)set break resume
)spool bugs.output
)set message test on
)set message auto off
)clear all

-- File of Currently active and recently fixed interpreter bugs

--- eval a polynomial with EXPR substitution values
--- Fixed by SCM, verified on 10/30/90

)clear all

--S 1 of 44 
eq1:= A*x**2 + B*x*y + C*y**2 +D*x + E*y + F
--R 
--R
--R           2                   2
--R   (1)  C y  + (B x + E)y + A x  + D x + F
--R                                                     Type: Polynomial Integer
--E 1

--S 2 of 44 
eq2:= eval(eq1,[x= xdot*cos(t) - ydot*sin(t), y=xdot*sin(t) + ydot*cos(t)])
--R 
--R
--R   (2)
--R            2                       2       2
--R     (A ydot  - B xdot ydot + C xdot )sin(t)
--R   + 
--R               2                              2
--R     ((- B ydot  + (2C - 2A)xdot ydot + B xdot )cos(t) - D ydot + E xdot)sin(t)
--R   + 
--R            2                       2       2
--R     (C ydot  + B xdot ydot + A xdot )cos(t)  + (E ydot + D xdot)cos(t) + F
--R                                                     Type: Expression Integer
--E 2

-- UTS coercions.  Fixed by SCM, verified on 10/30/90

)clear all

--S 3 of 44 
taylor exp x
--R 
--R
--R   (1)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 3

--S 4 of 44 
s := %
--R 
--R
--R   (2)
--R             1  2   1  3    1  4    1   5    1   6     1   7     1    8
--R     1 + x + - x  + - x  + -- x  + --- x  + --- x  + ---- x  + ----- x
--R             2      6      24      120      720      5040      40320
--R   + 
--R        1    9      1     10      11
--R     ------ x  + ------- x   + O(x  )
--R     362880      3628800
--R                         Type: UnivariateTaylorSeries(Expression Integer,x,0)
--E 4

--S 5 of 44 
s::(UTS(EXPR FLOAT, x, 0))
--R 
--R
--R   (3)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                         Type: UnivariateTaylorSeries(Expression Float,x,0.0)
--E 5

--S 6 of 44 
s::(UTS(FLOAT, x, 0))
--R 
--R
--R   (4)
--R                    2                            3
--R     1.0 + x + 0.5 x  + 0.1666666666 6666666667 x
--R   + 
--R                                4                               5
--R     0.0416666666 6666666666 7 x  + 0.0083333333 3333333333 34 x
--R   + 
--R                                 6                               7
--R     0.0013888888 8888888888 89 x  + 0.0001984126 9841269841 27 x
--R   + 
--R                                   8                                  9
--R     0.0000248015 8730158730 1587 x  + 0.0000027557 3192239858 90653 x
--R   + 
--R                                   10      11
--R     0.2755731922 3985890653 E -6 x   + O(x  )
--R                                    Type: UnivariateTaylorSeries(Float,x,0.0)
--E 6

--S 7 of 44 
eval(s,1)
--R 
--R
--R             5 8 65 163 1957 685 109601 98641
--R   (5)  [1,2,-,-,--,---,----,---,------,-----,...]
--R             2 3 24  60  720 252  40320 36288
--R                                              Type: Stream Expression Integer
--E 7

--S 8 of 44 
%::(Stream Float)
--R 
--R
--R   (6)
--R   [1.0, 2.0, 2.5, 2.6666666666 666666667, 2.7083333333 333333333,
--R    2.7166666666 666666667, 2.7180555555 555555556, 2.7182539682 53968254,
--R    2.7182787698 412698413, 2.7182815255 731922399, ...]
--R                                                           Type: Stream Float
--E 8

-- overloading interpreter maps on arity
--- Fixed by SCM, verified on 10/30/90

)clear all

--S 9 of 44 
f(x) == x+1
--R 
--R                                                                   Type: Void
--E 9

--S 10 of 44 
f(x,y) == x+y
--R 
--R                                                                   Type: Void
--E 10

--S 11 of 44 
f 3
--R 
--R   Compiling function f with type PositiveInteger -> PositiveInteger 
--R
--R   (3)  4
--R                                                        Type: PositiveInteger
--E 11

--S 12 of 44 
f(3,4)
--R 
--R   Compiling function f with type (PositiveInteger,PositiveInteger) -> 
--R      PositiveInteger 
--R
--R   (4)  7
--R                                                        Type: PositiveInteger
--E 12

--S 13 of 44 
f(5)
--R 
--R
--R   (5)  6
--R                                                        Type: PositiveInteger
--E 13

--S 14 of 44 
f(1,x)
--R 
--R   Compiling function f with type (PositiveInteger,Variable x) -> 
--R      Polynomial Integer 
--R
--R   (6)  x + 1
--R                                                     Type: Polynomial Integer
--E 14

-- targetted function requiring a coercion
--- Fixed by SCM, verified on 10/30/90

)clear all

--S 15 of 44 
series(n +-> bernoulli(n)/factorial(n), t=0)
--R 
--R
--R   (1)
--R       1      1  2    1   4     1    6      1     8       1     10      11
--R   1 - - t + -- t  - --- t  + ----- t  - ------- t  + -------- t   + O(t  )
--R       2     12      720      30240      1209600      47900160
--R                        Type: UnivariatePuiseuxSeries(Expression Integer,t,0)
--E 15

-- in-homogeneous list mapping
--- Fixed by SCM, verified on 10/30/90

)clear all

--S 16 of 44 
l := [1,2,-1]
--R 
--R
--R   (1)  [1,2,- 1]
--R                                                           Type: List Integer
--E 16

--S 17 of 44 
f : INT -> FRAC INT
--R 
--R                                                                   Type: Void
--E 17

--S 18 of 44 
f x == x
--R 
--R                                                                   Type: Void
--E 18

--S 19 of 44 
map(f, l)
--R 
--R   Compiling function f with type Integer -> Fraction Integer 
--R
--R   (4)  [1,2,- 1]
--R                                                  Type: List Fraction Integer
--E 19

-- Function args to interpreter functions
--- Fixed by SCM, verified on 10/30/90

)clear all
 
--S 20 of 44 
f: INT -> INT
--R 
--R                                                                   Type: Void
--E 20

--S 21 of 44 
f x == x+1
--R 
--R                                                                   Type: Void
--E 21

--S 22 of 44 
u g == g 3
--R 
--R                                                                   Type: Void
--E 22

--S 23 of 44 
u f
--R 
--R   Compiling function u with type (Integer -> Integer) -> Integer 
--R   Compiling function f with type Integer -> Integer 
--R
--R   (4)  4
--R                                                        Type: PositiveInteger
--E 23

-- category modemap requiring a field to be constructed
--- Fixed by SCM, verified on 10/30/90

)clear all

--S 24 of 44 
groebner [x**2 - y, y**3+1]
--R 
--R
--R              2  6
--R   (1)  [y - x ,x  + 1]
--R                                                Type: List Polynomial Integer
--E 24

-- operations requiring polynomials, passed variables
--- Fixed by SCM, verified on 10/30/90

)clear all

--S 25 of 44 
factor x
--R 
--R
--R   (1)  x
--R                                            Type: Factored Polynomial Integer
--E 25

-- bracket parsing and empty-set types
--- Fixed by SCM, verified on 10/30/90

)clear all
 
--S 26 of 44 
{}$(List INT)
--R 
--R 
--RDaly Bug
--R   The function SEQ is not implemented in List Integer .
--E 26

--S 27 of 44 
{1}
--R 
--R
--R   (1)  1
--R                                                        Type: PositiveInteger
--E 27

-- Shouldn't work, but no longer bombs the interpreter
--- Fixed by SCM, verified on 10/30/90

)clear all
 
--S 28 of 44 
map(variable, [x,y])
--R 
--R
--R   (1)  [x,y]
--R                         Type: List Union(OrderedVariableList [x,y],"failed")
--E 28

-- Recursive map type analysis bug
--- Fixed by SCM, verified on 10/30/90
)set fun recur off
 
)clear all
 
--S 29 of 44 
p(n,x) == if n=0 then 1 else (x+n-1)*p(n-1,x)
--R 
--R                                                                   Type: Void
--E 29

--S 30 of 44 
pp(n,x) == if n=0 then 1 else if n<0 then (-1)**n/p(-n,1-x) else p(n,x)
--R 
--R                                                                   Type: Void
--E 30

--S 31 of 44 
pp(-1,x) -- should be 1/(x-1)
--R 
--R   Compiling function p with type (Integer,Polynomial Integer) -> 
--R      Polynomial Integer 
--R   Compiling function p with type (Integer,Variable x) -> Polynomial 
--R      Integer 
--R   Compiling function pp with type (Integer,Variable x) -> Fraction 
--R      Polynomial Fraction Integer 
--R
--R          1
--R   (3)  -----
--R        x - 1
--R                                   Type: Fraction Polynomial Fraction Integer
--E 31

-- interpret-code mode for iterators is broken

)clear all

--S 32 of 44 
f n ==
  for i in 1..n repeat
    j:=2*i
    m:SQMATRIX(j,?):=1
    print m
--R 
--R                                                                   Type: Void
--E 32

--S 33 of 44 
g n ==
    j:=2*n
    m:SQMATRIX(j,?):=1
    print m
--R 
--R                                                                   Type: Void
--E 33

--S 34 of 44 
g 3 -- Should work
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 34

--S 35 of 44 
f 3 -- Bombs
--R 
--R   Cannot compile the declaration for m because its (possible partial) 
--R      type contains a local variable.
--R   AXIOM will attempt to step through and interpret the code.
--R   +1  0+
--R   |    |
--R   +0  1+
--R   +1  0  0  0+
--R   |          |
--R   |0  1  0  0|
--R   |          |
--R   |0  0  1  0|
--R   |          |
--R   +0  0  0  1+
--R   +1  0  0  0  0  0+
--R   |                |
--R   |0  1  0  0  0  0|
--R   |                |
--R   |0  0  1  0  0  0|
--R   |                |
--R   |0  0  0  1  0  0|
--R   |                |
--R   |0  0  0  0  1  0|
--R   |                |
--R   +0  0  0  0  0  1+
--R                                                                   Type: Void
--E 35

-- Test interpreter list destructuring

)clear all
 
--S 36 of 44 
mp(x,l) ==
  l is [a,:b] =>
    a*x**(#b)+ mp(x,b)
  0
--R 
--R                                                                   Type: Void
--E 36

--S 37 of 44 
mp(x, [1,3,4, 2])
--R 
--R   Compiling function mp with type (Variable x,List PositiveInteger)
--R       -> Polynomial Integer 
--R
--R         3     2
--R   (2)  x  + 3x  + 4x + 2
--R                                                     Type: Polynomial Integer
--E 37

--S 38 of 44 
mp(x, [1,2,-3, 4])
--R 
--R   Compiling function mp with type (Variable x,List Integer) -> 
--R      Polynomial Integer 
--R
--R         3     2
--R   (3)  x  + 2x  - 3x + 4
--R                                                     Type: Polynomial Integer
--E 38

-- Tests compilation of recursive functions

)clear all
 
--S 39 of 44 
f1 n ==
  if n=0 then 1 else if n=1 then 1 else f1(n-1)+f1(n-2)
--R 
--R                                                                   Type: Void
--E 39

--S 40 of 44 
f2 n ==
  m:=n
  if n=0 then 1 else if n=1 then 1 else f2(n-1)+f2(n-2)
--R 
--R                                                                   Type: Void
--E 40

--S 41 of 44 
f3 n ==
  n=0 => 1
  n=1 => 1
  f3(n-1)+f3(n-2)
--R 
--R                                                                   Type: Void
--E 41

--S 42 of 44 
f4 n ==
  m:=n
  n=0 => 1
  n=1 => 1
  m:=n
  f4(n-1)+f4(n-2)
--R 
--R                                                                   Type: Void
--E 42

--S 43 of 44 
f5 n == if n=0 or n=1 then 1 else f5(n-1)+f5(n-2)
--R 
--R                                                                   Type: Void
--E 43

--S 44 of 44 
[f1 3,f2 3, f3 3,f4 3,f5 3]
--R 
--R   Compiling function f1 with type Integer -> PositiveInteger 
--R   Compiling function f2 with type Integer -> PositiveInteger 
--R   Compiling function f3 with type Integer -> PositiveInteger 
--R   Compiling function f4 with type Integer -> PositiveInteger 
--R   Compiling function f5 with type Integer -> PositiveInteger 
--R
--R   (6)  [3,3,3,3,3]
--R                                                   Type: List PositiveInteger
--E 44
)spool
)lisp (bye)
 
