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| author | Adam Chlipala <adamc@hcoop.net> |
|---|---|
| date | Tue, 09 Dec 2008 14:43:43 -0500 |
| parents | 5d494183ca89 |
| children | af0df56ecc2c |
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| 559:5d494183ca89 | 560:d42431608856 |
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| 1007 | 1007 |
| 1008 The Ur/Web compiler uses \emph{heuristic type inference}, with no claims of completeness with respect to the declarative specification of the last section. The rules in use seem to work well in practice. This section summarizes those rules, to help Ur programmers predict what will work and what won't. | 1008 The Ur/Web compiler uses \emph{heuristic type inference}, with no claims of completeness with respect to the declarative specification of the last section. The rules in use seem to work well in practice. This section summarizes those rules, to help Ur programmers predict what will work and what won't. |
| 1009 | 1009 |
| 1010 \subsection{Basic Unification} | 1010 \subsection{Basic Unification} |
| 1011 | 1011 |
| 1012 Type-checkers for languages based on the Hindly-Milner type discipline, like ML and Haskell, take advantage of \emph{principal typing} properties, making complete type inference relatively straightforward. Inference algorithms are traditionally implemented using type unification variables, at various points asserting equalities between types, in the process discovering the values of type variables. The Ur/Web compiler uses the same basic strategy, but the complexity of the type system rules out easy completeness. | 1012 Type-checkers for languages based on the Hindley-Milner type discipline, like ML and Haskell, take advantage of \emph{principal typing} properties, making complete type inference relatively straightforward. Inference algorithms are traditionally implemented using type unification variables, at various points asserting equalities between types, in the process discovering the values of type variables. The Ur/Web compiler uses the same basic strategy, but the complexity of the type system rules out easy completeness. |
| 1013 | 1013 |
| 1014 Type-checking can require evaluating recursive functional programs, thanks to the type-level $\mt{fold}$ operator. When a unification variable appears in such a type, the next step of computation can be undetermined. The value of that variable might be determined later, but this would be ``too late'' for the unification problems generated at the first occurrence. This is the essential source of incompletness. | 1014 Type-checking can require evaluating recursive functional programs, thanks to the type-level $\mt{fold}$ operator. When a unification variable appears in such a type, the next step of computation can be undetermined. The value of that variable might be determined later, but this would be ``too late'' for the unification problems generated at the first occurrence. This is the essential source of incompleteness. |
| 1015 | 1015 |
| 1016 Nonetheless, the unification engine tends to do reasonably well. Unlike in ML, polymorphism is never inferred in definitions; it must be indicated explicitly by writing out constructor-level parameters. By writing these and other annotations, the programmer can generally get the type inference engine to do most of the type reconstruction work. | 1016 Nonetheless, the unification engine tends to do reasonably well. Unlike in ML, polymorphism is never inferred in definitions; it must be indicated explicitly by writing out constructor-level parameters. By writing these and other annotations, the programmer can generally get the type inference engine to do most of the type reconstruction work. |
| 1017 | 1017 |
| 1018 \subsection{Unifying Record Types} | 1018 \subsection{Unifying Record Types} |
| 1019 | 1019 |
| 1153 \hspace{.3in} [\mt{nm} = \mt{fields}.1 \rc \mt{fields}.2] \rc \mt{acc}) \; [] \; \mt{keep\_drop}) \\ | 1153 \hspace{.3in} [\mt{nm} = \mt{fields}.1 \rc \mt{fields}.2] \rc \mt{acc}) \; [] \; \mt{keep\_drop}) \\ |
| 1154 \hspace{.2in} (\mt{fold} \; (\lambda \mt{nm} \; (\mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\})) \; \mt{acc} \; [[\mt{nm}] \sim \mt{acc}] \Rightarrow [\mt{nm} = \mt{fields}.1] \rc \mt{acc}) \; [] \; \mt{keep\_drop}) \\ | 1154 \hspace{.2in} (\mt{fold} \; (\lambda \mt{nm} \; (\mt{fields} :: (\{\mt{Type}\} \times \{\mt{Type}\})) \; \mt{acc} \; [[\mt{nm}] \sim \mt{acc}] \Rightarrow [\mt{nm} = \mt{fields}.1] \rc \mt{acc}) \; [] \; \mt{keep\_drop}) \\ |
| 1155 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables} | 1155 \mt{val} \; \mt{sql\_subset\_all} : \mt{tables} :: \{\{\mt{Type}\}\} \to \mt{sql\_subset} \; \mt{tables} \; \mt{tables} |
| 1156 \end{array}$$ | 1156 \end{array}$$ |
| 1157 | 1157 |
| 1158 SQL expressions are used in several places, including $\mt{SELECT}$, $\mt{WHERE}$, $\mt{HAVING}$, and $\mt{ORDER} \; \mt{BY}$ clauses. They reify a fragment of the standard SQL expression language, while making it possible to inject ``native'' Ur values in some places. The arguments to the $\mt{sql\_exp}$ type family respectively give the unrestricted-availablity table fields, the table fields that may only be used in arguments to aggregate functions, the available selected expressions, and the type of the expression. | 1158 SQL expressions are used in several places, including $\mt{SELECT}$, $\mt{WHERE}$, $\mt{HAVING}$, and $\mt{ORDER} \; \mt{BY}$ clauses. They reify a fragment of the standard SQL expression language, while making it possible to inject ``native'' Ur values in some places. The arguments to the $\mt{sql\_exp}$ type family respectively give the unrestricted-availability table fields, the table fields that may only be used in arguments to aggregate functions, the available selected expressions, and the type of the expression. |
| 1159 $$\begin{array}{l} | 1159 $$\begin{array}{l} |
| 1160 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} | 1160 \mt{con} \; \mt{sql\_exp} :: \{\{\mt{Type}\}\} \to \{\{\mt{Type}\}\} \to \{\mt{Type}\} \to \mt{Type} \to \mt{Type} |
| 1161 \end{array}$$ | 1161 \end{array}$$ |
| 1162 | 1162 |
| 1163 Any field in scope may be converted to an expression. | 1163 Any field in scope may be converted to an expression. |