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The monoid comprehension calculus

We are now in a position to propose a programming calculus using monoid comprehensions. Figure 1 defines an abstract grammar for an expression e of the Monoid Comprehension Calculus and amounts to adding comprehensions to an extended Typed Polymorphic $\lambda $-Calculus. Figure 2 gives the typing rules for this calculus.


  
Figure 1: The monoid comprehension calculus
\begin{figure}\begin{center} \fbox{$\begin{array}{rrll} e & ::= & \bot & \mbox{n... ...]\;Q\}} & \mbox{monoid comprehension} \\ \end{array}$ }\end{center}\end{figure}


  
Figure 2: Typing rules for the Monoid Comprehension Calculus
\begin{figure}\begin{center} \fbox{\begin{tabular}{rl} \par $\displaystyle\frac{... ...lus\{e_1\;[\!]\;e_2,Q\}} : \tau}$ & \par \end{tabular}}\end{center}\end{figure}


Hassan Ait-Kaci
2001-10-22