/- Copyright (c) 2014 Microsoft Corporation. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Author: Leonardo de Moura This is just a trick to embed the 'tactic language' as a Lean expression. We should view 'tactic' as automation that when execute produces a term. tactic.builtin is just a "dummy" for creating the definitions that are actually implemented in C++ -/ prelude import init.datatypes init.reserved_notation init.num inductive tactic : Type := builtin : tactic namespace tactic -- Remark the following names are not arbitrary, the tactic module -- uses them when converting Lean expressions into actual tactic objects. -- The bultin 'by' construct triggers the process of converting a -- a term of type 'tactic' into a tactic that sythesizes a term definition and_then (t1 t2 : tactic) : tactic := builtin definition or_else (t1 t2 : tactic) : tactic := builtin definition append (t1 t2 : tactic) : tactic := builtin definition interleave (t1 t2 : tactic) : tactic := builtin definition par (t1 t2 : tactic) : tactic := builtin definition fixpoint (f : tactic → tactic) : tactic := builtin definition repeat (t : tactic) : tactic := builtin definition at_most (t : tactic) (k : num) : tactic := builtin definition discard (t : tactic) (k : num) : tactic := builtin definition focus_at (t : tactic) (i : num) : tactic := builtin definition try_for (t : tactic) (ms : num) : tactic := builtin definition all_goals (t : tactic) : tactic := builtin definition now : tactic := builtin definition assumption : tactic := builtin definition eassumption : tactic := builtin definition state : tactic := builtin definition fail : tactic := builtin definition id : tactic := builtin definition beta : tactic := builtin definition info : tactic := builtin definition whnf : tactic := builtin definition contradiction : tactic := builtin definition exfalso : tactic := builtin definition congruence : tactic := builtin definition rotate_left (k : num) := builtin definition rotate_right (k : num) := builtin definition rotate (k : num) := rotate_left k definition norm_num : tactic := builtin -- This is just a trick to embed expressions into tactics. -- The nested expressions are "raw". They tactic should -- elaborate them when it is executed. inductive expr : Type := builtin : expr inductive expr_list : Type := | nil : expr_list | cons : expr → expr_list → expr_list -- auxiliary type used to mark optional list of arguments definition opt_expr_list := expr_list -- auxiliary types used to mark that the expression is suppose to be an identifier, optional, or a list. definition identifier := expr definition identifier_list := expr_list definition opt_identifier_list := expr_list -- Marker for instructing the parser to parse it as '?(using )' definition using_expr := expr -- Constant used to denote the case were no expression was provided definition none_expr : expr := expr.builtin definition apply (e : expr) : tactic := builtin definition eapply (e : expr) : tactic := builtin definition fapply (e : expr) : tactic := builtin definition rename (a b : identifier) : tactic := builtin definition intro (e : identifier_list) : tactic := builtin definition generalize_tac (e : expr) (id : identifier) : tactic := builtin definition clear (e : identifier_list) : tactic := builtin definition revert (e : identifier_list) : tactic := builtin definition refine (e : expr) : tactic := builtin definition exact (e : expr) : tactic := builtin -- Relaxed version of exact that does not enforce goal type definition rexact (e : expr) : tactic := builtin definition check_expr (e : expr) : tactic := builtin definition trace (s : string) : tactic := builtin -- rewrite_tac is just a marker for the builtin 'rewrite' notation -- used to create instances of this tactic. definition rewrite_tac (e : expr_list) : tactic := builtin definition xrewrite_tac (e : expr_list) : tactic := builtin definition krewrite_tac (e : expr_list) : tactic := builtin -- simp_tac is just a marker for the builtin 'simp' notation -- used to create instances of this tactic. -- Arguments: -- - e : additional rewrites to be considered -- - n : add rewrites from the give namespaces -- - x : exclude the give global rewrites -- - t : tactic for discharging conditions -- - l : location definition simp_tac (e : expr_list) (n : identifier_list) (x : identifier_list) (t : option tactic) (l : expr) : tactic := builtin -- Arguments: -- - ls : lemmas to be used (if not provided, then blast will choose them) -- - ds : definitions that can be unfolded (if not provided, then blast will choose them) definition blast (ls : opt_identifier_list) (ds : opt_identifier_list) : tactic := builtin -- with_options_tac is just a marker for the builtin 'with_options' notation definition with_options_tac (o : expr) (t : tactic) : tactic := builtin definition simp : tactic := #tactic with_options [blast.strategy "simp"] blast definition simp_nohyps : tactic := #tactic with_options [blast.strategy "simp_nohyps"] blast definition cases (h : expr) (ids : opt_identifier_list) : tactic := builtin definition induction (h : expr) (rec : using_expr) (ids : opt_identifier_list) : tactic := builtin definition intros (ids : opt_identifier_list) : tactic := builtin definition generalizes (es : expr_list) : tactic := builtin definition clears (ids : identifier_list) : tactic := builtin definition reverts (ids : identifier_list) : tactic := builtin definition change (e : expr) : tactic := builtin definition assert_hypothesis (id : identifier) (e : expr) : tactic := builtin definition lettac (id : identifier) (e : expr) : tactic := builtin definition constructor (k : option num) : tactic := builtin definition fconstructor (k : option num) : tactic := builtin definition existsi (e : expr) : tactic := builtin definition split : tactic := builtin definition left : tactic := builtin definition right : tactic := builtin definition injection (e : expr) (ids : opt_identifier_list) : tactic := builtin definition subst (ids : identifier_list) : tactic := builtin definition substvars : tactic := builtin definition reflexivity : tactic := builtin definition symmetry : tactic := builtin definition transitivity (e : expr) : tactic := builtin definition try (t : tactic) : tactic := or_else t id definition repeat1 (t : tactic) : tactic := and_then t (repeat t) definition focus (t : tactic) : tactic := focus_at t 0 definition determ (t : tactic) : tactic := at_most t 1 definition trivial : tactic := or_else (or_else (apply eq.refl) (apply true.intro)) assumption definition do (n : num) (t : tactic) : tactic := nat.rec id (λn t', and_then t t') (nat.of_num n) end tactic tactic_infixl `;`:15 := tactic.and_then tactic_notation T1 `:`:15 T2 := tactic.focus (tactic.and_then T1 (tactic.all_goals T2)) tactic_notation `(` h `|` r:(foldl `|` (e r, tactic.or_else r e) h) `)` := r