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src/Doc/IsarRef/ML_Tactic.thy

author | wenzelm |

Sun, 04 Nov 2012 20:11:19 +0100 | |

changeset 50068 | 310e9b810bbf |

parent 48985 | 5386df44a037 |

child 51304 | 0e71a248cacb |

permissions | -rw-r--r-- |

tuned;

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 "@{simpset} 1"} & & @{method simp} \\ @{ML ALLGOALS}~(@{ML asm_full_simp_tac}~@{text "@{simpset}"}) & & @{method simp_all} \\[0.5ex] @{ML simp_tac}~@{text "@{simpset} 1"} & & @{method simp}~@{text "(no_asm)"} \\ @{ML asm_simp_tac}~@{text "@{simpset} 1"} & & @{method simp}~@{text "(no_asm_simp)"} \\ @{ML full_simp_tac}~@{text "@{simpset} 1"} & & @{method simp}~@{text "(no_asm_use)"} \\ @{ML asm_lr_simp_tac}~@{text "@{simpset} 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 strip_tac}~@{text 1} & @{text "\<approx>"} & @{text "intro strip"} \\ @{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