lean2/library/init/tactic.lean

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2014-12-01 04:34:12 +00:00
/-
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
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
opaque definition and_then (t1 t2 : tactic) : tactic := builtin
opaque definition or_else (t1 t2 : tactic) : tactic := builtin
opaque definition append (t1 t2 : tactic) : tactic := builtin
opaque definition interleave (t1 t2 : tactic) : tactic := builtin
opaque definition par (t1 t2 : tactic) : tactic := builtin
opaque definition fixpoint (f : tactic → tactic) : tactic := builtin
opaque definition repeat (t : tactic) : tactic := builtin
opaque definition at_most (t : tactic) (k : num) : tactic := builtin
opaque definition discard (t : tactic) (k : num) : tactic := builtin
opaque definition focus_at (t : tactic) (i : num) : tactic := builtin
opaque definition try_for (t : tactic) (ms : num) : tactic := builtin
opaque definition now : tactic := builtin
opaque definition assumption : tactic := builtin
opaque definition eassumption : tactic := builtin
opaque definition state : tactic := builtin
opaque definition fail : tactic := builtin
opaque definition id : tactic := builtin
opaque definition beta : tactic := builtin
opaque definition info : tactic := builtin
opaque definition whnf : tactic := builtin
opaque definition rotate_left (k : num) := builtin
opaque definition rotate_right (k : num) := builtin
definition rotate (k : num) := rotate_left k
-- 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
opaque definition apply (e : expr) : tactic := builtin
opaque definition rapply (e : expr) : tactic := builtin
opaque definition fapply (e : expr) : tactic := builtin
opaque definition rename (a b : expr) : tactic := builtin
opaque definition intro (e : expr) : tactic := builtin
opaque definition generalize (e : expr) : tactic := builtin
opaque definition clear (e : expr) : tactic := builtin
opaque definition revert (e : expr) : tactic := builtin
opaque definition unfold (e : expr) : tactic := builtin
opaque definition exact (e : expr) : tactic := builtin
opaque definition trace (s : string) : tactic := builtin
opaque definition inversion (id : expr) : tactic := builtin
notation a `↦` b:max := rename a b
inductive expr_list : Type :=
nil : expr_list,
cons : expr → expr_list → expr_list
opaque definition inversion_with (id : expr) (ids : expr_list) : tactic := builtin
notation `cases` a:max := inversion a
notation `cases` a:max `with` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := inversion_with a l
opaque definition intro_lst (ids : expr_list) : tactic := builtin
notation `intros` := intro_lst expr_list.nil
notation `intros` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := intro_lst l
opaque definition generalize_lst (es : expr_list) : tactic := builtin
notation `generalizes` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := generalize_lst l
opaque definition clear_lst (ids : expr_list) : tactic := builtin
notation `clears` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := clear_lst l
opaque definition revert_lst (ids : expr_list) : tactic := builtin
notation `reverts` `(` l:(foldr `,` (h t, expr_list.cons h t) expr_list.nil) `)` := revert_lst l
opaque definition assert_hypothesis (id : expr) (e : expr) : tactic := builtin
notation `assert` `(` id `:` ty `)` := assert_hypothesis id ty
infixl `;`:15 := and_then
notation `[` h:10 `|`:10 r:(foldl:10 `|` (e r, or_else r e) h) `]` := r
definition try (t : tactic) : tactic := [t | id]
definition repeat1 (t : tactic) : tactic := t ; repeat t
definition focus (t : tactic) : tactic := focus_at t 0
definition determ (t : tactic) : tactic := at_most t 1
end tactic