M1 >(defun g (n a) (if (zp n) a (g (- n 1) (* n a)))) The admission of G is trivial, using the relation O< (which is known to be well-founded on the domain recognized by O-P) and the measure (ACL2-COUNT N). We observe that the type of G is described by the theorem (OR (ACL2-NUMBERP (G N A)) (EQUAL (G N A) A)). We used primitive type reasoning. Summary Form: ( DEFUN G ...) Rules: ((:FAKE-RUNE-FOR-TYPE-SET NIL)) Warnings: None Time: 0.01 seconds (prove: 0.00, print: 0.00, other: 0.00) G M1 >(defconst *g* '((PUSH 1) (STORE 1) (LOAD 0) (IFLE 10) (LOAD 0) (LOAD 1) (MUL) (STORE 1) (LOAD 0) (PUSH 1) (SUB) (STORE 0) (GOTO -10) (LOAD 1) (HALT))) Summary Form: ( DEFCONST *G* ...) Rules: NIL Warnings: None Time: 0.00 seconds (prove: 0.00, print: 0.00, other: 0.00) *G* M1 >(defun g-sched-loop (n) (if (zp n) (repeat 0 4) (append (repeat 0 11) (g-sched-loop (- n 1))))) The admission of G-SCHED-LOOP is trivial, using the relation O< (which is known to be well-founded on the domain recognized by O-P) and the measure (ACL2-COUNT N). We observe that the type of G-SCHED-LOOP is described by the theorem (TRUE-LISTP (G-SCHED-LOOP N)). We used the :type-prescription rules ACL2::APPEND-TRUE-LISTP-TYPE-PRESCRIPTION, BINARY-APPEND and REPEAT. Summary Form: ( DEFUN G-SCHED-LOOP ...) Rules: ((:TYPE-PRESCRIPTION ACL2::APPEND-TRUE-LISTP-TYPE-PRESCRIPTION) (:TYPE-PRESCRIPTION BINARY-APPEND) (:TYPE-PRESCRIPTION REPEAT)) Warnings: None Time: 0.00 seconds (prove: 0.00, print: 0.00, other: 0.00) G-SCHED-LOOP M1 >(defun g-sched (n) (append (repeat 0 2) (g-sched-loop n))) Since G-SCHED is non-recursive, its admission is trivial. We observe that the type of G-SCHED is described by the theorem (TRUE-LISTP (G-SCHED N)). We used the :type-prescription rules ACL2::- APPEND-TRUE-LISTP-TYPE-PRESCRIPTION and G-SCHED-LOOP. Summary Form: ( DEFUN G-SCHED ...) Rules: ((:TYPE-PRESCRIPTION ACL2::APPEND-TRUE-LISTP-TYPE-PRESCRIPTION) (:TYPE-PRESCRIPTION G-SCHED-LOOP)) Warnings: None Time: 0.00 seconds (prove: 0.00, print: 0.00, other: 0.00) G-SCHED M1 >(defun run-g (n) (top (stack (run (g-sched n) (make-state 0 (list n 0) nil *g*))))) Since RUN-G is non-recursive, its admission is trivial. We could deduce no constraints on the type of RUN-G. Summary Form: ( DEFUN RUN-G ...) Rules: NIL Warnings: None Time: 0.00 seconds (prove: 0.00, print: 0.00, other: 0.00) RUN-G M1 >(run-g 5) 120 M1 >(run-g 1000) 402387260077093773543702433923003985719374864210714632543799910429938512398629020592044208486969404800479988610197196058631666872994808558901323829669944590997424504087073759918823627727188732519779505950995276120874975462497043601418278094646496291056393887437886487337119181045825783647849977012476632889835955735432513185323958463075557409114262417474349347553428646576611667797396668820291207379143853719588249808126867838374559731746136085379534524221586593201928090878297308431392844403281231558611036976801357304216168747609675871348312025478589320767169132448426236131412508780208000261683151027341827977704784635868170164365024153691398281264810213092761244896359928705114964975419909342221566832572080821333186116811553615836546984046708975602900950537616475847728421889679646244945160765353408198901385442487984959953319101723355556602139450399736280750137837615307127761926849034352625200015888535147331611702103968175921510907788019393178114194545257223865541461062892187960223838971476088506276862967146674697562911234082439208160153780889893964518263243671616762179168909779911903754031274622289988005195444414282012187361745992642956581746628302955570299024324153181617210465832036786906117260158783520751516284225540265170483304226143974286933061690897968482590125458327168226458066526769958652682272807075781391858178889652208164348344825993266043367660176999612831860788386150279465955131156552036093988180612138558600301435694527224206344631797460594682573103790084024432438465657245014402821885252470935190620929023136493273497565513958720559654228749774011413346962715422845862377387538230483865688976461927383814900140767310446640259899490222221765904339901886018566526485061799702356193897017860040811889729918311021171229845901641921068884387121855646124960798722908519296819372388642614839657382291123125024186649353143970137428531926649875337218940694281434118520158014123344828015051399694290153483077644569099073152433278288269864602789864321139083506217095002597389863554277196742822248757586765752344220207573630569498825087968928162753848863396909959826280956121450994871701244516461260379029309120889086942028510640182154399457156805941872748998094254742173582401063677404595741785160829230135358081840096996372524230560855903700624271243416909004153690105933983835777939410970027753472000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000 M1 >(len (g-sched 1000)) 11006 M1 >(quote (End of Demo 1)) (END OF DEMO 1) M1 >(include-book "compile") Summary Form: ( INCLUDE-BOOK "compile" ...) Rules: NIL Warnings: None Time: 0.06 seconds (prove: 0.00, print: 0.00, other: 0.06) "/v/filer4b/v11q001/text/marktoberdorf-08/scripts/compile.lisp" M1 >(compile '(n) ; Factorial '((a = 1) (while (n > 0) (a = (n * a)) (n = (n - 1))) (return a))) ((PUSH 1) (STORE 1) (LOAD 0) (IFLE 10) (LOAD 0) (LOAD 1) (MUL) (STORE 1) (LOAD 0) (PUSH 1) (SUB) (STORE 0) (GOTO -10) (LOAD 1) (RETURN)) M1 >(quote (End of Demo 2)) (END OF DEMO 2) M1 >