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theory Syntax |
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imports Base |
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begin |
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chapter {* Concrete syntax and type-checking *} |
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text {* Pure @{text "\<lambda>"}-calculus as introduced in \chref{ch:logic} is |
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an adequate foundation for logical languages --- in the tradition of |
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\emph{higher-order abstract syntax} --- but end-users require |
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additional means for reading and printing of terms and types. This |
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important add-on outside the logical core is called \emph{inner |
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syntax} in Isabelle jargon, as opposed to the \emph{outer syntax} of |
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the theory and proof language (cf.\ \cite{isabelle-isar-ref}). |
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For example, according to \cite{church40} quantifiers are |
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represented as higher-order constants @{text "All :: ('a \<Rightarrow> bool) \<Rightarrow> |
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bool"} such that @{text "All (\<lambda>x::'a. B x)"} faithfully represents |
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the idea that is displayed as @{text "\<forall>x::'a. B x"} via @{keyword |
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"binder"} notation. Moreover, type-inference in the style of |
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Hindley-Milner \cite{hindleymilner} (and extensions) enables users |
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to write @{text "\<forall>x. B x"} concisely, when the type @{text "'a"} is |
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already clear from the context.\footnote{Type-inference taken to the |
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extreme can easily confuse users, though. Beginners often stumble |
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over unexpectedly general types inferred by the system.} |
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\medskip The main inner syntax operations are \emph{read} for |
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parsing together with type-checking, and \emph{pretty} for formatted |
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output. See also \secref{sec:read-print}. |
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Furthermore, the input and output syntax layers are sub-divided into |
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separate phases for \emph{concrete syntax} versus \emph{abstract |
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syntax}, see also \secref{sec:parse-unparse} and |
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\secref{sec:term-check}, respectively. This results in the |
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following decomposition of the main operations: |
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\begin{itemize} |
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\item @{text "read = parse; check"} |
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\item @{text "pretty = uncheck; unparse"} |
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\end{itemize} |
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Some specification package might thus intercept syntax processing at |
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a well-defined stage after @{text "parse"}, to a augment the |
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resulting pre-term before full type-reconstruction is performed by |
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@{text "check"}, for example. Note that the formal status of bound |
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variables, versus free variables, versus constants must not be |
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changed between these phases! |
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\medskip In general, @{text check} and @{text uncheck} operate |
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simultaneously on a list of terms. This is particular important for |
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type-checking, to reconstruct types for several terms of the same context |
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and scope. In contrast, @{text parse} and @{text unparse} operate separately |
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in single terms. |
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There are analogous operations to read and print types, with the same |
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sub-division into phases. |
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*} |
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section {* Reading and pretty printing \label{sec:read-print} *} |
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text {* Read and print operations are roughly dual to each other, such |
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that for the user @{text "s' = pretty (read s)"} looks similar to |
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the original source text @{text "s"}, but the details depend on many |
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side-conditions. There are also explicit options to control |
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suppressing of type information in the output. The default |
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configuration routinely looses information, so @{text "t' = read |
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(pretty t)"} might fail, or produce a differently typed term, or a |
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completely different term in the face of syntactic overloading! *} |
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text %mlref {* |
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\begin{mldecls} |
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@{index_ML Syntax.read_typs: "Proof.context -> string list -> typ list"} \\ |
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@{index_ML Syntax.read_terms: "Proof.context -> string list -> term list"} \\ |
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@{index_ML Syntax.read_props: "Proof.context -> string list -> term list"} \\[0.5ex] |
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@{index_ML Syntax.read_typ: "Proof.context -> string -> typ"} \\ |
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@{index_ML Syntax.read_term: "Proof.context -> string -> term"} \\ |
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@{index_ML Syntax.read_prop: "Proof.context -> string -> term"} \\[0.5ex] |
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@{index_ML Syntax.pretty_typ: "Proof.context -> typ -> Pretty.T"} \\ |
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@{index_ML Syntax.pretty_term: "Proof.context -> term -> Pretty.T"} \\ |
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@{index_ML Syntax.string_of_typ: "Proof.context -> typ -> string"} \\ |
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@{index_ML Syntax.string_of_term: "Proof.context -> term -> string"} \\ |
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\end{mldecls} |
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\begin{description} |
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\item @{ML Syntax.read_typs}~@{text "ctxt strs"} reads and checks a |
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simultaneous list of source strings as types of the logic. |
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\item @{ML Syntax.read_terms}~@{text "ctxt strs"} reads and checks a |
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simultaneous list of source strings as terms of the logic. |
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Type-reconstruction puts all parsed terms into the same scope. |
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If particular type-constraints are required for some of the arguments, the |
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read operations needs to be split into its parse and check phases, using |
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@{ML Type.constraint} on the intermediate pre-terms. |
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\item @{ML Syntax.read_props} ~@{text "ctxt strs"} reads and checks a |
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simultaneous list of source strings as propositions of the logic, with an |
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implicit type-constraint for each argument to make it of type @{typ prop}; |
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this also affects the inner syntax for parsing. The remaining |
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type-reconstructions works as for @{ML Syntax.read_terms} above. |
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\item @{ML Syntax.read_typ}, @{ML Syntax.read_term}, @{ML Syntax.read_prop} |
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are like the simultaneous versions above, but operate on a single argument |
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only. This convenient shorthand is adequate in situations where a single |
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item in its own scope is processed. Never use @{ML "map o Syntax.read_term"} |
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where @{ML Syntax.read_terms} is actually intended! |
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\item @{ML Syntax.pretty_typ}~@{text "ctxt T"} and @{ML |
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Syntax.pretty_term}~@{text "ctxt t"} uncheck and pretty-print the given type |
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or term, respectively. Although the uncheck phase acts on a simultaneous |
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list as well, this is rarely relevant in practice, so only the singleton |
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case is provided as combined pretty operation. Moreover, the distinction of |
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term vs.\ proposition is ignored here. |
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\item @{ML Syntax.string_of_typ} and @{ML Syntax.string_of_term} are |
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convenient compositions of @{ML Syntax.pretty_typ} and @{ML |
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Syntax.pretty_term} with @{ML Pretty.string_of} for output. The result may |
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be concatenated with other strings, as long as there is no further |
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formatting and line-breaking involved. |
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\end{description} |
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The most important operations in practice are @{ML Syntax.read_term}, @{ML |
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Syntax.read_prop}, and @{ML Syntax.string_of_term}. |
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\medskip Note that the string values that are passed in and out here are |
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actually annotated by the system, to carry further markup that is relevant |
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for the Prover IDE \cite{isabelle-jedit}. User code should neither compose |
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its own strings for input, nor try to analyze the string for output. |
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The standard way to provide the required position markup for input works via |
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the outer syntax parser wrapper @{ML Parse.inner_syntax}, which is already |
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part of @{ML Parse.typ}, @{ML Parse.term}, @{ML Parse.prop}. So a string |
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obtained from one of the latter may be directly passed to the corresponding |
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read operation, in order to get PIDE markup of the input and precise |
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positions for warnings and errors. |
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*} |
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section {* Parsing and unparsing \label{sec:parse-unparse} *} |
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text {* Parsing and unparsing converts between actual source text and |
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a certain \emph{pre-term} format, where all bindings and scopes are |
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resolved faithfully. Thus the names of free variables or constants |
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are already determined in the sense of the logical context, but type |
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information might be still missing. Pre-terms support an explicit |
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language of \emph{type constraints} that may be augmented by user |
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code to guide the later \emph{check} phase. |
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Actual parsing is based on traditional lexical analysis and Earley |
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parsing for arbitrary context-free grammars. The user can specify |
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the grammar via mixfix annotations. Moreover, there are \emph{syntax |
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translations} that can be augmented by the user, either |
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declaratively via @{command translations} or programmatically via |
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@{command parse_translation}, @{command print_translation} etc. The |
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final scope resolution is performed by the system, according to name |
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spaces for types, term variables and constants etc.\ determined by |
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the context. |
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*} |
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text %mlref {* |
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\begin{mldecls} |
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@{index_ML Syntax.parse_typ: "Proof.context -> string -> typ"} \\ |
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@{index_ML Syntax.parse_term: "Proof.context -> string -> term"} \\ |
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@{index_ML Syntax.parse_prop: "Proof.context -> string -> term"} \\ |
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@{index_ML Syntax.unparse_typ: "Proof.context -> typ -> Pretty.T"} \\ |
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@{index_ML Syntax.unparse_term: "Proof.context -> term -> Pretty.T"} \\ |
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\end{mldecls} |
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%FIXME description |
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*} |
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section {* Checking and unchecking \label{sec:term-check} *} |
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text {* These operations define the transition from pre-terms and |
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fully-annotated terms in the sense of the logical core |
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(\chref{ch:logic}). |
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The \emph{check} phase is meant to subsume a variety of mechanisms |
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in the manner of ``type-inference'' or ``type-reconstruction'' or |
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``type-improvement'', not just type-checking in the narrow sense. |
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The \emph{uncheck} phase is roughly dual, it prunes type-information |
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before pretty printing. |
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A typical add-on for the check/uncheck syntax layer is the @{command |
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abbreviation} mechanism. Here the user specifies syntactic |
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definitions that are managed by the system as polymorphic @{text |
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"let"} bindings. These are expanded during the @{text "check"} |
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phase, and contracted during the @{text "uncheck"} phase, without |
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affecting the type-assignment of the given terms. |
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\medskip The precise meaning of type checking depends on the context |
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--- additional check/uncheck plugins might be defined in user space. |
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For example, the @{command class} command defines a context where |
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@{text "check"} treats certain type instances of overloaded |
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constants according to the ``dictionary construction'' of its |
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logical foundation. This involves ``type improvement'' |
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(specialization of slightly too general types) and replacement by |
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certain locale parameters. See also \cite{Haftmann-Wenzel:2009}. |
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*} |
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text %mlref {* |
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\begin{mldecls} |
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@{index_ML Syntax.check_typs: "Proof.context -> typ list -> typ list"} \\ |
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@{index_ML Syntax.check_terms: "Proof.context -> term list -> term list"} \\ |
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@{index_ML Syntax.check_props: "Proof.context -> term list -> term list"} \\ |
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@{index_ML Syntax.uncheck_typs: "Proof.context -> typ list -> typ list"} \\ |
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@{index_ML Syntax.uncheck_terms: "Proof.context -> term list -> term list"} \\ |
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\end{mldecls} |
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%FIXME description |
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*} |
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end |