The lexical and syntactic disparities among different programming languages (e.g., Java and Python) pose significant challenges for multi-language software engineering tasks such as cross-language code clone detection and code retrieval, since queries or code snippets written in one programming language often fail to match equivalent artifacts in another. To bridge this gap between different programming languages, we proposed a novel approach to construct a multi-language shared semantic space, in which functionally equivalent source code written in different programming languages are close to each other. In this approach, we first map the Abstract Syntax Tree (AST) node labels of the code snippets written in different programming languages into a unified label set, thus compressing high-dimensional language-specific tokens into a common embedding space. Then, we employ a Graph Matching Network (GMN) to encode the paired AST graphs into "semantic vectors" that capture functional equivalence between programming languages in a unified code vector space. In such a way, we can eliminate the differences in syntax between different programming languages. To validate the effectiveness of this approach, we apply it to two downstream tasks, including cross-language clone detection and cross-language code retrieval. Experiments demonstrate that our approach substantially outperforms the state-of-the-art baselines in cross-language clone detection, improving Precision from 95.62% to 99.94%, Recall from 97.72% to 99.92%, and F1 score from 96.94% to 99.93%. In terms of cross-language code retrieval, our approach raises the average Mean Reciprocal Rank (MRR) from 0.4909 to 0.5547, showing an absolute gain of 0.0638 (13% relative improvement), which demonstrates its superior ability to rank correct code snippets high across multiple programming languages.