v3.4.1 (28 April 2018)

Bugfix release: Fix a regression concerning type ascriptions in function position

v3.4.0 (16 April 2018)

Features

Implement RFC #1820
Add string.iterator abstraction for traversing strings. The VM contains an efficient implementation of this type.
Add support for non-ASCII char literals. Example: 'α'.
Unicode escape characters in string and char literals. For example, '\u03B1' is equivalent to 'α'.
Predictable runtime cost model for recursive functions. The equation compiler uses different techniques for converting recursive equations into recursors and/or well-founded fixed points. The new approach used in the code generator ignores these encoding tricks when producing byte code. So, the runtime cost model is identical to the one in regular strict functional languages.
Add d_array n α (array type where value type may depend on index), where (α : fin n → Type u).
Add instance for decidable_eq (d_array n α) and decidable_eq (array n α). The new instance is more efficient than the one in mathlib because it doesn't convert the array into a list.
Add aliasing pattern syntax id@pat, which introduces the name id for the value matched by the pattern pat.
Add alternative syntax {..., ..s} for the structure update {s with ...}. Multiple fallback sources can be given: {..., ..s, ..t} will fall back to searching a field in s, then in t. The last component can also be .., which will replace any missing fields with a placeholder. The old notation will be removed in the future.
Add support for structure instance notation {...} in patterns. Use .. to ignore unmatched fields.
Type class has_equiv for ≈ notation.
Add funext ids* tactic for applying the funext lemma.
Add iterate n { t } for applying tactic t n times. Remark: iterate { t } applies t until it fails.
Add with_cases { t }. This tactic applies t to the main goal, and reverts any new hypothesis in the resulting subgoals. with_cases also enable "goal tagging". Remark: induction and cases tag goals using constructor names. apply and constructor tag goals using parameter names. The case tactic can select goals using tags.
Add cases_matching p tactic for applying the cases tactic to a hypothesis h : t s.t. t matches the pattern p. Alternative versions: cases_matching* p and cases_matching [p_1, ..., p_n]. Example: cases_matching* [_ ∨ _, _ ∧ _] destructs all conjunctions and disjunctions in the main goal.
Add cases_type I tactic for applying the cases tactic to a hypothesis h : I .... cases_type! I only succeeds when the number of resulting goals is <= 1. Alternative versions: cases_type I_1 ... I_n, cases_type* I, cases_type!* I. Example: cases_type* and or destructs all conjunctions and disjunctions in the main goal.
Add constructor_matching p tactic. It is syntax sugar for match_target p; constructor. The variant constructor_matching* p is more efficient than focus1 { repeat { match_target p; constructor } } because the patterns are compiled only once.
injection h now supports nested and mutually recursive datatypes.
Display number of goals in the *Lean Goal* buffer (if number of goals > 1).
hide id* command for hiding aliases. The following command hides the alias is_true for decidable.is_true.
```
hide is_true
```
Add abbreviation declaration command. abbreviation d : t := v is equivalent to @[reducible, inline] def d : t := v and a kernel reducibility hint. Before this command, we had to use meta programming for setting the kernel reducibility hint. This was problematic because we could only define abbreviations after the meta programming framework was defined.
Add "smart unfolding". The idea is to prevent internal compilation details used by the equation compiler to "leak" during unification, tactic execution and reduction. With "smart unfolding", the term nat.add a (nat.succ b) reduces to nat.succ (nat.add a b) instead of nat.succ (... incomprehensible mess ...). This feature addresses a problem reported by many users. See issue #1794. The command set_option type_context.smart_unfolding false disables this feature.
Add support for "auto params" at simp tactic. Example: given
```
@[simp] lemma fprop1 (x : nat) (h : x > 0 . tactic.assumption) : f x = x := ...
```
The simplifier will try to use tactic assumption to synthesize parameter h.
Add interactive sorry tactic (alias for admit).
simp now reduces equalities c_1 ... = c_2 ... to false if c_1 and c_2 are distinct constructors. This feature can be disabled using simp {constructor_eq := ff}.
simp now reduces equalities c a_1 ... a_n = c b_1 ... b_n to a_1 = b_1 /\ ... /\ a_n = b_n if c is a constructor. This feature can be disabled using simp {constructor_eq := ff}.
subst and subst_vars now support heterogeneous equalities that are actually homogeneous (i.e., @heq α a β b where α and β are definitionally equal).
Add interactive subst_vars tactic.
Add leanpkg add foo/bar as a shorthand for leanpkg add https://github.com/foo/bar.
Add leanpkg help <command>.
Add [norm] simp set. It contains all lemmas tagged with [simp] plus any lemma tagged with [norm]. These rules are used to produce normal forms and/or reduce the number of constants used in a goal. For example, we plan to add the lemma f <$> x = x >>= pure ∘ f to [norm].
Add iota_eqn : bool field to simp_config. simp {iota_eqn := tt} uses all non trivial equation lemmas generated by equation/pattern-matching compiler. A lemma is considered non trivial if it is not of the form forall x_1 ... x_n, f x_1 ... x_n = t and a proof by reflexivity. simp! is a shorthand for simp {iota_eqn := tt}. For example, given the goal ... |- [1,2].map nat.succ = t, simp! reduces the left-hand-side of the equation to [nat.succ 1, nat.succ 2]. In this example, simp! is equivalent to simp [list.map].
Allow the Script, Double-struck, and Fractur symbols from Mathematical Alphanumeric Symbols: https://unicode.org/charts/PDF/U1D400.pdf to be used as variables Example: variables 𝓞 : Prop.
Structure instance notation now allows explicitly setting implicit structure fields
Structure instance notation now falls back to type inference for inferring the value of a superclass. This change eliminates the need for most .. source specifiers in instance declarations.
The --profile flag will now print cumulative profiling times at the end of execution
do notation now uses the top-level, overloadable bind function instead of has_bind.bind, allowing binds with different type signatures

Structures fields can now be defined with an implicitness infer annotation and parameters.

class has_pure (f : Type u → Type v) :=
-- make f implicit
(pure {} {α : Type u} : α → f α)

Add except_t and reader_t monad transformers
Add monad_{except,reader,state} classes for accessing effects anywhere in a monad stack without the need for explicit lifting. Add analogous monad_{except,reader,state}_adapter classes for translating a monad stack into another one with the same shape but different parameter types.

Changes

Command variable [io.interface] is not needed anymore to use the io monad. It is also easier to add new io primitives.
Replace inout modifier in type class declarations with out_param modifier. Reason: counterintuitive behavior in the type class resolution procedure. The result could depend on partial information available in the inout parameter. Now a parameter (R : inout α → β → Prop) should be written as (R : out_param (α → β → Prop)) or (R : out_param $ α → β → Prop). Remark: users may define their own notation for declaring out_params. Example:
```
notation `out`:1024 a:0 := out_param a
```
We did not include this notation in core lib because out is frequently used to name parameters, local variables, etc.
case tactic now supports the with_cases { t } tactic. See entry above about with_cases. The tag and new hypotheses are now separated with :. Example:
- case pos { t }: execute tactic t to goal tagged pos
- case pos neg { t }: execute tactic t to goal tagged pos neg
- case : x y { t }: execute tactic t to main goal after renaming the first two hypotheses produced by preceding with_case { t' }.
- case pos neg : x y { t } : execute tactic t to goal tagged pos neg after renaming the first two hypotheses produced by preceding with_case { t' }.
cases h now also tries to clear h when performing dependent elimination.
repeat { t } behavior changed. Now, it applies t to each goal. If the application succeeds, the tactic is applied recursively to all the generated subgoals until it eventually fails. The recursion stops in a subgoal when the tactic has failed to make progress. The previous repeat tactic was renamed to iterate.
The automatically generated recursor C.rec for an inductive datatype now uses ih to name induction hypotheses instead of ih_1 if there is only one. If there is more than one induction hypotheses, the name is generated by concatenating ih_ before the constructor field name. For example, for the constructor
```
| node (left right : tree) (val : A) : tree
```
The induction hypotheses are now named: ih_left and ih_right. This change only affects tactical proofs where explicit names are not provided to induction and cases tactics.
induction h and cases h tactic use a new approach for naming new hypotheses. If names are not provided by the user, these tactics will create a "base" name by concatenating the input hypothesis name with the constructor field name. If there is only one field, the tactic simply reuses the hypothesis name. The final name is generated by making sure the "base" name is unique. Remarks:
- If h is not a hypothesis, then no concatenation is performed.
- The old behavior can be obtained by using the following command
```
set_option tactic.induction.concat_names false
```
This change was suggested by Tahina Ramananandro. The idea is to have more robust tactic scripts when helper tactics that destruct many hypotheses automatically are used. Remark: The new guard_names { t } tactical can be used to generate robust tactic scripts that are not sensitive to naming generation strategies used by t.
Remove [simp] attribute from lemmas or.assoc, or.comm, or.left_comm, and.assoc, and.comm, and.left_comm, add_assoc, add_comm, add_left_com, mul_assoc, mul_comm and mul_left_comm. These lemmas were being used to "sort" arguments of AC operators: and, or, (+) and (*). This was producing unstable proofs. The old behavior can be retrieved by using the commands local attribute [simp] ... or attribute [simp] ... in the affected files.
string is now a list of unicode scalar values. Moreover, in the VM, strings are implemented as an UTF-8 encoded array of bytes.
array α n is now written array n α. Motivation: consistency d_array n α.
Move rb_map and rb_tree to the native namespace. We will later add pure Lean implementations. Use open native to port files.
apply t behavior changed when type of t is of the form forall (a_1 : A_1) ... (a_n : A_n), ?m ..., where ?m is an unassigned metavariable. In this case, apply t behaves as apply t _ ... _ where n _ have been added, independently of the goal target type. The new behavior is useful when using apply with eliminator-like definitions.
ginduction t with h h1 h2 is now induction h : t with h1 h2.
apply_core now also returns the parameter name associated with new metavariables.
apply now also returns the new metavariables (and the parameter name associated with them). Even the assigned metavariables are returned.
by_cases p with h ==> by_cases h : p
leanpkg now always stores .lean package files in a separate src directory.
Structure constructor parameters representing superclasses are now marked as instance implicit. Note: Instances using the {...} structure notation should not be affected by this change.
The monad laws have been separated into new type classes is_lawful_{functor,applicative,monad}.
unit is now an abbreviation of punit.{0}

API name changes

monad.has_monad_lift(_t) ~> has_monad_lift(_t)
monad.map_comp ~> comp_map
state(_t).{read,write} ~> {get,put} (general operations defined on any monad_state)
deleted monad.monad_transformer
deleted monad.lift{n}. Use f <$> a1 <*> ... <*> an instead of monad.lift{n} f a1 ... an.
merged has_map into functor
unit_eq(_unit) ~> punit_eq(_punit)

v3.3.0 (14 September 2017)

Features

In addition to user-defined notation parsers introduced in Lean 3.2.0, users may now also define top-level commands in Lean. For an example, see the coinductive command that has been ported to the new model.
Add new simplifier configuration option simp_config.single_pass. It is useful for simplification rules that may produce non-termination. Example: simp {single_pass := tt}
The rewrite tactic has support for equational lemmas. Example: Given a definition f, rw [f] will try to rewrite the goal using the equational lemmas for f. The tactic fails if none of the equational lemmas can be used.
Add simp * at * variant. It acts on all (non dependent propositional) hypotheses. Simplified hypotheses are automatically inserted into the simplification set as additional simplification rules.
Add «id» notation that can be used to declare and refer to identifiers containing prohibited characters. For example, a.«b.c» is a two-part identifier with parts a and b.c.
simp tactic now handles lemmas with metavariables. Example simp [add_comm _ b].
conv { ... } tactic for applying simplification and rewriting steps. In the block {...}, we can use tactics from conv.interactive. Examples:
- conv at h in (f _ _) { simp } applies simp to first subterm matching f _ _ at hypothesis h.
- conv in (_ = _) { to_lhs, whnf } replace the left-hand-side of the equality in target with its weak-head-normal-form.
- conv at h in (0 + _) { rw [zero_add] }
- conv { for (f _ _) [1, 3] {rw [h]}, simp }, first execute rw[h] to the first and third occurrences of an f-application, and then execute simp.
simp tactics in interactive mode have a new configuration parameter (discharger : tactic unit) a tactic for discharging subgoals created by the simplifier. If the tactic fails, the simplifier tries to discharge the subgoal by reducing it to true. Example: simp {discharger := assumption}.
simp and dsimp can be used to unfold projection applications when the argument is a type class instance. Example: simp [has_add.add] will replace @has_add.add nat nat.has_add a b with nat.add a b
dsimp has several new configuration options to control reduction (e.g., iota, beta, zeta, ...).
Non-exhaustive pattern matches now show missing cases.
induction e now also works on non-variable e. Unlike ginduction, it will not introduce equalities relating e to the inductive cases.
Add notation #[a, b, c, d] for bin_tree.node (bin_tree.node (bin_tree.leaf a) (bin_tree.leaf b)) (bin_tree.node (bin_tree.leaf c) (bin_tree.leaf d)). There is a coercion from bin_tree to list. The new notation allows to input long sequences efficiently. It also prevents system stack overflows.
Tactics that accept a location parameter, like rw thm at h, may now use ⊢ or the ASCII version |- to select the goal as well as any hypotheses, for example rw thm at h1 h2 ⊢.
Add user_attribute.after_set/before_unset handlers that can be used for validation as well as side-effecting attributes.
Field notation can now be used to make recursive calls.

def list.append : list α → list α → list α
| []       l := l
| (h :: s) t := h :: s.append t

leanpkg now stores the intended Lean version in the leanpkg.toml file and reports a warning if the version does not match the installed Lean version.
simp and dsimp can now unfold let-bindings in the local context. Use dsimp [x] or simp [x] to unfold the let-binding x : nat := 3.
User-defined attributes can now take parameters parsed by a lean.parser. A [derive] attribute that can derive typeclasses such as decidable_eq and inhabited has been implemented on top of this.

Changes

We now have two type classes for converting to string: has_to_string and has_repr. The has_to_string type class in v3.2.0 is roughly equivalent to has_repr. For more details, see discussion here.
Merged assert and note tactics and renamed -> have.
Renamed pose tactic -> let
assume is now a real tactic that does not exit tactic mode.
Modified apply tactic configuration object, and implemented RFC #1342. It now has support for auto_param and opt_param. The new eapply tactic only creates subgoals for non dependent premises, and it simulates the behavior of the apply tactic in version 3.2.0.
Add configuration object rewrite_cfg to rw/rewrite tactic. It now has support for auto_param and opt_param. The new goals are ordered using the same strategies available for apply.
All dsimp tactics fail if they did not change anything. We can simulate the v3.2.0 using dsimp {fail_if_unchaged := ff} or try dsimp.
dsimp does not unfold reducible definitions by default anymore. Example: function.comp applications will not be unfolded by default. We should use dsimp [f] if we want to reduce a reducible definition f. Another option is to use the new configuration parameter unfold_reducible. Example dsimp {unfold_reducible := tt}
All dunfold and unfold tactics fail if they did not unfold anything. We can simulate the v3.2.0 using unfold f {fail_if_unchaged := ff} or try {unfold f}.
dunfold_occs was deleted, the new conv tactical should be used instead.
unfold tactic is now implemented on top of the simp tactics. So, we can use it to unfold declarations defined using well founded recursion. The unfold1 variant does not unfold recursively, and it is shorthand for unfold f {single_pass := tt}. Remark: in v3.2.0, unfold was just an alias for the dunfold tactic.
Deleted simph and simp_using_hs tactics. We should use simp [*] instead.
Use simp [-h] and dsimp [-h] instead of simp without h and dsimp without h. Moreover, simp [*, -h] if h is a hypothesis, we are adding all hypotheses but h as additional simplification lemmas.
Changed notation rw [-h] to rw [← h] to avoid confusion with the new simp [-h] notation. The ASCII version rw [<- h] is also supported.
rw [t] at * now skips any hypothesis used by t. See discussion here.
Removed the redundant keywords take (replace with assume) and suppose (replace with the new anonymous assume :)
Universes max u v + 1 and imax u v + 1 are now parsed as (max u v) + 1 and (imax u v) + 1.
Merged generalize and generalize2 tactics into new generalize id? : expr = id tactic
standard.lean has been removed. Any files that import standard can simply remove the line as most things that were once imported by this are now imported by default.
The type classes for orders have been refactored to combine both the (<) and (≤) operations. The new classes are preorder, partial_order, and linear_order. The partial_order class corresponds to weak_order, strict_order, order_pair, and strong_order_pair. The linear_order class corresponds to linear_order_pair, and linear_strong_order_pair.
injection and injections tactics generate fresh names when user does not provide names. The fresh names are of the form h_<idx>. See discussion here.
Use structure to declare and. This change allows us to use h.1 and h.2 as shorthand for h.left and h.right.
Add attribute [pp_using_anonymous_constructor] to and. Now, and.intro h1 h2 is pretty printed as ⟨h1, h2⟩. This change is motivated by the previous one. Without it, and.intro h1 h2 would be pretty printed as {left := h1, right := h2}.
User attributes can no longer be set with set_basic_attribute. You need to use user_attribute.set now.
The Emacs mode has been moved into its own repository and MELPA packages: https://github.com/leanprover/lean-mode

API name changes

list.dropn => list.drop
list.taken => list.take
tactic.dsimp and tactic.dsimp_core => tactic.dsimp_target
tactic.dsimp_at_core and tactic.dsimp_at => tactic.dsimp_hyp
tactic.delta_expr => tactic.delta
tactic.delta => tactic.delta_target
tactic.delta_at => tactic.delta_hyp
tactic.simplify_goal => tactic.simp_target
tactic.unfold_projection => tactic.unfold_proj
tactic.unfold_projections_core => tactic.unfold_projs
tactic.unfold_projections => tactic.unfold_projs_target
tactic.unfold_projections_at => tactic.unfold_projs_hyp
tactic.simp_intros_using, tactic.simph_intros_using, tactic.simp_intro_lst_using, tactic.simph_intro_lst_using => tactic.simp_intros
tactic.simp_at => tactic.simp_hyp
deleted tactic.simp_at_using
deleted tactic.simph_at

v3.2.0 (18 June 2017)

Lean is still evolving rapidly, and we apologize for the resulting instabilities. The lists below summarizes some of the new features and incompatibilities with respect to release 3.1.0.

Features

Holes {! ... !} expressions and (user-defined) hole commands. In Emacs, hole commands are executed using the keybinding C-c SPC. The available commands can be found here.
The leanpkg package manager now manages projects and dependencies. See the documentation here. Parts of the standard library, like the superposition theorem prover super, have been moved to their own repositories. .project files are no longer needed to use emacs with projects.
Well-founded recursion is now supported. (Details and examples for this and the next two items will soon appear in Theorem Proving in Lean.)
Mutually (non meta) recursive definitions are now supported.
Nested and mutual inductive data types are now supported.
There is support for coinductive predicates.
The simp tactic has been improved and supports more options, like wildcards. Hover over simp in an editor to see the documentation string (docstring).
Additional interactive tactics have been added, and can be found here.
A case tactic can now be used to structure proofs by cases and by induction. See here.
Various data structures, such as hash maps, have been added to the standard library here.
There is preliminary support for user-defined parser extensions. More information can be found here, and some examples can be found here.
Numerous improvements have been made to the parallel compilation infrastructure and editor interfaces, for example, as described here and here.
There is a transfer method that can be used to transfer results e.g. to isomorphic structures; see here.
The monadic hierarchy now includes axioms for monadic classes. (See here.)
The tactic notation tac ; [tac_1, ..., tac_n] has been added.
The type classes has_well_founded, has_map, has_seq, has_orelse have been added.
Type classes can have input/output parameters. Some examples can be found here.
tactic.run_io can now be used to perform IO in tactics.

Changes

Type class instances are not [reducible] by default anymore.
Commands that produce output are now preceded by a hash symbol, as in #check, #print, #eval and #reduce. The #eval command calls the bytecode evaluator, and #reduce does definitional reduction in the kernel. Many instances of alternative syntax like premise for variable and hypothesis for parameter have been eliminated. See the discussion here.
The hierarchy of universes is now named Sort 0, Sort 1, Sort 2, and so on. Prop is alternative syntax for Sort 0, Type is alternative syntax for Sort 1, and Type n is alternative syntax for Sort (n + 1). Many general constructors have been specialized from arbitrary Sorts to Type in order to simplify elaboration.
Automatically generate dependent eliminators for inductive predicates.
Improve unification hint matcher.
Improve unifier. In function applications, explicit arguments are unified before implicit ones. Moreover, more aggresive unfolding is used when processing implicit arguments.
Use universe u instead of universe variable u to declare a universe variable.
The syntax l^.map f for projections is now deprecated in favor of l.map f.
The behavior of the show tactic in interactive tactic mode has changed. It no longer leaves tactic mode. Also, it can now be used to select a goal other than the current one.
The assertv and definev tactics have been eliminated in favor of note and pose.
has_andthen type class is now heterogeneous,
The encoding of structures has been changed, following the strategy described here. Generic operations like add and mul are replaced by has_add.add and has_mul.mul, respectively. One can provisionally obtain the old encodings with set_option old_structure_cmd true .
Syntax for quotations in metaprograms has changed. The notation `(t) elaborates t at definition time and produces an expression. The notation ``(t) resolves names at definition time produces a pre-expression, and ```(t) resolves names at tactic execution time, and produces a pre-expression. Details can be found in the paper Ebner et al, A Metaprogramming Framework for Formal Verification.
The types expr for expressions and pexpr for pre-expressions have been unified, so that pexpr is defined as expr ff. See here.
Handling of the io monad has changed. Examples can be found here in the code for leanpkg, which is written in Lean itself.

state and state_t are universe polymorphic.

option_map and option_bind have been renamed to option.map and option.bind, respectively.
GCC 7 compatibility
Use single quotes for character literals (e.g., 'a').

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v3.4.1 (28 April 2018)

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