# Local Refinement Typing

## TL;DR

The paper presents Fusion, an SMT-based local refinement type inference algorithm that efficiently verifies programs with polymorphic and higher-order functions, reducing false alarms and improving speed.

## Contribution

Fusion introduces a concise, SMT-based approach for local refinement type inference that synthesizes the most precise types for program verification.

## Key findings

- Fusion checks benchmarks with half as many templates as before
- Fusion is 10-50x faster on theorem proving benchmarks
- Fusion avoids false alarms by synthesizing precise types

## Abstract

We introduce the Fusion algorithm for local refinement type inference, yielding a new SMT-based method for verifying programs with polymorphic data types and higher-order functions. Fusion is concise as the programmer need only write signatures for (externally exported) top-level functions and places with cyclic (recursive) dependencies, after which Fusion can predictably synthesize the most precise refinement types for all intermediate terms (expressible in the decidable refinement logic), thereby checking the program without false alarms. We have implemented Fusion and evaluated it on the benchmarks from the LiquidHaskell suite totalling about 12KLOC. Fusion checks an existing safety benchmark suite using about half as many templates as previously required and nearly 2x faster. In a new set of theorem proving benchmarks Fusion is both 10 - 50x faster and, by synthesizing the most precise types, avoids false alarms to make verification possible.