lean4-htt/library/init/meta/expr.lean

/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Leonardo de Moura
-/
prelude
import init.meta.level

inductive binder_info :=
| default | implicit | strict_implicit | inst_implicit | other

meta_constant macro_def : Type₁

/- Reflect a C++ expr object. The VM replaces it with the C++ implementation. -/
inductive expr :=
| var         : unsigned → expr
| sort        : level → expr
| const       : name → list level → expr
| meta        : name → expr → expr
| local_const : name → name → binder_info → expr → expr
| app         : expr → expr → expr
| lam         : name → binder_info → expr → expr → expr
| pi          : name → binder_info → expr → expr → expr
| elet        : name → expr → expr → expr → expr
| macro       : macro_def → ∀ n : unsigned, (fin (unsigned.to_nat n) → expr) → expr

attribute [instance]
definition expr.is_inhabited : inhabited expr :=
inhabited.mk (expr.sort level.zero)

meta_constant expr.mk_macro (d : macro_def) : list expr → expr
meta_definition expr.mk_var (n : nat) : expr :=
expr.var (unsigned.of_nat n)

meta_constant expr.has_decidable_eq : decidable_eq expr
attribute [instance] expr.has_decidable_eq
meta_constant expr.alpha_eqv : expr → expr → bool
notation a ` =ₐ `:50 b:50 := expr.alpha_eqv a b = bool.tt

meta_constant expr.to_string : expr → string
attribute [instance]
meta_definition expr.has_to_string : has_to_string expr :=
has_to_string.mk expr.to_string

meta_constant expr.hash : expr → nat

meta_constant expr.lt : expr → expr → bool
meta_constant expr.lex_lt : expr → expr → bool
meta_definition expr.cmp (a b : expr) : ordering :=
if expr.lt a b = bool.tt then ordering.lt
else if a = b then ordering.eq
else ordering.gt

meta_constant expr.fold {A :Type} : expr → A → (expr → unsigned → A → A) → A

meta_constant expr.abstract_local  : expr → name → expr
meta_constant expr.abstract_locals : expr → list name → expr

meta_constant expr.instantiate_var  : expr → expr → expr
meta_constant expr.instantiate_vars : expr → list expr → expr

meta_constant expr.has_var      : expr → bool
meta_constant expr.has_var_idx  : expr → nat → bool
meta_constant expr.has_local    : expr → bool
meta_constant expr.has_meta_var : expr → bool
meta_constant expr.lift_vars    : expr → nat → nat → expr
meta_constant expr.lower_vars   : expr → nat → nat → expr

namespace expr
open decidable

meta_definition app_of_list : expr → list expr → expr
| f []      := f
| f (p::ps) := app_of_list (expr.app f p) ps

meta_definition is_app : expr → bool
| (app _ _ ) := tt
| _          := ff

meta_definition app_fn : expr → expr
| (app f a) := f
| a         := a

meta_definition app_arg : expr → expr
| (app f a) := a
| a         := a

meta_definition get_app_fn : expr → expr
| (app f a) := get_app_fn f
| a         := a

meta_definition get_app_num_args : expr → nat
| (app f a) := get_app_num_args f + 1
| _         := 0

meta_definition get_app_args_aux : list expr → expr → list expr
| r (app f a) := get_app_args_aux (a::r) f
| r _         := r

meta_definition get_app_args : expr → list expr :=
get_app_args_aux []

meta_definition const_name : expr → name
| (const n ls) := n
| _            := name.anonymous

meta_definition is_constant : expr → bool
| (const n ls) := tt
| _            := ff

meta_definition is_local_constant : expr → bool
| (local_const _ _ _ _) := tt
| _                     := ff

meta_definition local_uniq_name : expr → name
| (local_const n _ _ _) := n
| _                     := name.anonymous

meta_definition local_pp_name : expr → name
| (local_const _ n _ _) := n
| _                     := name.anonymous

meta_definition is_constant_of : expr → name → bool
| (const n₁ ls) n₂ := to_bool (n₁ = n₂)
| _             _  := ff

meta_definition is_app_of (e : expr) (n : name) : bool :=
is_app e && is_constant_of (get_app_fn e) n

meta_definition is_false (e : expr) : bool :=
is_constant_of e `false

meta_definition is_not : expr → option expr
| (app f a)    := if is_constant_of f `not = tt then some a else none
| (pi _ _ a b) := if is_false b = tt then some a else none
| _            := none

meta_definition is_eq (e : expr) : option (expr × expr) :=
if is_app_of e `eq = tt ∧ get_app_num_args e = 3
then some (app_arg (app_fn e), app_arg e)
else none

meta_definition is_ne (e : expr) : option (expr × expr) :=
if is_app_of e `ne = tt ∧ get_app_num_args e = 3
then some (app_arg (app_fn e), app_arg e)
else none

meta_definition is_heq (e : expr) : option (expr × expr × expr × expr) :=
if is_app_of e `heq = tt ∧ get_app_num_args e = 4
then some (app_arg (app_fn (app_fn (app_fn e))),
           app_arg (app_fn (app_fn e)),
           app_arg (app_fn e),
           app_arg e)
else none

meta_definition is_pi : expr → bool
| (pi _ _ _ _) := tt
| _            := ff

meta_definition is_let : expr → bool
| (elet _ _ _ _) := tt
| _              := ff

meta_definition binding_name : expr → name
| (pi n _ _ _)  := n
| (lam n _ _ _) := n
| e             := name.anonymous

meta_definition binding_info : expr → binder_info
| (pi _ bi _ _)  := bi
| (lam _ bi _ _) := bi
| e              := binder_info.default

meta_definition binding_domain : expr → expr
| (pi _ _ d b)  := d
| (lam _ _ d b) := d
| e             := e

meta_definition binding_body : expr → expr
| (pi _ _ d b)  := b
| (lam _ _ d b) := b
| e             := e

meta_definition prop : expr := expr.sort level.zero

end expr