR $* 1 l`--));
val MULTL = |- !l. MULTL l = FOLDR $* 1 l : thm
- let val {{Fold_thms = fold_thms, Aux_thms = aux_thms}} =
list_thm_database()
= in
=
set_list_thm_database{{Fold_thms = MULTL::fold_thms,Aux_thms =
aux_thms}}
= end;
val it = () : unit
- LIST_CONV (--`MULTL (CONS x l)`--);
|- MULTL (CONS x l) = x * MULTL l
}
\FAILURE
Never fails.
\SEEALSO
LIST_CONV, list_thm_database, X_LIST_CONV.
\ENDDOC