Mixed integer linear programming is a powerful and widely used approach to solving optimization problems, but its expressiveness is limited. In this paper we introduce the optimization-aided language Scimitar, which encodes optimization problems using an expressive functional language, with a compiler that targets a mixed integer linear program solver. Scimitar provides easy access to encoding techniques that normally require expert knowledge, enabling solve-time conditional constraints, inlining, loop unrolling, and many other high-level language constructs. We give operational semantics for Scimitar and constraint encodings of various features. To demonstrate Scimitar, we present a number of examples and benchmarks including classic optimization domains and more complex problems. Our results indicate that Scimitar's use of a dedicated MILP solver is effective for expressively modeling optimization problems embedded within functional programs.

Abstract Sketch is a popular program synthesis tool that solves for unknowns in a sketch or partial program. However, while Sketch is powerful, it does not directly support modular synthesis of dependencies, potentially limiting scalability. In this paper, we introduce Sketcham, a new technique that modularizes a regular sketch by automatically generating mocks—functions that approximate the behavior of complete implementations—from the sketch’s test suite. For example, if the function f originally calls g, Sketcham creates a mock $$g_m$$ g m from g’s tests and augments the sketch with a version of f that calls $$g_m$$ g m . This change allows the unknowns in f and g to be solved separately, enabling modular synthesis with no extra work from the Sketch user. We evaluated Sketcham on ten benchmarks, performing enough runs to show at a 95% confidence level that Sketcham improves median synthesis performance on six of our ten benchmarks by a factor of up to 5 $$\times $$ × compared to plain Sketch, including one benchmark that times out on Sketch, while exhibiting similar performance on the remaining four. Our results show that Sketcham can achieve modular synthesis by automatically generating mocks from tests.