This article presents a polymorphic modal type system and its principal type inference algorithm that conservatively extend ML by all of Lisp's staging constructs (the quasi-quotation system). The combination is meaningful because ML is a practical higher-order, impure, and typed language, while Lisp's quasi-quotation system has long evolved complying with the demands from multi-staged programming practices. Our type system supports open code, unrestricted operations on references, intentional variable-capturing substitution as well as capture-avoiding substitution, and lifting values into code, whose combination escaped all the previous systems.

When the compiler encounters an error symbol in an erroneous input, the local error-repair method repairs the input by either inserting a repair string before the error symbol or deleting the error symbol. Although the extended FMQ of Fischer et al. and the method of McKenzie et al. report the improved quality of diagnostic messages, they suffer from redundant parse stack configurations.This article proposes an efficient LR error-recovery method, with validation-removing repairs that give the same validation result as a previously considered, lower-cost repair. Moreover, its execution speed is proportional to the length of the stack configuration. The algorithm is implemented on a Bison, GNU LALR(1), parser generating system. Experimental results are presented.