feat(frontends/lean): add coercion modifier

Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>

src/frontends/lean/decl_cmds.cpp

@@ -13,6 +13,7 @@ Author: Leonardo de Moura
 #include "library/placeholder.h"
 #include "library/locals.h"
 #include "library/explicit.h"
+#include "library/coercion.h"
 #include "frontends/lean/parser.h"
 #include "frontends/lean/util.h"
 #include "frontends/lean/class.h"
@@ -25,6 +26,7 @@ static name g_assign(":=");
 static name g_private("[private]");
 static name g_inline("[inline]");
 static name g_instance("[instance]");
+static name g_coercion("[coercion]");
 
 environment universe_cmd(parser & p) {
     name n = p.check_id_next("invalid universe declaration, identifier expected");
@@ -167,10 +169,12 @@ struct decl_modifiers {
     bool m_is_private;
     bool m_is_opaque;
     bool m_is_instance;
+    bool m_is_coercion;
     decl_modifiers() {
         m_is_private  = false;
         m_is_opaque   = true;
         m_is_instance = false;
+        m_is_coercion = false;
     }
 
     void parse(parser & p) {
@@ -184,6 +188,9 @@ struct decl_modifiers {
             } else if (p.curr_is_token(g_instance)) {
                 m_is_instance = true;
                 p.next();
+            } else if (p.curr_is_token(g_coercion)) {
+                m_is_coercion = true;
+                p.next();
             } else {
                 break;
             }
@@ -281,6 +288,8 @@ environment definition_cmd_core(parser & p, bool is_theorem, bool _is_opaque) {
     }
     if (modifiers.m_is_instance)
         env = add_instance(env, real_n);
+    if (modifiers.m_is_coercion)
+        env = add_coercion(env, real_n, p.ios());
     return env;
 }
 environment definition_cmd(parser & p) {

src/frontends/lean/token_table.cpp

@@ -73,7 +73,7 @@ token_table init_token_table() {
          {"+", g_plus_prec}, {g_cup, g_cup_prec}, {"->", g_arrow_prec}, {nullptr, 0}};
 
     char const * commands[] = {"theorem", "axiom", "variable", "definition", "coercion",
-                               "variables", "[private]", "[inline]", "[fact]", "[instance]", "[class]", "[module]",
+                               "variables", "[private]", "[inline]", "[fact]", "[instance]", "[class]", "[module]", "[coercion]",
                                "abbreviation", "opaque_hint", "evaluate", "check", "print", "end", "namespace", "section", "import",
                                "abbreviation", "inductive", "record", "structure", "module", "universe",
                                "precedence", "infixl", "infixr", "infix", "postfix", "prefix", "notation",

tests/lean/run/algebra1.lean

@@ -0,0 +1,110 @@
+import standard
+using num
+
+abbreviation Type1 := Type.{1}
+
+section
+  parameter {A  : Type}
+  parameter f   : A → A → A
+  parameter one : A
+  parameter inv : A → A
+  infixl `*`:75     := f
+  postfix `^-1`:100 := inv
+  definition is_assoc := ∀ a b c, (a*b)*c = a*b*c
+  definition is_id    := ∀ a, a*one = a
+  definition is_inv   := ∀ a, a*a^-1 = one
+end
+
+namespace algebra
+  inductive mul_struct (A : Type) : Type :=
+  | mk_mul_struct : (A → A → A) → mul_struct A
+
+  inductive add_struct (A : Type) : Type :=
+  | mk_add_struct : (A → A → A) → add_struct A
+
+  definition mul [inline] {A : Type} {s : mul_struct A} (a b : A)
+  := mul_struct_rec (fun f, f) s a b
+
+  infixl `*`:75 := mul
+
+  definition add [inline] {A : Type} {s : add_struct A} (a b : A)
+  := add_struct_rec (fun f, f) s a b
+
+  infixl `+`:65 := add
+end
+
+namespace nat
+  inductive nat : Type :=
+  | zero : nat
+  | succ : nat → nat
+
+  variable add : nat → nat → nat
+  variable mul : nat → nat → nat
+
+  definition is_mul_struct [inline] [instance] : algebra.mul_struct nat
+  := algebra.mk_mul_struct mul
+
+  definition is_add_struct [inline] [instance] : algebra.add_struct nat
+  := algebra.mk_add_struct add
+
+  definition to_nat (n : num) : nat
+  := #algebra
+    num_rec zero (λ n, pos_num_rec (succ zero) (λ n r, r + r) (λ n r, r + r + succ zero) n) n
+end
+
+namespace algebra
+namespace semigroup
+  inductive semigroup_struct (A : Type) : Type :=
+  | mk_semigroup_struct : Π (mul : A → A → A), is_assoc mul → semigroup_struct A
+
+  definition mul [inline] {A : Type} (s : semigroup_struct A) (a b : A)
+  := semigroup_struct_rec (fun f h, f) s a b
+
+  definition assoc [inline] {A : Type} (s : semigroup_struct A) : is_assoc (mul s)
+  := semigroup_struct_rec (fun f h, h) s
+
+  definition is_mul_struct [inline] [instance] (A : Type) (s : semigroup_struct A) : mul_struct A
+  := mk_mul_struct (mul s)
+
+  inductive semigroup : Type :=
+  | mk_semigroup : Π (A : Type), semigroup_struct A → semigroup
+
+  definition carrier [inline] [coercion] (g : semigroup)
+  := semigroup_rec (fun c s, c) g
+
+  definition is_semigroup [inline] [instance] (g : semigroup) : semigroup_struct (carrier g)
+  := semigroup_rec (fun c s, s) g
+end
+
+namespace monoid
+  inductive monoid_struct (A : Type) : Type :=
+  | mk_monoid_struct : Π (mul : A → A → A) (id : A), is_assoc mul → is_id mul id → monoid_struct A
+
+  definition mul [inline] {A : Type} (s : monoid_struct A) (a b : A)
+  := monoid_struct_rec (fun mul id a i, mul) s a b
+
+  definition assoc [inline] {A : Type} (s : monoid_struct A) : is_assoc (mul s)
+  := monoid_struct_rec (fun mul id a i, a) s
+
+  using algebra.semigroup -- Fix: allow user to write just semigroup
+  definition is_semigroup_struct [inline] [instance] (A : Type) (s : monoid_struct A) : semigroup_struct A
+  := mk_semigroup_struct (mul s) (assoc s)
+
+  inductive monoid : Type :=
+  | mk_monoid : Π (A : Type), monoid_struct A → monoid
+
+  definition carrier [inline] [coercion] (m : monoid)
+  := monoid_rec (fun c s, c) m
+
+  definition is_monoid [inline] [instance] (m : monoid) : monoid_struct (carrier m)
+  := monoid_rec (fun c s, s) m
+end
+end
+
+section
+  using algebra algebra.semigroup algebra.monoid
+  variable M : monoid
+  variables a b c : M
+  check a*b*c*a*b*c*a*b*a*b*c*a
+  check a*b
+end