Constructing Canonical LR(1) & LALR Parsing Tables

Lecture 27 of CS606 Compiler Construction synthesizes LR state machines into executable parsing tables: Canonical LR(1) and Lookahead LR (LALR). An LR parsing table consists of two components: the ACTION table, indexed by state and terminal symbol (containing shift s_i, reduce r_j, accept acc, or error blank), and the GOTO table, indexed by state and non-terminal symbol. The lecture details how items with the dot at the end [A -> gamma ., a] populate reduce actions strictly under lookahead column a. While Canonical LR(1) tables are extremely powerful and free of conflict bugs, they suffer from explosive table size (often thousands of states). Students study LALR(1) parsing, which merges states that share identical LR(0) cores (differing only in lookaheads). The lecture proves that merging cores never introduces shift-reduce conflicts, though it can occasionally produce reduce-reduce conflicts on flawed grammars. Consistent evaluation of grammatical derivations, item closure sets, and shift-reduce actions ensures robust preparation for academic assessments. Students investigate the role of intermediate representations in decoupling front-end language syntax from target machine instruction architectures. The discussion highlights how syntax-directed definitions associate computable semantic attributes with context-free production rules. Key concepts such as viable prefixes, handle pruning, and parser stack configurations are analyzed to understand deterministic bottom-up parsing. The lecture details algorithmic subset construction and Hopcroft state minimization to produce space-efficient deterministic finite automata. Control flow graph analysis is demonstrated to partition linear three-address instruction sequences into maximal basic blocks. Directed acyclic graph representations provide deterministic frameworks for common subexpression elimination and local code optimization. Data flow equations and backward liveness analysis are formulated to determine the exact variable live ranges required for optimal register allocation. Automated compiler generation utilities such as Lex and YACC are presented as indispensable instruments for industrial language processing. Top-down and bottom-up parsing techniques are contrasted regarding grammatical expressive power, lookahead requirements, and implementation complexity. Shift-reduce and reduce-reduce grammatical conflicts are analyzed alongside operator precedence declarations to eliminate parsing ambiguities.