9c8a63caec
see issue #500 Remark: this tactic also applies no_confusion to take care of a contradiction
112 lines
5 KiB
Text
112 lines
5 KiB
Text
/-
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Copyright (c) 2014 Microsoft Corporation. All rights reserved.
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Released under Apache 2.0 license as described in the file LICENSE.
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Module: init.tactic
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Author: Leonardo de Moura
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This is just a trick to embed the 'tactic language' as a Lean
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expression. We should view 'tactic' as automation that when execute
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produces a term. tactic.builtin is just a "dummy" for creating the
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definitions that are actually implemented in C++
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-/
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prelude
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import init.datatypes init.reserved_notation init.num
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inductive tactic :
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Type := builtin : tactic
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namespace tactic
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-- Remark the following names are not arbitrary, the tactic module
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-- uses them when converting Lean expressions into actual tactic objects.
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-- The bultin 'by' construct triggers the process of converting a
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-- a term of type 'tactic' into a tactic that sythesizes a term
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opaque definition and_then (t1 t2 : tactic) : tactic := builtin
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opaque definition or_else (t1 t2 : tactic) : tactic := builtin
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opaque definition append (t1 t2 : tactic) : tactic := builtin
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opaque definition interleave (t1 t2 : tactic) : tactic := builtin
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opaque definition par (t1 t2 : tactic) : tactic := builtin
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opaque definition fixpoint (f : tactic → tactic) : tactic := builtin
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opaque definition repeat (t : tactic) : tactic := builtin
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opaque definition at_most (t : tactic) (k : num) : tactic := builtin
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opaque definition discard (t : tactic) (k : num) : tactic := builtin
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opaque definition focus_at (t : tactic) (i : num) : tactic := builtin
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opaque definition try_for (t : tactic) (ms : num) : tactic := builtin
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opaque definition all_goals (t : tactic) : tactic := builtin
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opaque definition now : tactic := builtin
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opaque definition assumption : tactic := builtin
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opaque definition eassumption : tactic := builtin
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opaque definition state : tactic := builtin
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opaque definition fail : tactic := builtin
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opaque definition id : tactic := builtin
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opaque definition beta : tactic := builtin
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opaque definition info : tactic := builtin
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opaque definition whnf : tactic := builtin
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opaque definition contradiction : tactic := builtin
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opaque definition rotate_left (k : num) := builtin
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opaque definition rotate_right (k : num) := builtin
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definition rotate (k : num) := rotate_left k
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-- This is just a trick to embed expressions into tactics.
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-- The nested expressions are "raw". They tactic should
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-- elaborate them when it is executed.
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inductive expr : Type :=
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builtin : expr
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inductive expr_list : Type :=
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| nil : expr_list
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| cons : expr → expr_list → expr_list
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-- auxiliary type used to mark optional list of arguments
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definition opt_expr_list := expr_list
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-- auxiliary types used to mark that the expression (list) is an identifier (list)
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definition identifier := expr
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definition identifier_list := expr_list
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definition opt_identifier_list := expr_list
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opaque definition apply (e : expr) : tactic := builtin
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opaque definition fapply (e : expr) : tactic := builtin
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opaque definition rename (a b : identifier) : tactic := builtin
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opaque definition intro (e : identifier_list) : tactic := builtin
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opaque definition generalize_tac (e : expr) (id : identifier) : tactic := builtin
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opaque definition clear (e : identifier_list) : tactic := builtin
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opaque definition revert (e : identifier_list) : tactic := builtin
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opaque definition refine (e : expr) : tactic := builtin
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opaque definition exact (e : expr) : tactic := builtin
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-- Relaxed version of exact that does not enforce goal type
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opaque definition rexact (e : expr) : tactic := builtin
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opaque definition check_expr (e : expr) : tactic := builtin
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opaque definition trace (s : string) : tactic := builtin
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-- rewrite_tac is just a marker for the builtin 'rewrite' notation
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-- used to create instances of this tactic.
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opaque definition rewrite_tac (e : expr_list) : tactic := builtin
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opaque definition cases (id : identifier) (ids : opt_identifier_list) : tactic := builtin
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opaque definition intros (ids : opt_identifier_list) : tactic := builtin
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opaque definition generalizes (es : expr_list) : tactic := builtin
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opaque definition clears (ids : identifier_list) : tactic := builtin
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opaque definition reverts (ids : identifier_list) : tactic := builtin
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opaque definition change (e : expr) : tactic := builtin
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opaque definition assert_hypothesis (id : identifier) (e : expr) : tactic := builtin
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opaque definition lettac (id : identifier) (e : expr) : tactic := builtin
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definition try (t : tactic) : tactic := or_else t id
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definition repeat1 (t : tactic) : tactic := and_then t (repeat t)
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definition focus (t : tactic) : tactic := focus_at t 0
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definition determ (t : tactic) : tactic := at_most t 1
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definition trivial : tactic := or_else (apply eq.refl) assumption
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definition do (n : num) (t : tactic) : tactic :=
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nat.rec id (λn t', and_then t t') (nat.of_num n)
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end tactic
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tactic_infixl `;`:15 := tactic.and_then
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tactic_notation `(` h `|` r:(foldl `|` (e r, tactic.or_else r e) h) `)` := r
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