--* From adk@mailer.scri.fsu.edu Fri Jul 4 18:47:39 1997 --* Received: from nagmx1.nag.co.uk by red.nag.co.uk via SMTP (920330.SGI/920502.SGI) --* for /home/red5/axiom/support/recvbug id AA12996; Fri, 4 Jul 97 18:47:39 +0100 --* Received: from mailer.scri.fsu.edu (mailer.scri.fsu.edu [144.174.112.142]) --* by nagmx1.nag.co.uk (8.8.4/8.8.4) with ESMTP --* id SAA05072 for ; Fri, 4 Jul 1997 18:48:50 +0100 (BST) --* Received: from ibm4.scri.fsu.edu (ibm4.scri.fsu.edu [144.174.131.4]) by mailer.scri.fsu.edu (8.8.5/8.7.5) with ESMTP id NAA22867; Fri, 4 Jul 1997 13:47:29 -0400 (EDT) --* From: Tony Kennedy --* Received: by ibm4.scri.fsu.edu (8.8.5) id RAA39944; Fri, 4 Jul 1997 17:44:32 GMT --* Date: Fri, 4 Jul 1997 17:44:32 GMT --* Message-Id: <199707041744.RAA39944@ibm4.scri.fsu.edu> --* To: adk@scri.fsu.edu, ax-bugs@nag.co.uk, edwards@scri.fsu.edu --* Subject: [5] What does this warning mean? --@ Fixed by: --@ Tested by: --@ Summary: -- Command line: axiomxl -V -Fao countable.as > countable.log -- Version: 1.1.9a -- Original bug file name: countable.as --+ AXIOM-XL version 1.1.9a for AIX RS/6000 --+ "countable.as", line 215: extend Integer: CountablyInfinite Integer == --+ ^ --+ [L215 C1] #1 (Warning) Couldn't find identifier for documentation --+ --+ "countable.as", line 229: --+ extend SingleInteger: CountablyInfinite SingleInteger == --+ ^ --+ [L229 C1] #2 (Warning) Couldn't find identifier for documentation --+ --+ ld in sc sy li pa ma ab ck sb ti gf of pb pl pc po mi --+ Time 11.3 s 0 1 .4 1 .3 1 .1 .3 .1 2 62 6 8 18 .1 0 0 .4 % --+ --+ Source 458 lines, 2425 lines per minute --+ Lib 65533 bytes, 13685syme 30975foam 604fsyme 2909name 595kind 552file 2026lazy 9767type 2inl 826twins 48ext 3371doc 14id 3macros --+ Store 5856 K pool #include "axllib.as" #pile SI ==> SingleInteger SINS ==> Join(Steppable, IntegerNumberSystem) +++ `Countable' provides a one-to-one mapping to the Integer Number System I, +++ and thus to produce a generator `all' which enumerate element of any +++ domain belonging to this category. +++ +++ Author: ADK +++ Date Created: 26-APR-1995 17:54:53.00 +++ Modifications: +++ 1-APR-1996 18:18:39.00 (ADK) Any type which is countable must at +++ least be a set (`BasicType'). This +++ means that `= : (%,%) -> Boolean' is +++ guaranteed to exist. define Countable(I: SINS): Category == BasicType with ord: % -> I ++ Index within enumeration val: I -> % ++ Enumeration of countable set all: () -> Generator % ++ Generator which enumerates set +++ `CountablyInfinite' provides a one-to-one mapping to the Integer Number +++ System I, and thus to produce a generator `all' which enumerate element of +++ any domain belonging to this category. +++ +++ Author: ADK +++ Date Created: 26-APR-1995 17:54:53.00 +++ Modifications: +++ 1-APR-1996 18:18:39.00 (ADK) Added default definitions for `val' and +++ `ord'. Note that at least one of `all' and +++ `val' must be explicitly defined or these +++ default definitions will suffer infinite +++ recursion with no compile-time warning. define CountablyInfinite(I: SINS): Category == Countable I with default all(): Generator % == import from I, Segment I generate for i: I in 1 .. repeat yield val i val(i: I): % == import from Segment I for a: % in all() for j: I in 1 .. repeat i = j => return a never ord(a: %): I == import from Segment I for b: % in all() for j: I in 1 .. repeat a = b => return j never +++ `CountablyFinite' provides a one-to-one mapping to the Integer Number +++ System I in the range 1 .. card, and thus to produce a generator which +++ enumerates element of any domain belonging to this category. +++ +++ Author: ADK +++ Date Created: 27-APR-1995 13:09:53.00 +++ Modifications: +++ 1-APR-1996 18:18:39.00 (ADK) Added default definitions for `val' and +++ `ord'. Note that at least one of `all' and +++ `val' must be explicitly defined or these +++ default definitions will suffer infinite +++ recursion with no compile-time warning. define CountablyFinite(I: SINS): Category == Countable I with card: I ++ Cardinality of domain default all(): Generator % == import from I, Segment I generate for i: I in 1 .. card repeat yield val i val(i: I): % == import from Segment I for a: % in all() for j: I in 1 .. repeat i = j => return a error "val$CountablyFinite: out of range" ord(a: %): I == import from Segment I for b: % in all() for j: I in 1 .. repeat a = b => return j error "ord$CountablyFinite: out of range" +++ `DirectProduct' produces a domain which is the direct product of two +++ countable sets. +++ +++ Author: ADK +++ Date Created: 26-APR-1995 17:54:53.00 +++ Modifications: DirectProduct(I: SINS, A: Countable I, B: Countable I): with if A has CountablyFinite I and B has CountablyFinite I then CountablyFinite I else CountablyInfinite I coerce: (A, B) -> % ++ constructor coerce: % -> Cross(A, B) ++ deconstructor == add Rep == Record(first: A, second: B) import from Rep, I (a: %) = (b: %): Boolean == (rep a) = (rep b) (p: TextWriter) << (a: %): TextWriter == p << "DirectProduct(" << rep(a).first << "," << rep(a).second << ")" card: I == -- if % has CountablyFinite I then -- doesn't work!!! if A has CountablyFinite I and B has CountablyFinite I then card$A * card$B else -- this shouldn't have to be here!!! -1 ord(a: %): I == local alpha: I == ord((rep a).first) beta: I == ord((rep a).second) A has CountablyFinite I => alpha + card$A * (beta - 1) B has CountablyFinite I => beta + card$B * (alpha - 1) n * (n+1) quo 2 + alpha where n: I == alpha + beta - 2 -- iSqrt(a) gives the largest b such that b*b <= a local iSqrt(a: I): I == import from I local b: I == approxSqrt a not ((b-1)*(b-1) < a < (b+1)*(b+1)) => error "iSqrt$DirectProduct: this cannot happen" b * b > a => b - 1 b -- approxSqrt(a) returns b such that (b-1)^2 < a < (b+1)^2 local approxSqrt(a: I): I == import from I, SingleInteger (n := length a) > 100 => n := n quo 4 s := approxSqrt shift(a, -2 * n) s := shift(s, n) return ((1 + s + a quo s) quo 2) local (b, old): I := (shift(1, n quo 2), 1) while b ~= old repeat (b, old) := ((1 + b + a quo b) quo 2, b) b val(a: I): % == a < 1 => error "val$DirectProduct: out of range" A has CountablyFinite I => ( per [val(alpha + 1), val(beta + 1)] where (beta: I, alpha: I) == divide(a - 1, card$A) ) B has CountablyFinite I => ( per [val(alpha + 1), val(beta + 1)] where (alpha: I, beta: I) == divide(a - 1, card$B) ) per [val(alpha), val(beta)] where n: I == ( iSqrt(8*a - 7) - 1 ) quo 2 alpha: I == a - n * (n+1) quo 2 beta: I == n - alpha + 2 coerce(a: A, b: B): % == per [a, b] sample: % == coerce (sample$A, sample$B) coerce(a: %): Cross(A, B) == ((rep a).first, (rep a).second) +++ `Bounded Integer' produces a domain of integers suitable for indexing +++ a one-dimensional array. The idea is that one gets bounds checking for +++ free. Note the distinction between the functions `ord' and `val' +++ (inherited from `Countable') and `coerce' for the case where low ~= 1. +++ +++ Author: ADK +++ Date Created: 26-APR-1995 17:54:53.00 +++ Modifications: BoundedInteger(I: SINS, low: I, high: I): CountablyFinite I with coerce: % -> I ++ Embedding of % into I coerce: I -> % ++ Retraction of I into % == I add import from FormattedOutput Rep == I if low > high then error(string . "BoundedInteger(I, ~a, ~a) is empty, so what is sample?" . (<< low, << high)) sample: % == coerce low card: I == high - low + 1 ord(a: %): I == (rep a) - low + 1 val(a: I): % == a < 1 or a > card => error "val$BoundedInteger: out of range" per (a + low - 1) coerce(a: %): I == rep a coerce(a: I): % == a < low or a > high => error "coerce$BoundedInteger: out of range" per a +++ `Integer' is extended to make it belong to `Countable' +++ +++ Author: ADK +++ Date Created: 27-APR-1995 15:42:12.00 +++ Modifications: extend Integer: CountablyInfinite Integer == add Rep ==> Integer ord(a: %): Integer == rep a val(a: Integer): % == per a +++ `SingleInteger' is extended to make it belong to `Countable' +++ +++ Author: ADK +++ Date Created: 4-APR-1996 11:41:49.00 +++ Modifications: extend SingleInteger: CountablyInfinite SingleInteger == add Rep ==> SingleInteger ord(a: %): SingleInteger == rep a val(a: SingleInteger): % == per a +++ `FiniteSet' is a domain defined by a set of strings. This should +++ be an extension of `Enumeration' when the compiler gets fixed! +++ +++ Author: ADK +++ Date Created: 23-APR-1996 14:48:11.00 +++ Modifications FiniteSet(ts: Tuple String): CountablyFinite SI with coerce: String -> % coerce: % -> String == add Rep == SI import from SI card: SI == length ts all(): Generator % == generate for i in 1 .. card repeat yield per i ord(a: %): SI == rep a val(i: SI): % == i < 1 or i > card => error "val$FiniteSet: out of range" per i sample: % == per 1 -- What if card = 0? (a: %) = (b: %): Boolean == rep.a = rep.b (p: TextWriter) << (a: %): TextWriter == p << a::String coerce(a: %): String == element(ts, rep a) coerce(s: String): % == for a: % in all() repeat s = a::String => return a error "coerce$FiniteSet: string not in set"