lean4-htt/library/init/data/to_string.lean
Leonardo de Moura d85c30fde1 perf(library/init/data): mark usize, uint16, uint32 and uint64 as [irreducible]
Without these annotations, Lean will timeout when trying to synthesize
the type class instance `decidable_eq uint32`. The type class resolution
problem will produce the unification problem:
```
decidable (@eq uint32 a b) =?= decidable (@eq usize ?x ?y)
```
which Lean tries to solve by assigning `?x := a`.
During the assignment, the types of `?x` and `a` are unified with "full
force". Thus, we get the constraint
```
usize_sz =?= uint32_sz
```
which will take forever to be solved when peforming the computation in
unary arithmetic.

Remark: this commit also makes sure that `type_context` will not unfold
irreducible definitions when trying to unify/match the types.

The new test `type_class_performance1.lean` exposes the problem fixed
by this commit.
2018-05-07 18:07:04 -07:00

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/-
Copyright (c) 2016 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
-/
prelude
import init.data.string.basic init.data.uint init.data.nat.div init.data.repr
open sum subtype nat
universes u v
class has_to_string (α : Type u) :=
(to_string : α → string)
def to_string {α : Type u} [has_to_string α] : α → string :=
has_to_string.to_string
instance : has_to_string string :=
⟨λ s, s⟩
instance : has_to_string string.iterator :=
⟨λ it, it.next_to_string⟩
instance : has_to_string bool :=
⟨λ b, cond b "tt" "ff"⟩
instance {p : Prop} : has_to_string (decidable p) :=
-- Remark: type class inference will not consider local instance `b` in the new elaborator
⟨λ b : decidable p, @ite p b _ "tt" "ff"⟩
protected def list.to_string_aux {α : Type u} [has_to_string α] : bool → list α → string
| b [] := ""
| tt (x::xs) := to_string x ++ list.to_string_aux ff xs
| ff (x::xs) := ", " ++ to_string x ++ list.to_string_aux ff xs
protected def list.to_string {α : Type u} [has_to_string α] : list α → string
| [] := "[]"
| (x::xs) := "[" ++ list.to_string_aux tt (x::xs) ++ "]"
instance {α : Type u} [has_to_string α] : has_to_string (list α) :=
⟨list.to_string⟩
instance : has_to_string unit :=
⟨λ u, "()"⟩
instance : has_to_string nat :=
⟨λ n, repr n⟩
instance : has_to_string char :=
⟨λ c, c.to_string⟩
instance (n : nat) : has_to_string (fin n) :=
⟨λ f, to_string (fin.val f)⟩
instance : has_to_string uint16 :=
⟨λ n, to_string n.to_nat⟩
instance : has_to_string uint32 :=
⟨λ n, to_string n.to_nat⟩
instance : has_to_string uint64 :=
⟨λ n, to_string n.to_nat⟩
instance {α : Type u} [has_to_string α] : has_to_string (option α) :=
⟨λ o, match o with | none := "none" | (some a) := "(some " ++ to_string a ++ ")"⟩
instance {α : Type u} {β : Type v} [has_to_string α] [has_to_string β] : has_to_string (α ⊕ β) :=
⟨λ s, match s with | (inl a) := "(inl " ++ to_string a ++ ")" | (inr b) := "(inr " ++ to_string b ++ ")"⟩
instance {α : Type u} {β : Type v} [has_to_string α] [has_to_string β] : has_to_string (α × β) :=
⟨λ ⟨a, b⟩, "(" ++ to_string a ++ ", " ++ to_string b ++ ")"⟩
instance {α : Type u} {β : α → Type v} [has_to_string α] [s : ∀ x, has_to_string (β x)] : has_to_string (sigma β) :=
⟨λ ⟨a, b⟩, "⟨" ++ to_string a ++ ", " ++ to_string b ++ "⟩"⟩
instance {α : Type u} {p : α → Prop} [has_to_string α] : has_to_string (subtype p) :=
⟨λ s, to_string (val s)⟩