Learning language of protein sequences, which captures non-local interactions between amino acids close in the spatial structure, is a long-standing bioinformatics challenge, which requires at least context-free grammars. However, complex character of protein interactions impedes unsupervised learning of context-free grammars. Using structural information to constrain the syntactic trees proved effective in learning probabilistic natural and RNA languages. In this work, we establish a framework for learning probabilistic context-free grammars for protein sequences from syntactic trees partially constrained using amino acid contacts obtained from wet experiments or computational predictions, whose reliability has substantially increased recently. Within the framework, we implement the maximum-likelihood and contrastive estimators of parameters for simple yet practical grammars. Tested on samples of protein motifs, grammars developed within the framework showed improved precision in recognition and higher fidelity to protein structures. The framework is applicable to other biomolecular languages and beyond wherever knowledge of non-local dependencies is available.