Accessible
Combinatorial Programming
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- Declare function signatures
- Optionally: define functions explicitly
- Post constraints over these functions
- Reason over set of admissible functions
Functions are total and strongly typed along
bool
,int
,string
= != > < >= =< + - * /
not and or xor implies
div rem abs min max count
distinct same if-then-else
Builtins
Explanation for unexpected satisfiability
Try it online at manyworlds.site
Explanation for unexpected unsatisfiability
declare drinksAlcohol: -> bool.
declare age: -> {0..150}.
age() >= 18 implies drinksAlcohol().
define drinksAlcohol() as true.
define age() as 0.
· · age() [0]
· >= [false]
· · 18
implies
[true]
· drinksAlcohol() [true].
1 declare color: string -> {"r", "g", "b", "y"}.
2 declare border: string, string -> bool.
3
4 define border as {("NL","BE"), ("NL","DE"),
5 ("BE","LU"), ("BE","DE"), ("BE","FR"),
6 ("FR","LU"), ("FR","DE"), ("LU","DE")} default false.
7
8 all[ color(x)!=color(y) for x,y where border(x,y) ].
Bug: forget color "y"
BASIC BLOCKERS
Line 8: all[ color(x)!=color(y) for x,y where border(x,y) ].
DETAILED BLOCKERS
Line 8: not color("BE")=color("DE")
Line 8: not color("BE")=color("FR")
Line 8: not color("BE")=color("LU")
Line 8: not color("DE")=color("FR")
Line 8: not color("DE")=color("LU")
Line 8: not color("FR")=color("LU")
Bug: wrong use of implication
Incorrect world returned
Explain in detail why constraints hold in world
Jo Devriendt
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A knowledge base
system in the spirit of
Reasoning modes (inferences)
find intersect count
@minimize @maximize @mode
Fold-Map-Filter expressions
all any none
odd even count
sum product min max distinct same
ManyWorlds: Combinatorial Programming Summary
By Jo Devriendt
ManyWorlds: Combinatorial Programming Summary
Poster for XAI - the Explainable Symbolic AI workshop
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