We present a new pure functional language and type system with borrows with lifetimes, and a corresponding fully-automatic type inference procedure. Inference provides users the performance benefits of borrows with lifetimes without requiring user annotation. If the user's program cannot be typed, inference inserts a handful of reference count operations so that it can be typed. We provide a heap semantics for our borrowing language and prove a soundness theorem, guaranteeing that well-typed programs do not violate memory safety. We implement our memory management strategy as part of the Morphic language stack and compare it to Perceus, a state-of-the-art reference-counting technique based on linear type inference. We find that our system is able to eliminate almost all reference count operations across a range of programs, reducing reference count increments by 75-100% on all benchmarks with reference count increments under the baseline. As a result, we achieve a 1.48x geomean speedup overall on all benchmarks.

Higher-order functions pose a challenge for both static program analyses and optimizing compilers. To simplify the analysis and compilation of languages with higher-order functions, a rich body of prior work has proposed a variety of defunctionalization techniques, which can eliminate higher-order functions from a program by transforming the program to a semantically-equivalent first-order representation. Several modern languages take this a step further, specializing higher-order functions with respect to the functions on which they operate, and in turn allowing compilers to generate more efficient code. However, existing specializing defunctionalization techniques restrict how function values may be used, forcing implementations to fall back on costly dynamic alternatives. We propose lambda set specialization (LSS), the first specializing defunctionalization technique which imposes no restrictions on how function values may be used. We formulate LSS in terms of a polymorphic type system which tracks the flow of function values through the program, and use this type system to recast specialization of higher-order functions with respect to their arguments as a form of type monomorphization. We show that our type system admits a simple and tractable type inference algorithm, and give a formalization and fully-mechanized proof in the Isabelle/HOL proof assistant showing soundness and completeness of the type inference algorithm with respect to the type system. To show the benefits of LSS, we evaluate its impact on the run time performance of code generated by the MLton compiler for Standard ML, the OCaml compiler, and the new Morphic functional programming language. We find that pre-processing with LSS achieves run time speedups of up to 6.85x under MLton, 3.45x for OCaml, and 78.93x for Morphic.