mapsto-mapsfrom-algebra.groovy

// there is an interesting algebra we need to define

mmadt> int{3} <= [start,1,2,3]                                // int{3} is a 'reference' to the stream 1,2,3
==>1
==>2
==>3
mmadt> int{3} <= [start,1,2,3] => int                         // the int{3} reference is => (mapped-to) the int type.
==>1                                                          // the RHS int serves as a filter instruction (compiles to [is,[a,int]])
==>2
==>3
mmadt> int{3} <= [start,1,2,3] => str                         // the streaming ints are not strs so they are filtered out.
mmadt>

/*
Whats interesting is that each obj has a "maps from" and a "maps to" instruction sequence.

  int{3} <= [start,1,2,3] => int
      int{3} "maps from" [start,1,2,3]
      int{3} "maps to" int

How does <= and => mutate when chained?

  int{3} <= [start,1,2,3] => int <= [plus,10] => [mult,5]
*/

// maps-to
  
mmadt> int{3} <= [start,1,2,3] => (int <= [plus,10] => [mult,5])             // the second int is "dependently generated" via [plus,10]
==>int{0,3} <= [start,1,2,3][plus,10][is,[a,int]][mult,5]                    // hence the compilation to int{0,3}
mmadt> int{0,3} <= [start,1,2,3][plus,10][is,[a,int]][mult,5]
==>55
==>60
==>65

// maps-from

mmadt> int <= (int{3} <= [start,1,2,3][plus,10] => [mult,5])  // note that [mult,5] is placed after the int <= generator. this could lead to a type error as it is not definitial/generating of int. Is this bad? 
==>55
==>60
==>65


///////////

// here is the algebra I have thus far. It tells you how <= is related to =>.

    public default <O extends Obj> O mapFrom(final Obj obj) {
        return obj instanceof Inst ? this.appendFrom((Inst) obj) : this.q(this.q().mult(obj.q())).accessFrom(obj.accessFrom()).appendFrom(obj.accessTo()).appendFrom(this.accessFrom()).appendFrom(IsInst.isA(this));
    }

    public default <O extends Obj> O mapTo(final Obj obj) {
        return obj instanceof Inst ? this.appendTo((Inst) obj) : obj.mapFrom(this);
        // mapTo is defined in terms of mapFrom (symmetric)
        // obj.q(obj.q().mult(this.q())).accessFrom(this.accessFrom()).appendFrom(this.accessTo()).appendFrom(obj.accessFrom()).appendFrom(IsInst.isA(obj));
    }