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Diffstat (limited to 'doc')
| -rw-r--r-- | doc/sphinx/proof-engine/ssreflect-proof-language.rst | 115 |
1 files changed, 96 insertions, 19 deletions
diff --git a/doc/sphinx/proof-engine/ssreflect-proof-language.rst b/doc/sphinx/proof-engine/ssreflect-proof-language.rst index b664eb4ec5..bffbe3e284 100644 --- a/doc/sphinx/proof-engine/ssreflect-proof-language.rst +++ b/doc/sphinx/proof-engine/ssreflect-proof-language.rst @@ -1550,20 +1550,26 @@ whose general syntax is :undocumented: .. prodn:: - i_item ::= @i_pattern %| @s_item %| @clear_switch %| {? %{%} } /@term + i_item ::= @i_pattern %| @s_item %| @clear_switch %| @i_view %| @i_block .. prodn:: s_item ::= /= %| // %| //= .. prodn:: - i_pattern ::= @ident %| _ %| ? %| * %| {? @occ_switch } -> %| {? @occ_switch }<- %| [ {?| @i_item } ] %| - %| [: {+ @ident } ] + i_view ::= {? %{%} } /@term %| /ltac:( @tactic ) -The ``=>`` tactical first executes tactic, then the :token:`i_item` s, +.. prodn:: + i_pattern ::= @ident %| > @ident %| _ %| ? %| * %| + %| {? @occ_switch } -> %| {? @occ_switch }<- %| [ {?| @i_item } ] %| - %| [: {+ @ident } ] + +.. prodn:: + i_block ::= [^ @ident ] %| [^~ @ident ] %| [^~ @num ] + +The ``=>`` tactical first executes :token:`tactic`, then the :token:`i_item`\s, left to right. An :token:`s_item` specifies a simplification operation; a :token:`clear_switch` -h specifies context pruning as in :ref:`discharge_ssr`. -The :token:`i_pattern` s can be seen as a variant of *intro patterns* -:ref:`tactics`: each performs an introduction operation, i.e., pops some +specifies context pruning as in :ref:`discharge_ssr`. +The :token:`i_pattern`\s can be seen as a variant of *intro patterns* +(see :tacn:`intros`:) each performs an introduction operation, i.e., pops some variables or assumptions from the goal. An :token:`s_item` can simplify the set of subgoals or the subgoals themselves: @@ -1572,7 +1578,7 @@ An :token:`s_item` can simplify the set of subgoals or the subgoals themselves: |SSR| tactic :tacn:`done` described in :ref:`terminators_ssr`, i.e., it executes ``try done``. + ``/=`` simplifies the goal by performing partial evaluation, as per the - tactic ``simpl`` [#5]_. + tactic :tacn:`simpl` [#5]_. + ``//=`` combines both kinds of simplification; it is equivalent to ``/= //``, i.e., ``simpl; try done``. @@ -1583,21 +1589,42 @@ When an :token:`s_item` bears a :token:`clear_switch`, then the possibly using the fact ``IHn``, and will erase ``IHn`` from the context of the remaining subgoals. -The last entry in the :token:`i_item` grammar rule, ``/``:token:`term`, +The first entry in the :token:`i_view` grammar rule, :n:`/@term`, represents a view (see section :ref:`views_and_reflection_ssr`). +It interprets the top of the stack with the view :token:`term`. +It is equivalent to ``move/term``. The optional flag ``{}`` can +be used to signal that the :token:`term`, when it is a context entry, +has to be cleared. If the next :token:`i_item` is a view, then the view is applied to the assumption in top position once all the previous :token:`i_item` have been performed. -The view is applied to the top assumption. +The second entry in the :token:`i_view` grammar rule, +``/ltac:(`` :token:`tactic` ``)``, executes :token:`tactic`. +Notations can be used to name tactics, for example:: + + Notation myop := (ltac:(some ltac code)) : ssripat_scope. -|SSR| supports the following :token:`i_pattern` s: +lets one write just ``/myop`` in the intro pattern. Note the scope +annotation: views are interpreted opening the ``ssripat`` scope. + +|SSR| supports the following :token:`i_pattern`\s: :token:`ident` pops the top variable, assumption, or local definition into a new constant, fact, or defined constant :token:`ident`, respectively. Note that defined constants cannot be introduced when δ-expansion is required to expose the top variable or assumption. +``>``:token:`ident` + pops the first assumption. Type class instances are not considered + as assumptions. + The tactic ``move=> >H`` is equivalent to + ``move=> ? ? H`` with enough ``?`` to name ``H`` the first assumption. + On a goal:: + + forall x y, x < y -> G + + it names ``H`` the assumption ``x < y``. ``?`` pops the top variable into an anonymous constant or fact, whose name is picked by the tactic interpreter. |SSR| only generates names that cannot @@ -1620,7 +1647,17 @@ The view is applied to the top assumption. a first ``move=> *`` adds only ``_a_ : bool`` and ``_b_ : bool`` to the context; it takes a second ``move=> *`` to add ``_Hyp_ : _a_ = _b_``. -:token:`occ_switch` ``->`` +``+`` + temporarily introduces the top variable. It is discharged at the end + of the intro pattern. For example ``move=> + y`` on a goal:: + + forall x y, P + + is equivalent to ``move=> _x_ y; move: _x_`` that results in the goal:: + + forall x, P + +:n:`{? occ_switch } ->` (resp. :token:`occ_switch` ``<-``) pops the top assumption (which should be a rewritable proposition) into an anonymous fact, rewrites (resp. rewrites right to left) the goal with this @@ -1645,18 +1682,13 @@ The view is applied to the top assumption. variable, using the |SSR| ``case`` tactic described in :ref:`the_defective_tactics_ssr`. It then behaves as the corresponding branching :token:`i_pattern`, executing the - sequence:token:`i_item`:math:`_i` in the i-th subgoal generated by the + sequence :n:`@i_item__i` in the i-th subgoal generated by the case analysis; unless we have the trivial destructing :token:`i_pattern` ``[]``, the latter should generate exactly m subgoals, i.e., the top variable should have an inductive type with exactly m constructors [#7]_. While it is good style to use the :token:`i_item` i * to pop the variables and assumptions corresponding to each constructor, this is not enforced by |SSR|. -``/`` :token:`term` - Interprets the top of the stack with the view :token:`term`. - It is equivalent to ``move/term``. The optional flag ``{}`` can - be used to signal that the :token:`term`, when it is a context entry, - has to be cleared. ``-`` does nothing, but counts as an intro pattern. It can also be used to force the interpretation of ``[`` :token:`i_item` * ``| … |`` @@ -1721,6 +1753,40 @@ interpretation, e.g.: are all equivalent. +|SSR| supports the following :token:`i_block`\s: + +:n:`[^ @ident ]` + *block destructing* :token:`i_pattern`. It performs a case analysis + on the top variable and introduces, in one go, all the variables coming + from the case analysis. The names of these variables are obtained by + taking the names used in the inductive type declaration and prefixing them + with :token:`ident`. If the intro pattern immediately follows a call + to ``elim`` with a custom eliminator (see :ref:`custom_elim_ssr`) then + the names are taken from the ones used in the type of the eliminator. + + .. example:: + + .. coqtop:: reset + + From Coq Require Import ssreflect. + Set Implicit Arguments. + Unset Strict Implicit. + Unset Printing Implicit Defensive. + + .. coqtop:: all + + Record r := { a : nat; b := (a, 3); _ : bool; }. + + Lemma test : r -> True. + Proof. move => [^ x ]. + +:n:`[^~ @ident ]` + *block destructing* using :token:`ident` as a suffix. +:n:`[^~ @num ]` + *block destructing* using :token:`num` as a suffix. + + Only a :token:`s_item` is allowed between the elimination tactic and + the block destructing. .. _generation_of_equations_ssr: @@ -4160,6 +4226,7 @@ interpretation operations with the proof stack operations. This *view mechanism* relies on the combination of the ``/`` view switch with bookkeeping tactics and tacticals. +.. _custom_elim_ssr: Interpreting eliminations ~~~~~~~~~~~~~~~~~~~~~~~~~ @@ -5238,11 +5305,21 @@ discharge item see :ref:`discharge_ssr` generalization item see :ref:`structure_ssr` -.. prodn:: i_pattern ::= @ident %| _ %| ? %| * %| {? @occ_switch } -> %| {? @occ_switch } <- %| [ {*| {* @i_item } } %| - %| [: {+ @ident } ] +.. prodn:: i_pattern ::= @ident %| > @ident %| _ %| ? %| * %| + %| {? @occ_switch } -> %| {? @occ_switch } <- %| [ {?| @i_item } ] %| - %| [: {+ @ident } ] intro pattern :ref:`introduction_ssr` -.. prodn:: i_item ::= @clear_switch %| @s_item %| @i_pattern %| {? %{%} } / @term +.. prodn:: i_item ::= @clear_switch %| @s_item %| @i_pattern %| @i_view %| @i_block + +view :ref:`introduction_ssr` + +.. prodn:: + i_view ::= {? %{%} } /@term %| /ltac:( @tactic ) + +intro block :ref:`introduction_ssr` + +.. prodn:: + i_block ::= [^ @ident ] %| [^~ @ident ] %| [^~ @num ] intro item see :ref:`introduction_ssr` |