A strategy for parsing sentences of a context-free grammar that attempts to construct a parse tree beginning at the leaf nodes and working “bottom-up” toward the root.
Bottom-up (or shift-reduce) parsers work by “shifting” symbols onto a stack until the top of the stack contains a right-hand side of a production. The stack is then “reduced” by replacing the production's right-hand side by its left-hand side. This process continues until the string has been “reduced” to the start symbol of the grammar.
The string of symbols to be replaced at each stage is called a handle. Bottom-up parsers that proceed from left to right in the input string must always replace the leftmost handle and, in so doing, they effectively construct a rightmost derivation sequence in reverse order. For example, a rightmost derivation of the string abcde might beS ⇒ ACD ⇒ ACde ⇒ Acde ⇒ abcde A bottom-up parser would construct this derivation in reverse, first reducing abcde to Acde, then to ACde, then to ACD, and finally to the start symbol S. The handle at each stage is respectively ab, c, de, and ACD.
S ⇒ ACD ⇒ ACde ⇒
Acde ⇒ abcde
See also LR parsing, precedence parsing.