210 lines
6.2 KiB
Text
210 lines
6.2 KiB
Text
/-
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Copyright (c) 2016 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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Authors: Leonardo de Moura
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-/
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prelude
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import init.meta.level
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inductive binder_info
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| default | implicit | strict_implicit | inst_implicit | other
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meta constant macro_def : Type
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/- Reflect a C++ expr object. The VM replaces it with the C++ implementation. -/
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meta inductive expr
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| var : unsigned → expr
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| sort : level → expr
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| const : name → list level → expr
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| mvar : name → expr → expr
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| local_const : name → name → binder_info → expr → expr
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| app : expr → expr → expr
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| lam : name → binder_info → expr → expr → expr
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| pi : name → binder_info → expr → expr → expr
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| elet : name → expr → expr → expr → expr
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| macro : macro_def → ∀ n : unsigned, (fin (unsigned.to_nat n) → expr) → expr
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meta instance : inhabited expr :=
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⟨expr.sort level.zero⟩
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meta constant expr.mk_macro (d : macro_def) : list expr → expr
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meta def expr.mk_var (n : nat) : expr :=
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expr.var (unsigned.of_nat n)
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-- Compares expressions, including binder names.
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meta constant expr.has_decidable_eq : decidable_eq expr
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attribute [instance] expr.has_decidable_eq
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-- Compares expressions while ignoring binder names.
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meta constant expr.alpha_eqv : expr → expr → bool
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notation a ` =ₐ `:50 b:50 := expr.alpha_eqv a b = bool.tt
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meta constant expr.to_string : expr → string
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meta instance : has_to_string expr :=
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has_to_string.mk expr.to_string
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/- Coercion for letting users write (f a) instead of (expr.app f a) -/
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meta instance : has_coe_to_fun expr :=
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{ F := λ e, expr → expr, coe := λ e, expr.app e }
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meta constant expr.hash : expr → nat
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-- Compares expressions, ignoring binder names, and sorting by hash.
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meta constant expr.lt : expr → expr → bool
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-- Compares expressions, ignoring binder names.
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meta constant expr.lex_lt : expr → expr → bool
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-- Compares expressions, ignoring binder names, and sorting by hash.
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meta def expr.cmp (a b : expr) : ordering :=
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if expr.lt a b then ordering.lt
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else if a =ₐ b then ordering.eq
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else ordering.gt
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meta constant expr.fold {A : Type} : expr → A → (expr → nat → A → A) → A
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meta constant expr.replace : expr → (expr → nat → option expr) → expr
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meta constant expr.abstract_local : expr → name → expr
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meta constant expr.abstract_locals : expr → list name → expr
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meta def expr.abstract : expr → expr → expr
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| e (expr.local_const n m bi t) := e^.abstract_local n
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| e _ := e
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meta constant expr.instantiate_var : expr → expr → expr
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meta constant expr.instantiate_vars : expr → list expr → expr
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meta constant expr.has_var : expr → bool
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meta constant expr.has_var_idx : expr → nat → bool
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meta constant expr.has_local : expr → bool
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meta constant expr.has_meta_var : expr → bool
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meta constant expr.lift_vars : expr → nat → nat → expr
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meta constant expr.lower_vars : expr → nat → nat → expr
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/- (copy_pos_info src tgt) copy position information from src to tgt. -/
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meta constant expr.copy_pos_info : expr → expr → expr
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namespace expr
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open decidable
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-- Compares expressions, ignoring binder names, and sorting by hash.
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meta instance : has_ordering expr :=
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⟨ expr.cmp ⟩
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meta def app_of_list : expr → list expr → expr
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| f [] := f
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| f (p::ps) := app_of_list (f p) ps
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meta def is_app : expr → bool
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| (app f a) := tt
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| e := ff
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meta def app_fn : expr → expr
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| (app f a) := f
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| a := a
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meta def app_arg : expr → expr
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| (app f a) := a
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| a := a
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meta def get_app_fn : expr → expr
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| (app f a) := get_app_fn f
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| a := a
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meta def get_app_num_args : expr → nat
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| (app f a) := get_app_num_args f + 1
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| e := 0
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meta def get_app_args_aux : list expr → expr → list expr
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| r (app f a) := get_app_args_aux (a::r) f
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| r e := r
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meta def get_app_args : expr → list expr :=
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get_app_args_aux []
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meta def const_name : expr → name
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| (const n ls) := n
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| e := name.anonymous
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meta def is_constant : expr → bool
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| (const n ls) := tt
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| e := ff
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meta def is_local_constant : expr → bool
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| (local_const n m bi t) := tt
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| e := ff
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meta def local_uniq_name : expr → name
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| (local_const n m bi t) := n
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| e := name.anonymous
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meta def local_pp_name : expr → name
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| (local_const x n bi t) := n
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| e := name.anonymous
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meta def is_constant_of : expr → name → bool
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| (const n₁ ls) n₂ := to_bool (n₁ = n₂)
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| e n := ff
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meta def is_app_of (e : expr) (n : name) : bool :=
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is_app e && is_constant_of (get_app_fn e) n
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meta def is_false (e : expr) : bool :=
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is_constant_of e `false
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meta def is_not : expr → option expr
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| (app f a) := if is_constant_of f `not then some a else none
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| (pi n bi a b) := if is_false b then some a else none
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| e := none
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meta def is_eq (e : expr) : option (expr × expr) :=
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if is_app_of e `eq ∧ get_app_num_args e = 3
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then some (app_arg (app_fn e), app_arg e)
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else none
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meta def is_ne (e : expr) : option (expr × expr) :=
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if is_app_of e `ne ∧ get_app_num_args e = 3
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then some (app_arg (app_fn e), app_arg e)
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else none
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meta def is_heq (e : expr) : option (expr × expr × expr × expr) :=
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if is_app_of e `heq ∧ get_app_num_args e = 4
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then some (app_arg (app_fn (app_fn (app_fn e))),
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app_arg (app_fn (app_fn e)),
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app_arg (app_fn e),
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app_arg e)
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else none
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meta def is_pi : expr → bool
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| (pi n bi d b) := tt
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| e := ff
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meta def is_arrow : expr → bool
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| (pi n bi d b) := bnot (has_var b)
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| e := ff
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meta def is_let : expr → bool
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| (elet n t v b) := tt
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| e := ff
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meta def binding_name : expr → name
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| (pi n m d b) := n
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| (lam n m d b) := n
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| e := name.anonymous
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meta def binding_info : expr → binder_info
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| (pi n bi d b) := bi
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| (lam n bi d b) := bi
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| e := binder_info.default
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meta def binding_domain : expr → expr
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| (pi n bi d b) := d
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| (lam n bi d b) := d
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| e := e
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meta def binding_body : expr → expr
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| (pi n bi d b) := b
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| (lam n bi d b) := b
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| e := e
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meta def prop : expr := expr.sort level.zero
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end expr
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