feat(library/init/lean/ir/ir): use name

library/init/core.lean

@@ -573,6 +573,7 @@ attribute [elab_simple] bin_tree.node bin_tree.leaf
 
 /-- Like `by apply_instance`, but not dependent on the tactic framework. -/
 @[reducible] def infer_instance {α : Type u} [i : α] : α := i
+@[reducible, elab_simple] def infer_instance_as (α : Type u) [i : α] : α := i
 
 /- Boolean operators -/
 

library/init/lean/ir/ir.lean

@@ -5,6 +5,7 @@ Authors: Leonardo de Moura
 -/
 prelude
 import init.data.rbmap init.data.int init.control.state init.control.except init.control.combinators
+import init.lean.name
 
 /-
 Missing
@@ -34,15 +35,15 @@ inductive literal
 | float   : string → literal  -- for float/double literals
 
 def tag     := uint16
-def var     := string
-def fid     := string
-def blockid := string
+def var     := name
+def fid     := name
+def blockid := name
 
 instance var_has_lt : has_lt var :=
-show has_lt string, from infer_instance
+show has_lt name, from name.has_lt_quick
 
 instance blockid_has_lt : has_lt blockid :=
-show has_lt string, from infer_instance
+show has_lt name, from name.has_lt_quick
 
 def var_set        := rbtree var (<)
 def blockid_set    := rbtree blockid (<)

library/init/lean/name.lean

@@ -80,6 +80,9 @@ instance has_decidable_eq : decidable_eq name
 protected def has_lt_quick : has_lt name :=
 ⟨λ a b, name.quick_lt a b = tt⟩
 
+instance : decidable_rel (@has_lt.lt name name.has_lt_quick) :=
+infer_instance_as (decidable_rel (λ a b, name.quick_lt a b = tt))
+
 def to_string_with_sep (sep : string) : name → string
 | anonymous                := "[anonymous]"
 | (mk_string anonymous s)  := s