Logic-based inductive synthesis of efficient programs Andrew - PowerPoint PPT Presentation

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Logic-based inductive synthesis of efficient programs Andrew Cropper Imperial College London String transformations Outpu Input t Computer Aided Verification CAV Principles Of Programming Languages POPL International Conference on

Logic-based inductive synthesis of efficient programs Andrew Cropper Imperial College London
String transformations Outpu Input t Computer Aided Verification CAV Principles Of Programming Languages POPL International Conference on Functional Programming ??? International Joint Conference Artificial Intelligence ??? Neural Information Processing Systems ???
% prolog % python f([],[]). def f(input): f([X|Input],[X|Output]):- output=[] is_uppercase(X), for x in string: f(Input,Output). if x.isupper(): f([X|Input],Output):- output.append(x) not_uppercase(X), return output f(Input,Output).
Sorting Input Output [9,13,1,8,4] [1,4,8,9,13] [1,18,20,6,15,5] [1,5,6,15,18,20] [12,16,18,6,15,3,5] ??? [16,1,4,12,3,18,2,14] ??? [12,17,5,13,6,4,14,2,15] ???
Learning efficient robot strategies [IJCAI15] Initial state Final state 3 3 2 2 1 1 0 0 0 1 2 3 0 1 2 3
move(X,Y):-p3(X,Z),p3(Z,Y). move(X,Y):-p3(X,Z),drop(Z,Y). p3(X,Y):-p2(X,Z),drop(Z,Y). p3(X,Y):-grab(X,Z),p2(Z,Y). p2(X,Y):-grab(X,Z),p1(Z,Y). p2(X,Y):-p1(X,Z),p1(Z,Y). p1(X,Y):-north(X,Z),east(Z,Y). p1(X,Y):-north(X,Z),east(Z,Y).
grab drop Inefficient solution Efficient solution 3 3 2 2 1 1 0 0 0 1 2 3 0 1 2 3 resource complexity: 8 resource complexity: 6 Action drop grab north east Cost 1 1 1 1
Meta-interpretive learning (MIL) A form of inductive logic programming based on Prolog meta-interpreter which supports: • predicate invention • learning recursive programs • learning efficient programs • learning higher-order programs https://github.com/metagol
Sorting experiment Input Output [9,13,1,8,4] [1,4,8,9,13] [1,18,20,6,15,5] [1,5,6,15,18,20] [12,16,18,6,15,3,5] ??? [16,1,4,12,3,18,2,14] ??? [12,17,5,13,6,4,14,2,15] ???
5 , 000 Metagol O Metagol D Mean resource complexity Tight bound n log n 4 , 000 Tight bound n(n-1)/2 3 , 000 2 , 000 1 , 000 0 20 40 60 80 100 List length
Conclusions • pruning the search space [IJCAI15] • higher-order programs [IJCAI16] Future work • Demonstrate generality • Use to discover novel algorithms
Thank you

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