As compared to traditional cloud computing, edge computing provides computational, sensor, and storage resources co-located with client requests, thereby reducing network transmission and providing context-awareness. While server farms can allocate cloud computing resources on demand at runtime, edge-based heterogeneous devices, ranging from stationary servers to mobile, IoT, and energy harvesting devices are not nearly as reliable and abundant. As a result, edge application developers face the following obstacles: 1) heterogeneous devices provide hard-to-access resources, due to dissimilar capabilities, operating systems, execution platforms, and communication interfaces; 2) unreliable resources cause high failure rates, due to device mobility, low energy status, and other environmental factors; 3) resource scarcity hinders the performance; 4) the dissimilar and dynamic resources across edge environments make QoS impossible to guarantee. Edge environments are characterized by the prevalence of equivalent functionalities, which satisfy the same application requirements by different means. The thesis of this research is that equivalent functionalities can be exploited to improve the reliability, efficiency, and adaptiveness of edge-based services. To prove this thesis, this dissertation comprises three key interrelated research thrusts: 1) create a system architecture and programming support for providing edge services that run on heterogeneous and ever changing edge devices; 2) introduce programming abstractions for executing equivalent functionalities; 3) apply equivalent functionalities to improve the reliability, efficiency, and adaptiveness of edge services. We demonstrate how the connected devices with unreliable, dynamic, and scarce resources can automatically form a reliable, adaptive, and efficient execution environment for sensing, computing, and other non-trivial tasks. This dissertation is based on 5 conference papers, presented at ICDCS'20, ICWS'19, EDGE'19, CLOUD'18, and MobileSoft'18