MathAction SandBoxTryOutSPAD

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- FriCAS language
  - ProgrammingSPAD
    - SandBoxTryOutSPAD <-- You are here.

Everyone is allowed to try out SPAD by editing this page. Don't be affraid to destroy anything. The purpose of this page is exactly to give a place for everyone to experiment.

Just hit the "edit" link in the upper right corner.

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(1) -> <spad>

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)abbrev category MYMON MyMonoid
MyMonoid: Category == with
    1: %
    _*: (%, %) -> %

rep x ==> (x@%) pretend Rep
per x ==> (x@Rep) pretend %

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)abbrev domain MYFUN MyFun
MyFun(S: SetCategory): MyMonoid with
    coerce:  (S -> S) -> %
    coerce: % -> (S -> S)
 == add
    Rep ==> S -> S
    coerce(f: S -> S): % == per f
    coerce(x: %): S -> S == rep x
    1: % == per((s: S): S +-> s)
    ((x: %) * (y: %)): % == per( (s: S): S +-> (rep x)(rep y)s )</spad>

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Compiling FriCAS source code from file 
      /var/lib/zope2.10/instance/axiom-wiki/var/LatexWiki/5443222399567089399-25px001.spad
      using old system compiler.
   MYMON abbreviates category MyMonoid 
------------------------------------------------------------------------
   initializing NRLIB MYMON for MyMonoid 
   compiling into NRLIB MYMON 
Time: 0 SEC.

   finalizing NRLIB MYMON 
   Processing MyMonoid for Browser database:
--->-->MyMonoid(constructor): Not documented!!!!
--->-->MyMonoid(((One) (%) constant)): Not documented!!!!
--->-->MyMonoid((* (% % %))): Not documented!!!!
--->-->MyMonoid(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYMON.NRLIB/MYMON.lsp" (written 07 AUG 2025 10:00:35 PM):

; wrote /var/aw/var/LatexWiki/MYMON.NRLIB/MYMON.fasl
; compilation finished in 0:00:00.004
------------------------------------------------------------------------
   MyMonoid is now explicitly exposed in frame initial 
   MyMonoid will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYMON.NRLIB/MYMON

   MYFUN abbreviates domain MyFun 
------------------------------------------------------------------------
   initializing NRLIB MYFUN for MyFun 
   compiling into NRLIB MYFUN 
   processing macro definition Rep ==> S -> S 
   compiling exported coerce : S -> S -> %
      MYFUN;coerce;M%;1 is replaced by f 
Time: 0 SEC.

   compiling exported coerce : % -> S -> S
      MYFUN;coerce;%M;2 is replaced by x 
Time: 0 SEC.

   compiling exported One : () -> %
Time: 0 SEC.

   compiling exported * : (%,%) -> %
Time: 0 SEC.

(time taken in buildFunctor:  0)
Time: 0 SEC.

   Warnings: 
      [1] coerce:  elt has no value
      [2] *:  elt has no value

   Cumulative Statistics for Constructor MyFun
      Time: 0 seconds

   finalizing NRLIB MYFUN 
   Processing MyFun for Browser database:
--->-->MyFun(constructor): Not documented!!!!
--->-->MyFun((coerce (% (Mapping S S)))): Not documented!!!!
--->-->MyFun((coerce ((Mapping S S) %))): Not documented!!!!
--->-->MyFun(): Missing Description
; compiling file "/var/aw/var/LatexWiki/MYFUN.NRLIB/MYFUN.lsp" (written 07 AUG 2025 10:00:35 PM):

; wrote /var/aw/var/LatexWiki/MYFUN.NRLIB/MYFUN.fasl
; compilation finished in 0:00:00.012
------------------------------------------------------------------------
   MyFun is now explicitly exposed in frame initial 
   MyFun will be automatically loaded when needed from 
      /var/aw/var/LatexWiki/MYFUN.NRLIB/MYFUN

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I ==> Integer

Type: Void

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II ==> I -> I

Type: Void

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MI ==> MyFun I

Type: Void

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inc(i: I): I == i+1

   Function declaration inc : Integer -> Integer has been added to 
      workspace.

Type: Void

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double(i: I): I == 2*i

   Function declaration double : Integer -> Integer has been added to 
      workspace.

Type: Void

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minc := inc :: MI

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Compiling function inc with type Integer -> Integer 

 LISP output:
(#<FUNCTION |*1;inc;1;initial|>)

Type: MyFun?(Integer)

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mdouble := double :: MI

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Compiling function double with type Integer -> Integer 

 LISP output:
(#<FUNCTION |*1;double;1;initial|>)

Type: MyFun?(Integer)

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f := (mdouble * minc) :: II

$\label{eq1}\mbox{theMap (...)}$

(1)

Type: (Integer -> Integer)

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g := (minc * mdouble) :: II

$\label{eq2}\mbox{theMap (...)}$

(2)

Type: (Integer -> Integer)

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f 1

$\label{eq3}4$

(3)

Type: PositiveInteger?

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g 1

$\label{eq4}3$

(4)

Type: PositiveInteger?

Subject: Be Bold !!

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