src/Doc/Isar-Ref/ML_Tactic.thy

+theory ML_Tactic
+imports Base Main
+begin
+
+chapter {* ML tactic expressions *}
+
+text {*
+  Isar Proof methods closely resemble traditional tactics, when used
+  in unstructured sequences of @{command "apply"} commands.
+  Isabelle/Isar provides emulations for all major ML tactics of
+  classic Isabelle --- mostly for the sake of easy porting of existing
+  developments, as actual Isar proof texts would demand much less
+  diversity of proof methods.
+
+  Unlike tactic expressions in ML, Isar proof methods provide proper
+  concrete syntax for additional arguments, options, modifiers etc.
+  Thus a typical method text is usually more concise than the
+  corresponding ML tactic.  Furthermore, the Isar versions of classic
+  Isabelle tactics often cover several variant forms by a single
+  method with separate options to tune the behavior.  For example,
+  method @{method simp} replaces all of @{ML simp_tac}~/ @{ML
+  asm_simp_tac}~/ @{ML full_simp_tac}~/ @{ML asm_full_simp_tac}, there
+  is also concrete syntax for augmenting the Simplifier context (the
+  current ``simpset'') in a convenient way.
+*}
+
+
+section {* Resolution tactics *}
+
+text {*
+  Classic Isabelle provides several variant forms of tactics for
+  single-step rule applications (based on higher-order resolution).
+  The space of resolution tactics has the following main dimensions.
+
+  \begin{enumerate}
+
+  \item The ``mode'' of resolution: intro, elim, destruct, or forward
+  (e.g.\ @{ML resolve_tac}, @{ML eresolve_tac}, @{ML dresolve_tac},
+  @{ML forward_tac}).
+
+  \item Optional explicit instantiation (e.g.\ @{ML resolve_tac} vs.\
+  @{ML res_inst_tac}).
+
+  \item Abbreviations for singleton arguments (e.g.\ @{ML resolve_tac}
+  vs.\ @{ML rtac}).
+
+  \end{enumerate}
+
+  Basically, the set of Isar tactic emulations @{method rule_tac},
+  @{method erule_tac}, @{method drule_tac}, @{method frule_tac} (see
+  \secref{sec:tactics}) would be sufficient to cover the four modes,
+  either with or without instantiation, and either with single or
+  multiple arguments.  Although it is more convenient in most cases to
+  use the plain @{method_ref (Pure) rule} method, or any of its
+  ``improper'' variants @{method erule}, @{method drule}, @{method
+  frule}.  Note that explicit goal addressing is only supported by the
+  actual @{method rule_tac} version.
+
+  With this in mind, plain resolution tactics correspond to Isar
+  methods as follows.
+
+  \medskip
+  \begin{tabular}{lll}
+    @{ML rtac}~@{text "a 1"} & & @{text "rule a"} \\
+    @{ML resolve_tac}~@{text "[a\<^sub>1, \<dots>] 1"} & & @{text "rule a\<^sub>1 \<dots>"} \\
+    @{ML res_inst_tac}~@{text "ctxt [(x\<^sub>1, t\<^sub>1), \<dots>] a 1"} & &
+    @{text "rule_tac x\<^sub>1 = t\<^sub>1 \<AND> \<dots> \<IN> a"} \\[0.5ex]
+    @{ML rtac}~@{text "a i"} & & @{text "rule_tac [i] a"} \\
+    @{ML resolve_tac}~@{text "[a\<^sub>1, \<dots>] i"} & & @{text "rule_tac [i] a\<^sub>1 \<dots>"} \\
+    @{ML res_inst_tac}~@{text "ctxt [(x\<^sub>1, t\<^sub>1), \<dots>] a i"} & &
+    @{text "rule_tac [i] x\<^sub>1 = t\<^sub>1 \<AND> \<dots> \<IN> a"} \\
+  \end{tabular}
+  \medskip
+
+  Note that explicit goal addressing may be usually avoided by
+  changing the order of subgoals with @{command "defer"} or @{command
+  "prefer"} (see \secref{sec:tactic-commands}).
+*}
+
+
+section {* Simplifier tactics *}
+
+text {* The main Simplifier tactics @{ML simp_tac} and variants are
+  all covered by the @{method simp} and @{method simp_all} methods
+  (see \secref{sec:simplifier}).  Note that there is no individual
+  goal addressing available, simplification acts either on the first
+  goal (@{method simp}) or all goals (@{method simp_all}).
+
+  \medskip
+  \begin{tabular}{lll}
+    @{ML asm_full_simp_tac}~@{text "@{context} 1"} & & @{method simp} \\
+    @{ML ALLGOALS}~(@{ML asm_full_simp_tac}~@{text "@{context}"}) & & @{method simp_all} \\[0.5ex]
+    @{ML simp_tac}~@{text "@{context} 1"} & & @{method simp}~@{text "(no_asm)"} \\
+    @{ML asm_simp_tac}~@{text "@{context} 1"} & & @{method simp}~@{text "(no_asm_simp)"} \\
+    @{ML full_simp_tac}~@{text "@{context} 1"} & & @{method simp}~@{text "(no_asm_use)"} \\
+    @{ML asm_lr_simp_tac}~@{text "@{context} 1"} & & @{method simp}~@{text "(asm_lr)"} \\
+  \end{tabular}
+  \medskip
+*}
+
+
+section {* Classical Reasoner tactics *}
+
+text {* The Classical Reasoner provides a rather large number of
+  variations of automated tactics, such as @{ML blast_tac}, @{ML
+  fast_tac}, @{ML clarify_tac} etc.  The corresponding Isar methods
+  usually share the same base name, such as @{method blast}, @{method
+  fast}, @{method clarify} etc.\ (see \secref{sec:classical}).  *}
+
+
+section {* Miscellaneous tactics *}
+
+text {*
+  There are a few additional tactics defined in various theories of
+  Isabelle/HOL, some of these also in Isabelle/FOL or Isabelle/ZF.
+  The most common ones of these may be ported to Isar as follows.
+
+  \medskip
+  \begin{tabular}{lll}
+    @{ML stac}~@{text "a 1"} & & @{text "subst a"} \\
+    @{ML hyp_subst_tac}~@{text 1} & & @{text hypsubst} \\
+    @{ML split_all_tac}~@{text 1} & & @{text "simp (no_asm_simp) only: split_tupled_all"} \\
+      & @{text "\<approx>"} & @{text "simp only: split_tupled_all"} \\
+      & @{text "\<lless>"} & @{text "clarify"} \\
+  \end{tabular}
+*}
+
+
+section {* Tacticals *}
+
+text {*
+  Classic Isabelle provides a huge amount of tacticals for combination
+  and modification of existing tactics.  This has been greatly reduced
+  in Isar, providing the bare minimum of combinators only: ``@{text
+  ","}'' (sequential composition), ``@{text "|"}'' (alternative
+  choices), ``@{text "?"}'' (try), ``@{text "+"}'' (repeat at least
+  once).  These are usually sufficient in practice; if all fails,
+  arbitrary ML tactic code may be invoked via the @{method tactic}
+  method (see \secref{sec:tactics}).
+
+  \medskip Common ML tacticals may be expressed directly in Isar as
+  follows:
+
+  \medskip
+  \begin{tabular}{lll}
+    @{text "tac\<^sub>1"}~@{ML_text THEN}~@{text "tac\<^sub>2"} & & @{text "meth\<^sub>1, meth\<^sub>2"} \\
+    @{text "tac\<^sub>1"}~@{ML_text ORELSE}~@{text "tac\<^sub>2"} & & @{text "meth\<^sub>1 | meth\<^sub>2"} \\
+    @{ML TRY}~@{text tac} & & @{text "meth?"} \\
+    @{ML REPEAT1}~@{text tac} & & @{text "meth+"} \\
+    @{ML REPEAT}~@{text tac} & & @{text "(meth+)?"} \\
+    @{ML EVERY}~@{text "[tac\<^sub>1, \<dots>]"} & & @{text "meth\<^sub>1, \<dots>"} \\
+    @{ML FIRST}~@{text "[tac\<^sub>1, \<dots>]"} & & @{text "meth\<^sub>1 | \<dots>"} \\
+  \end{tabular}
+  \medskip
+
+  \medskip @{ML CHANGED} (see \cite{isabelle-implementation}) is
+  usually not required in Isar, since most basic proof methods already
+  fail unless there is an actual change in the goal state.
+  Nevertheless, ``@{text "?"}''  (try) may be used to accept
+  \emph{unchanged} results as well.
+
+  \medskip @{ML ALLGOALS}, @{ML SOMEGOAL} etc.\ (see
+  \cite{isabelle-implementation}) are not available in Isar, since
+  there is no direct goal addressing.  Nevertheless, some basic
+  methods address all goals internally, notably @{method simp_all}
+  (see \secref{sec:simplifier}).  Also note that @{ML ALLGOALS} can be
+  often replaced by ``@{text "+"}'' (repeat at least once), although
+  this usually has a different operational behavior: subgoals are
+  solved in a different order.
+
+  \medskip Iterated resolution, such as
+  @{ML_text "REPEAT (FIRSTGOAL (resolve_tac ...))"}, is usually better
+  expressed using the @{method intro} and @{method elim} methods of
+  Isar (see \secref{sec:classical}).
+*}
+
+end