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last edited 15 years ago by Bill Page |
Edit detail for SandBoxCachedFunction revision 1 of 10
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Editor: hemmecke
Time: 2009/10/27 16:17:37 GMT-7 |
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changed: - A generic way to define function that cache their values. \begin{spad} )abbrev domain CACHEDF CachedFunction ++ Author: Ralf Hemmecke ++ Date Created: 2009 ++ Date Last Updated: Oct 27, 2009 ++ Basic Operations: ++ Related Domains: Table, AssociationList ++ Also See: ++ AMS Classifications: ++ Keywords: ++ Examples: ++ References: ++ Description: ++ This domain is a domain of functions with associated cache. CachedFunction(A: SetCategory, B: SetCategory): Exports == Implementation where Exports ==> with function: % -> (A -> B) cachedFunction: (A -> B) -> % apply: (%, A) -> B recursiveDefine: (%, f: A -> B) -> % Implementation ==> add Rep := Record(cache: Table(A, B), fun: A -> B); function(x: %): A -> B == x.fun cachedFunction(f: A -> B): % == [empty()$Table(A, B), f] apply(x: %, a: A): B == c := x.cache u: Union(B, "failed") := search(a, c) if u case B then u :: B else f: A -> B := x.fun c.a := f(a) recursiveDefine(x: %, f: A -> B): % == x.fun := f; x \end{spad} \begin{axiom} )set message time on I := Integer f(n:I): I ==1 fib: CachedFunction(I,I) := cachedFunction(f) recursiveDefine(fib,(n:I):I+->if n<2 then 1 else fib(n-1) + fib(n-2)) fib 40 g(n:I): I == if n<2 then 1 else g(n-1)+g(n-2) g 40 \end{axiom}
A generic way to define function that cache their values.
spad
)abbrev domain CACHEDF CachedFunction
++ Author: Ralf Hemmecke
++ Date Created: 2009
++ Date Last Updated: Oct 27, 2009
++ Basic Operations:
++ Related Domains: Table, AssociationList
++ Also See:
++ AMS Classifications:
++ Keywords:
++ Examples:
++ References:
++ Description:
++ This domain is a domain of functions with associated cache.
CachedFunction(A: SetCategory, B: SetCategory): Exports == Implementation where
Exports ==> with
function: % -> (A -> B)
cachedFunction: (A -> B) -> %
apply: (%, A) -> B
recursiveDefine: (%, f: A -> B) -> %
Implementation ==> add
Rep := Record(cache: Table(A, B), fun: A -> B);
function(x: %): A -> B == x.fun
cachedFunction(f: A -> B): % == [empty()$Table(A, B), f]
apply(x: %, a: A): B ==
c := x.cache
u: Union(B, "failed") := search(a, c)
if u case B
then u :: B
else
f: A -> B := x.fun
c.a := f(a)
recursiveDefine(x: %, f: A -> B): % ==
x.fun := f;
x
spad
Compiling FriCAS source code from file
/var/zope2/var/LatexWiki/8303643491408128431-25px001.spad using
old system compiler.
CACHEDF abbreviates domain CachedFunction
processing macro definition Exports ==> -- the constructor category
processing macro definition Implementation ==> -- the constructor capsule
------------------------------------------------------------------------
initializing NRLIB CACHEDF for CachedFunction
compiling into NRLIB CACHEDF
compiling exported function : $ -> A -> B
CACHEDF;function;$M;1 is replaced by QCDR
Time: 0.04 SEC.
compiling exported cachedFunction : A -> B -> $
Time: 0.02 SEC.
compiling exported apply : ($,A) -> B
Time: 0.01 SEC.
compiling exported recursiveDefine : ($,A -> B) -> $
Time: 0 SEC.
(time taken in buildFunctor: 0)
;;; *** |CachedFunction| REDEFINED
;;; *** |CachedFunction| REDEFINED
Time: 0.01 SEC.
Cumulative Statistics for Constructor CachedFunction
Time: 0.08 seconds
finalizing NRLIB CACHEDF
Processing CachedFunction for Browser database:
--->-->CachedFunction((function ((Mapping B A) %))): Not documented!!!!
--->-->CachedFunction((cachedFunction (% (Mapping B A)))): Not documented!!!!
--->-->CachedFunction((apply (B % A))): Not documented!!!!
--->-->CachedFunction((recursiveDefine (% % (Mapping B A)))): Not documented!!!!
--------constructor---------
; compiling file "/var/zope2/var/LatexWiki/CACHEDF.NRLIB/CACHEDF.lsp" (written 27 OCT 2009 07:27:03 PM):
; compiling (/VERSIONCHECK 2)
; compiling (PUT (QUOTE |CACHEDF;function;$M;1|) ...)
; compiling (DEFUN |CACHEDF;function;$M;1| ...)
; compiling (DEFUN |CACHEDF;cachedFunction;M$;2| ...)
; compiling (DEFUN |CACHEDF;apply;$AB;3| ...)
; compiling (DEFUN |CACHEDF;recursiveDefine;$M$;4| ...)
; compiling (DEFUN |CachedFunction| ...)
; compiling (DEFUN |CachedFunction;| ...)
; compiling (MAKEPROP (QUOTE |CachedFunction|) ...)
; /var/zope2/var/LatexWiki/CACHEDF.NRLIB/CACHEDF.fasl written
; compilation finished in 0:00:00.074
------------------------------------------------------------------------
CachedFunction is now explicitly exposed in frame initial
CachedFunction will be automatically loaded when needed from
/var/zope2/var/LatexWiki/CACHEDF.NRLIB/CACHEDFaxiom
)set message time on
I := Integer
 | (1) |
Type: Domain
axiom
Time: 0.07 (OT) = 0.07 sec f(n:I): I ==1
Function declaration f : Integer -> Integer has been added to workspace.
Type: Void
axiom
Time: 0 sec fib: CachedFunction(I,I) := cachedFunction(f)
axiom
Compiling function f with type Integer -> Integer
LISP output: (#<HASH-TABLE :TEST EQUAL :COUNT 0 {1005B48391}> #<FUNCTION |*1;f;1;initial|>)
Type: CachedFunction?(Integer,Integer)
axiom
Time: 0.02 (IN) + 0.01 (EV) + 0.01 (OT) = 0.04 sec recursiveDefine(fib,(n:I):I+->if n<2 then 1 else fib(n-1) + fib(n-2))
LISP output: (#<HASH-TABLE :TEST EQUAL :COUNT 0 {1005B48391}> #<FUNCTION |*1;anonymousFunction;0;initial;internal|>)
Type: CachedFunction?(Integer,Integer)
axiom
Time: 0.03 (IN) + 0.01 (OT) = 0.04 sec fib 40
 | (2) |
Type: PositiveInteger?
axiom
Time: 0.01 (IN) = 0.01 sec g(n:I): I == if n<2 then 1 else g(n-1)+g(n-2)
Function declaration g : Integer -> Integer has been added to workspace.
Type: Void
axiom
Time: 0 sec g 40
axiom
Compiling function g with type Integer -> Integer
 | (3) |
Type: PositiveInteger?
axiom
Time: 11.48 (EV) + 0.01 (OT) = 11.49 sec