DemeterF

Illustration of combine for capacity constraint violation 19 :C (w1+w2+w3+w4,2) :Cons (w1+w2+w3+w4,1) :E (w4,0) 1 20 2 18a 3 18 3a 13a :Cons (w1+w2+w3,1) after blue arrow combine is active (like after) 17a :C (w2+w3,1) 4 12a 17 :Cons (w1,0) 5 13 14 12 16a :Cons (w2+w3,0) 15a 6 :E (w1,0) :Empty (0,0) 11a 7a 15 16 11 :E (w3,0) :Cons (w2,0) 8 both containers (C) violate capacity constraints 7 10a 9a :E (w2,0) :Empty (0,0) 9 10

The default Builder for PathSpec after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

well-formed movie show how the default builder is modified to combine Boolean objects.

The default Builder for PathSpec well-formed specialization 1 #t: true #f: false after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J #t :J 5 2 :S :S :S :S 3 #t 7 #f 8 #t 4 #t

The default Builder for PathSpec well-formed specialization 2 #t: true #f: false after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J #t :J #t 5 2 :S :S :S :S #t 7 #f 8 #t 3 4 #t

The default Builder for PathSpec well-formed specialization 3 #t: true #f: false after blue arrow copy is built (like after) #t 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 3 #t 7 #f 8 #t 4 #t

The default Builder for PathSpec well-formed specialization 4 #t: true #f: false after blue arrow copy is built (like after) #t 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. #f 6 :J :J 5 2 :S :S :S :S 3 #t 7 #f 8 #t 4 #t

The default Builder for PathSpec well-formed specialization 5 #t: true #f: false after blue arrow copy is built (like after) #t 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. #f 6 :J #t :J 5 2 :S :S :S :S #t 7 #f 8 #t 3 4 #t

The default Builder for PathSpec well-formed specialization 6 #t: true #f: false after blue arrow copy is built (like after) #t 10 #f :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 3 #t 7 #f 8 #t 4 #t

The default Builder for PathSpec well-formed specialization 7 #t: true #f: false after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 3 #t 7 #f 8 #t 4 #t

The default Builder for PathSpec well-formed specialization #t: true #f: false after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 #f 8 #t 3 #t 4 #t

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization after blue arrow copy is built (like after) 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization insert NOT after blue arrow copy is built (like after) :N 10 :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

The default Builder for PathSpec NOT_JOIN_MERGE specialization insert NOT :M after blue arrow copy is built (like after) :N 10 :N :M 1 9 Count only upon first visit (red) and upon final visit (blue). For leaf nodes, count only in red. 6 :J :J 5 2 :S :S :S :S 7 8 3 4

Illustration of combine for capacity constraint violation (w1+w2+w3+w4,2) :Cons (w1+w2+w3+w4,1) :E (w4,0) :Cons (w1+w2+w3,1) :C (w2+w3,1) :Cons (w1,0) :Cons (w2+w3,0) :E (w1,0) :Empty (0,0) :E (w3,0) :Cons (w2,0) both containers (C) violate capacity constraints :E (w2,0) :Empty (0,0)

Theory t[f,b](d) => d’, where d’=f(d), d is atomic On left side of => the term c(…) only indicates a compound object. Theory t[f,b](d) => d’, where d’=f(d), d is atomic t[f,b](c(d0, … ,dn)) => f(b(c(d0, … ,dn), d’0, … ,d’n)), where d’i = t[f,b](di) Default functions: id[f](d) => d id[b](c(d0, … ,dn), d’0, … ,d’n) => c(d0, … ,dn) b[c](c(d0, … ,dn), d’0, … ,d’n) => c(d’0, … ,d’n)

Theory f is a polymorphic function that takes a single argument and returns a result. b is a function object that is responsible for reconstruction of data types.