Edit detail for FriCAS Syntax revision 3 of 3

On January 19, 2006 5:53 AM Fabio Stumbo wrote:

if-then-else: what is wrong?

I am having some problem with the if-then-else syntax in the .input files.

Problem 1: I refer to the axiom book which ships with the program (version 2005/09). At page 204 it says that the usual rules for piling are suspended in conditional expressions and it gives 5 different ways which should be equivalent, namely::

(1) -> i := 2

(1)

if i>0 then output("positive") else output("nonpositive")

   positive

if i > 0 then output("positive")
    else output("nonpositive")

   positive

if true then
    if i > 0 then output("positive")
    else output("nonpositive")

   positive

if true then
   if i > 0
   then output("positive")
   else output("nonpositive")

   positive

if i > 0
    then output("positive")
    else output("nonpositive")

  Line  15: 
  Line  16: if i > 0
  Line  17:     then output("positive")
           ....A
  Error  A: (from A and on) Ignored from here
  Error  A: Improper syntax.
  Line  18:     else output("nonpositive")
           .............................A
  Error  A: (up to A) to here.
  Error  A: syntax error at top level
  Error  A: Possibly missing a then 
   5 error(s) parsing

Well, I tried all of them, creating each time a blank r.input file with inside only:

i := 2

(2)

followed by one of the "if...".

The result is that the first two are ok, where as the other three give some syntax error (different each time).

for i in 2..2 repeat
  if i>0 then output("positive") else output("nonpositive")

   positive

for i in 2..2 repeat
  if i > 0 then output("positive")
    else output("nonpositive")

   positive

for i in 2..2 repeat
  if i > 0 then output("positive")
  else output("nonpositive")

   positive

for i in 2..2 repeat
  if i > 0
  then output("positive")
  else output("nonpositive")

   positive

The ones above works OK. The following one looks like a bug...

for i in 2..2 repeat
  if i > 0
    then output("positive")
    else output("nonpositive")

  Line   1: for i in 2..2 repeat
  Line   2:   if i > 0
           ..A
  Error  A: (from A and on) Ignored from here
  Line   3:     then output("positive")
           ....A
  Error  A: Improper syntax.
  Error  A: (from A and on) Ignored from here
  Line   4:     else output("nonpositive")
           .............................A
  Error  A: (up to A) to here.
  Error  A: Possibly missing a then 
  Error  A: (up to A) to here.
   6 error(s) parsing

for i in 2..2 repeat
  if i > 0 then
    output(i)
    output("positive")
  else
    output(i)
    output("nonpositive")

   2
   positive

i:=1.5

(3)

a :=
  if i > 0 then
    j := sin(i * pi())
    exp(j + 1/j)
  else
    j := cos(i * 0.5 * pi())
    log(abs(j)**5 + 1)

(4)

Problem 2: again with if then else, in a complex function I noticed a wrong result (the function itself was ok... ;-) Simplifying, you can produce the same error with something like:

test: (INT,INT) -> List(INT)

test(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then
    x := 1
    y := 1
  [x,y]

Then,

4 rem -2

(5)

test(4,-2)

Compiling function test with type (Integer, Integer) -> List(Integer
      )

(6)

returns correctly '[1,1]?', but

4 rem -3

(7)

test(4,-3)

(8)

or

4 rem 2

(9)

test(4,2)

(10)

returns wrongly '[0,1]?'. Actually the result is '[0, 0]?' which is correct.

The same happens if I write

test: (INT,INT) -> List(INT)

   Compiled code for test has been cleared.

test(a,b) ==
  x := 0; y := 0
  if (a rem b = 0) and b < 0 then  x := 1 ; y := 1
  [x,y]

   1 old definition(s) deleted for function or rule test

Why?

Another small question. Is there a way to obtain on line the syntax of a command in a more extensive way? I mean, for example, that writing

)di op extendedEuclidean

There are 2 exposed functions called extendedEuclidean :
   [1] (D,D,D) -> Union(Record(coef1: D,coef2: D),"failed") from D
            if D has EUCDOM
   [2] (D,D) -> Record(coef1: D,coef2: D,generator: D) from D if D has 
            EUCDOM

which is not too useful. Moreover, how can I just ask about, say, the second function extendedEuclidean?

If I wanted to ask about the syntax of if-then-else, I would like to write something like:

  )? if
  or
  )ap if

but nothing gives clues on how to use it.

Thank you for all your help