feat(frontends/lean): use '(* ... *)' instead of '(** ... **)' for script code blocks
Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
parent
028a9bd9bd
commit
ce1213a020
62 changed files with 141 additions and 162 deletions
|
@ -1,7 +1,7 @@
|
|||
-- This example demonstrates how to specify a proof skeleton that contains
|
||||
-- "holes" that must be filled using user-defined tactics.
|
||||
|
||||
(**
|
||||
(*
|
||||
-- Import useful macros for creating tactics
|
||||
import("tactic.lua")
|
||||
|
||||
|
@ -10,7 +10,7 @@ auto = Repeat(OrElse(assumption_tac(), conj_tac(), conj_hyp_tac()))
|
|||
|
||||
conj_hyp = conj_hyp_tac()
|
||||
conj = conj_tac()
|
||||
**)
|
||||
*)
|
||||
|
||||
-- The (by [tactic]) expression is essentially creating a "hole" and associating a "hint" to it.
|
||||
-- The "hint" is a tactic that should be used to fill the "hole".
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(**
|
||||
(*
|
||||
-- This example demonstrates how to create a new tactic using Lua.
|
||||
-- The basic idea is to reimplement the tactic conj_tactic in Lua.
|
||||
|
||||
|
@ -62,10 +62,10 @@
|
|||
end
|
||||
conj_in_lua = tactic(conj_fn) -- Create a new tactic object using the Lua function conj_fn
|
||||
-- Now, the tactic conj_in_lua can be used when proving theorems in Lean.
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T (a b : Bool) : a => b => a /\ b := _.
|
||||
(** Then(Repeat(OrElse(imp_tac(), conj_in_lua)), assumption_tac()) **)
|
||||
(* Then(Repeat(OrElse(imp_tac(), conj_in_lua)), assumption_tac()) *)
|
||||
done
|
||||
|
||||
-- Show proof created using our script
|
||||
|
|
|
@ -380,23 +380,11 @@ scanner::token scanner::read_script_block() {
|
|||
next();
|
||||
if (c1 == '*') {
|
||||
char c2 = curr();
|
||||
next();
|
||||
if (c2 == EOF)
|
||||
throw_exception("unexpected end of script");
|
||||
next();
|
||||
if (c2 == '*') {
|
||||
char c3 = curr();
|
||||
if (c3 == EOF)
|
||||
throw_exception("unexpected end of script");
|
||||
next();
|
||||
if (c3 == ')') {
|
||||
if (c2 == ')') {
|
||||
return token::ScriptBlock;
|
||||
} else {
|
||||
if (c3 == '\n')
|
||||
new_line();
|
||||
m_buffer += c1;
|
||||
m_buffer += c2;
|
||||
m_buffer += c3;
|
||||
}
|
||||
} else {
|
||||
if (c2 == '\n')
|
||||
new_line();
|
||||
|
@ -438,16 +426,10 @@ scanner::token scanner::scan() {
|
|||
return token::Period;
|
||||
}
|
||||
case '(':
|
||||
next();
|
||||
if (curr() == '*') {
|
||||
next();
|
||||
if (curr() == '*') {
|
||||
next();
|
||||
return read_script_block();
|
||||
} else {
|
||||
throw_exception("old comment style");
|
||||
break;
|
||||
}
|
||||
} else {
|
||||
return token::LeftParen;
|
||||
}
|
||||
|
|
|
@ -11,9 +11,9 @@ Theorem T1 (a : Int) : (P a a) => (f a a).
|
|||
done.
|
||||
Variable b : Int
|
||||
Axiom Ax2 (x : Int) : (f x b)
|
||||
(**
|
||||
(*
|
||||
simple_tac = Repeat(OrElse(imp_tac(), assumption_tac(), apply_tac("Ax2"), apply_tac("Ax1")))
|
||||
**)
|
||||
*)
|
||||
Theorem T2 (a : Int) : (P a a) => (f a a).
|
||||
simple_tac.
|
||||
done.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Check @Discharge
|
||||
Theorem T (a b : Bool) : a => b => b => a.
|
||||
apply Discharge.
|
||||
|
|
|
@ -2,17 +2,17 @@ Import tactic
|
|||
|
||||
Theorem T1 (a b : Bool) : a \/ b => b \/ a.
|
||||
apply Discharge.
|
||||
(** disj_hyp_tac() **)
|
||||
(** disj_tac() **)
|
||||
(* disj_hyp_tac() *)
|
||||
(* disj_tac() *)
|
||||
back
|
||||
exact.
|
||||
(** disj_tac() **)
|
||||
(* disj_tac() *)
|
||||
exact.
|
||||
done.
|
||||
|
||||
(**
|
||||
(*
|
||||
simple_tac = Repeat(OrElse(imp_tac(), assumption_tac(), disj_hyp_tac(), disj_tac())) .. now_tac()
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T2 (a b : Bool) : a \/ b => b \/ a.
|
||||
simple_tac.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Variables a b c : Bool
|
||||
Axiom H : a \/ b
|
||||
Theorem T (a b : Bool) : a \/ b => b \/ a.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("find.lua") **)
|
||||
(* import("find.lua") *)
|
||||
Find "^.ongr"
|
||||
Find "foo"
|
||||
Find "(ab"
|
|
@ -1,9 +1,9 @@
|
|||
(**
|
||||
(*
|
||||
-- The elaborator does not expand definitions marked as 'opaque'.
|
||||
-- To be able to prove the following theorem, we have to unmark the
|
||||
-- 'forall'
|
||||
local env = get_environment()
|
||||
env:set_opaque("forall", false)
|
||||
**)
|
||||
*)
|
||||
Theorem ForallIntro2 (A : (Type U)) (P : A -> Bool) (H : Pi x, P x) : forall x, P x :=
|
||||
Abst (fun x, EqTIntro (H x))
|
||||
|
|
|
@ -1,12 +1,12 @@
|
|||
Theorem T2 (a b : Bool) : a => b => a /\ b.
|
||||
done.
|
||||
done.
|
||||
(** imp_tac() **).
|
||||
(* imp_tac() *).
|
||||
imp_tac2.
|
||||
foo.
|
||||
(** imp_tac() **).
|
||||
(** imp_tac() **).
|
||||
(** conj_tac() **).
|
||||
(* imp_tac() *).
|
||||
(* imp_tac() *).
|
||||
(* conj_tac() *).
|
||||
back.
|
||||
(** assumption_tac() **).
|
||||
(* assumption_tac() *).
|
||||
done.
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
(**
|
||||
(*
|
||||
simple_tac = Repeat(OrElse(conj_hyp_tac(), conj_tac(), assumption_tac()))
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T2 (A B : Bool) : A /\ B => B /\ A :=
|
||||
Discharge (fun H : A /\ B,
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
(**
|
||||
(*
|
||||
auto = Repeat(OrElse(conj_hyp_tac(), conj_tac(), assumption_tac()))
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T2 (A B : Bool) : A /\ B -> B /\ A :=
|
||||
fun assumption : A /\ B,
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
(**
|
||||
(*
|
||||
import("tactic.lua")
|
||||
-- Define a simple tactic using Lua
|
||||
auto = Repeat(OrElse(assumption_tac(), conj_tac(), conj_hyp_tac()))
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
|
||||
fun assumption : A /\ B,
|
||||
|
|
|
@ -1,7 +1,7 @@
|
|||
(**
|
||||
(*
|
||||
-- Define a simple tactic using Lua
|
||||
auto = Repeat(OrElse(assumption_tac(), conj_tac(), conj_hyp_tac()))
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T1 (A B : Bool) : A /\ B -> B /\ A :=
|
||||
fun assumption : A /\ B,
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
Theorem T2 (a b : Bool) : a => b => a /\ b.
|
||||
(** imp_tac() **)
|
||||
(** imp_tac2() **)
|
||||
(* imp_tac() *)
|
||||
(* imp_tac2() *)
|
||||
foo.
|
||||
(** imp_tac() **)
|
||||
(* imp_tac() *)
|
||||
abort.
|
||||
|
||||
Variables a b : Bool.
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
|
||||
Theorem T2 (a b : Bool) : b => a \/ b.
|
||||
(** imp_tac() **).
|
||||
(** disj_tac() **).
|
||||
(* imp_tac() *).
|
||||
(* disj_tac() *).
|
||||
back.
|
||||
back.
|
||||
exact.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Axiom magic (a : Bool) : a.
|
||||
|
||||
Theorem T (a : Bool) : a.
|
||||
|
|
|
@ -1,7 +1,7 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T1 (a b : Bool) : a => b => a /\ b.
|
||||
(** imp_tac() **).
|
||||
(** imp_tac() **).
|
||||
(* imp_tac() *).
|
||||
(* imp_tac() *).
|
||||
apply Conj.
|
||||
exact.
|
||||
done.
|
||||
|
|
|
@ -1,11 +1,11 @@
|
|||
Import Int.
|
||||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Variable q : Int -> Int -> Bool.
|
||||
Variable p : Int -> Bool.
|
||||
Axiom Ax (a b : Int) (H : q a b) : p b.
|
||||
Variable a : Int.
|
||||
Theorem T (x : Int) : (q a x) => (p x).
|
||||
(** imp_tac() **).
|
||||
(* imp_tac() *).
|
||||
apply (Ax a).
|
||||
exact.
|
||||
done.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
SetOption tactic::proof_state::goal_names true.
|
||||
Theorem T (a : Bool) : a => a /\ a.
|
||||
apply Discharge.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T1 (A B : Bool) : A /\ B => B /\ A :=
|
||||
Discharge (fun H : A /\ B,
|
||||
let main : B /\ A :=
|
||||
|
@ -16,9 +16,9 @@ Theorem T1 (A B : Bool) : A /\ B => B /\ A :=
|
|||
exact.
|
||||
done.
|
||||
|
||||
(**
|
||||
(*
|
||||
simple_tac = Repeat(OrElse(conj_hyp_tac(), conj_tac(), assumption_tac()))
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T2 (A B : Bool) : A /\ B => B /\ A :=
|
||||
Discharge (fun H : A /\ B,
|
||||
|
|
|
@ -1,11 +1,11 @@
|
|||
(**
|
||||
(*
|
||||
-- This example ask uses the parses to process a Lean string that
|
||||
-- contains a nested script block. The nexted script block will
|
||||
-- invoke the leanlua_state recursively. It also demonstrates that we
|
||||
-- need to use std::recursive_mutex instead of std::mutex at
|
||||
-- leanlua_state. Otherwise, it will deadlock trying to get a lock on
|
||||
-- the mutex.
|
||||
code = "(*" .. "*" .. "print('hello')" .. "*" .. "*)"
|
||||
code = "(" .. "*" .. "print('hello')" .. "*" .. ")"
|
||||
print("executing: " .. code)
|
||||
parse_lean_cmds(code)
|
||||
**)
|
||||
*)
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
Set: pp::colors
|
||||
Set: pp::unicode
|
||||
executing: (**print('hello')**)
|
||||
executing: (*print('hello')*)
|
||||
hello
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
Import Int.
|
||||
|
||||
(**
|
||||
(*
|
||||
function add_paren(code)
|
||||
return "(" .. "** " .. code .. " **" .. ")"
|
||||
return "(" .. "* " .. code .. " *" .. ")"
|
||||
end
|
||||
parse_lean_cmds(add_paren([[
|
||||
local env = get_environment()
|
||||
|
@ -10,4 +10,4 @@ Import Int.
|
|||
print(env:find_object("x"))
|
||||
]]))
|
||||
print("done")
|
||||
**)
|
||||
*)
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
Import Int.
|
||||
Variable x : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
print("hello world from Lua")
|
||||
**)
|
||||
*)
|
||||
|
||||
Variable y : Int
|
||||
|
|
|
@ -1,8 +1,7 @@
|
|||
|
||||
Variables x1 x2 x3 : Bool
|
||||
Definition F : Bool := x1 /\ (x2 \/ x3)
|
||||
|
||||
(**
|
||||
(*
|
||||
local env = get_environment()
|
||||
local F = env:find_object("F"):get_value()
|
||||
print(F)
|
||||
|
@ -15,5 +14,4 @@ Definition F : Bool := x1 /\ (x2 \/ x3)
|
|||
|
||||
print(expr_size(F))
|
||||
|
||||
**)
|
||||
|
||||
*)
|
||||
|
|
|
@ -1,5 +1,5 @@
|
|||
Import Int.
|
||||
(**
|
||||
(*
|
||||
|
||||
local env = get_environment()
|
||||
local o1 = env:find_object(name("Int", "add"))
|
||||
|
@ -49,4 +49,4 @@ Import Int.
|
|||
assert(env:find_object("Refl"):is_axiom())
|
||||
assert(env:find_object(name("Int", "sub")):is_definition())
|
||||
assert(env:find_object("x"):is_var_decl())
|
||||
**)
|
||||
*)
|
||||
|
|
|
@ -1,7 +1,7 @@
|
|||
Import Int.
|
||||
Variables x y z : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
import("util.lua")
|
||||
local env = get_environment()
|
||||
local plus = Const{"Int", "add"}
|
||||
|
@ -9,6 +9,6 @@ Variables x y z : Int
|
|||
local def = plus(plus(x, y), iVal(1000))
|
||||
print(def, ":", env:type_check(def))
|
||||
env:add_definition("sum", def)
|
||||
**)
|
||||
*)
|
||||
|
||||
Eval sum + 3
|
||||
|
|
|
@ -2,7 +2,7 @@ Import Int.
|
|||
Variables x y z : Int
|
||||
Variable f : Int -> Int -> Int
|
||||
|
||||
(**
|
||||
(*
|
||||
local t = parse_lean("fun w, f w (f y 0)")
|
||||
print(t)
|
||||
assert(t:closed())
|
||||
|
@ -11,4 +11,4 @@ Variable f : Int -> Int -> Int
|
|||
assert(not b:closed())
|
||||
local env = get_environment()
|
||||
assert(env:find_object("Int"):get_name() == name("Int"))
|
||||
**)
|
||||
*)
|
||||
|
|
|
@ -2,7 +2,7 @@ Import Int.
|
|||
Variables x y z : Int
|
||||
Variable f : Int -> Int -> Int
|
||||
|
||||
(**
|
||||
(*
|
||||
local t = parse_lean("fun w, f w (f y 0)")
|
||||
print(t)
|
||||
assert(t:closed())
|
||||
|
@ -17,6 +17,6 @@ Variable f : Int -> Int -> Int
|
|||
Variable g : Int -> Int
|
||||
]])
|
||||
|
||||
**)
|
||||
*)
|
||||
|
||||
Check g (f x 10)
|
||||
|
|
|
@ -2,7 +2,7 @@ Import Int.
|
|||
Variables i j : Int
|
||||
Variable p : Bool
|
||||
|
||||
(**
|
||||
(*
|
||||
local env = get_environment()
|
||||
ok, ex = pcall(
|
||||
function()
|
||||
|
@ -12,4 +12,4 @@ Variable p : Bool
|
|||
assert(is_exception(ex))
|
||||
print(ex:what())
|
||||
ex:rethrow()
|
||||
**)
|
||||
*)
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
Import Int.
|
||||
Variables a b : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
local ios = io_state()
|
||||
ios:print(parse_lean("a + b"))
|
||||
print(parse_lean("a + b"))
|
||||
**)
|
||||
*)
|
|
@ -1,7 +1,7 @@
|
|||
Import Int.
|
||||
Variables a b : Int
|
||||
Show Options
|
||||
(**
|
||||
(*
|
||||
local ios = io_state()
|
||||
|
||||
print(get_options())
|
||||
|
@ -9,6 +9,6 @@ Show Options
|
|||
ios:print(parse_lean("a + b"))
|
||||
print(parse_lean("fun x, a + x"))
|
||||
print(get_options())
|
||||
**)
|
||||
*)
|
||||
Show Options
|
||||
Show Environment 2
|
|
@ -1,5 +1,5 @@
|
|||
Import Int.
|
||||
(**
|
||||
(*
|
||||
macro("MyMacro", { macro_arg.Expr, macro_arg.Comma, macro_arg.Expr },
|
||||
function (env, e1, e2)
|
||||
return Const({"Int", "add"})(e1, e2)
|
||||
|
@ -16,7 +16,7 @@ macro("Sum", { macro_arg.Exprs },
|
|||
end
|
||||
return r
|
||||
end)
|
||||
**)
|
||||
*)
|
||||
|
||||
Show (MyMacro 10, 20) + 20
|
||||
Show (Sum)
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
Variable x : Bool
|
||||
|
||||
(**
|
||||
(*
|
||||
a = {}
|
||||
print("hello world")
|
||||
print ("ok")
|
||||
|
@ -9,7 +9,6 @@ Variable x : Bool
|
|||
y = 20
|
||||
}
|
||||
rint ("ok")
|
||||
**)
|
||||
*)
|
||||
|
||||
Variable y : Bool
|
||||
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
Import Int.
|
||||
Variable x : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
dofile("script.lua")
|
||||
**)
|
||||
*)
|
|
@ -1,7 +1,7 @@
|
|||
Import Int.
|
||||
Variable x : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
-- Add a variable to the environment using Lua
|
||||
-- The type of the new variable is equal to the type
|
||||
-- of x
|
||||
|
@ -9,6 +9,6 @@ local env = get_environment()
|
|||
typeofx = env:type_check(Const("x"))
|
||||
print("type of x is " .. tostring(typeofx))
|
||||
env:add_var("y", typeofx)
|
||||
**)
|
||||
*)
|
||||
|
||||
Check x + y
|
||||
|
|
|
@ -1,7 +1,7 @@
|
|||
Import Int.
|
||||
Variable x : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
local N = 100
|
||||
local env = get_environment()
|
||||
-- Create N variables with the same type of x
|
||||
|
@ -9,7 +9,7 @@ typeofx = env:type_check(Const("x"))
|
|||
for i = 1, N do
|
||||
env:add_var("y_" .. i, typeofx)
|
||||
end
|
||||
**)
|
||||
*)
|
||||
|
||||
Show Environment 101
|
||||
Check x + y_1 + y_2
|
|
@ -1,20 +1,20 @@
|
|||
Import Int.
|
||||
Variable x : Int
|
||||
SetOption pp::notation false
|
||||
(**
|
||||
(*
|
||||
print(get_options())
|
||||
**)
|
||||
*)
|
||||
Check x + 2
|
||||
(**
|
||||
(*
|
||||
o = get_options()
|
||||
o = o:update(name('lean', 'pp', 'notation'), true)
|
||||
set_options(o)
|
||||
print(get_options())
|
||||
**)
|
||||
*)
|
||||
Check x + 2
|
||||
(**
|
||||
(*
|
||||
set_option(name('lean', 'pp', 'notation'), false)
|
||||
print(get_options())
|
||||
**)
|
||||
*)
|
||||
Variable y : Int
|
||||
Check x + y
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
(**
|
||||
(*
|
||||
x = Const("x")
|
||||
y = Const("y")
|
||||
N = Const("N")
|
||||
print(fun({{x, N}, {y, N}}, x))
|
||||
**)
|
||||
*)
|
|
@ -1,7 +1,7 @@
|
|||
Import Int.
|
||||
Variable x : Int
|
||||
|
||||
(**
|
||||
(*
|
||||
local env = get_environment()
|
||||
ty_x = env:type_check(Const("x"))
|
||||
c = context()
|
||||
|
@ -12,4 +12,4 @@ o = env:find_object("x")
|
|||
print(o)
|
||||
o = env:find_object("y")
|
||||
print(o)
|
||||
**)
|
||||
*)
|
|
@ -1,7 +1,7 @@
|
|||
Import Int.
|
||||
Variable x : Bool
|
||||
|
||||
(**
|
||||
(*
|
||||
import("util.lua")
|
||||
local env = get_environment()
|
||||
local Int = Const("Int")
|
||||
|
@ -31,7 +31,7 @@ Variable x : Bool
|
|||
print(s)
|
||||
print(env:type_check(s))
|
||||
env:add_definition("sum1", s)
|
||||
**)
|
||||
*)
|
||||
|
||||
Show Environment 1
|
||||
Eval sum1
|
||||
|
|
|
@ -1,11 +1,11 @@
|
|||
Import cast
|
||||
Import cast
|
||||
(**
|
||||
(*
|
||||
local env = environment() -- create new environment
|
||||
parse_lean_cmds([[
|
||||
Import cast
|
||||
Import cast
|
||||
Check @cast
|
||||
]], env)
|
||||
**)
|
||||
*)
|
||||
Check @cast
|
|
@ -1,4 +1,4 @@
|
|||
(**
|
||||
(*
|
||||
cmd_macro("Simple",
|
||||
{ macro_arg.String },
|
||||
function (env, str)
|
||||
|
@ -9,12 +9,12 @@ cmd_macro("Simple",
|
|||
parse_lean_cmds([[
|
||||
Simple "foo"
|
||||
]])
|
||||
**)
|
||||
*)
|
||||
|
||||
Simple "testing"
|
||||
|
||||
(**
|
||||
(*
|
||||
parse_lean_cmds([[
|
||||
Simple "bla"
|
||||
]])
|
||||
**)
|
||||
*)
|
||||
|
|
|
@ -10,4 +10,4 @@ Definition D := read V1 1 (by trivial)
|
|||
Show Environment 1
|
||||
Variable b : Bool
|
||||
Definition a := b
|
||||
Theorem T : b => a := (by (** imp_tac() .. normalize_tac() .. assumption_tac() **))
|
||||
Theorem T : b => a := (by (* imp_tac() .. normalize_tac() .. assumption_tac() *))
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T (C A B : Bool) : C -> A -> B -> A.
|
||||
exact.
|
||||
done.
|
||||
|
|
|
@ -2,7 +2,7 @@ Import Int.
|
|||
Definition double {A : Type} (f : A -> A) : A -> A := fun x, f (f x).
|
||||
Definition big {A : Type} (f : A -> A) : A -> A := (double (double (double (double (double (double (double f))))))).
|
||||
|
||||
(**
|
||||
(*
|
||||
|
||||
-- Tactic for trying to prove goal using Reflexivity, Congruence and available assumptions
|
||||
local congr_tac = Repeat(OrElse(apply_tac("Refl"), apply_tac("Congr"), assumption_tac()))
|
||||
|
@ -18,7 +18,7 @@ eager_tac = Then(-- unfold homogeneous equality
|
|||
lazy_tac = OrElse(Then(Try(unfold_tac("eq")), congr_tac, now_tac()),
|
||||
eager_tac)
|
||||
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T1 (a b : Int) (f : Int -> Int) (H : a = b) : (big f a) = (big f b).
|
||||
eager_tac.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T (A : Type) (p : A -> Bool) (f : A -> A -> A) : forall x y z, p (f x x) => x = y => x = z => p (f y z).
|
||||
apply ForallIntro.
|
||||
beta.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("macros.lua") **)
|
||||
(* import("macros.lua") *)
|
||||
|
||||
Theorem T (A : Type) (p : A -> Bool) (f : A -> A -> A) : forall x y z, p (f x x) => x = y => x = z => p (f y z) :=
|
||||
For x y z, Assume (H1 : p (f x x)) (H2 : x = y) (H3 : x = z),
|
||||
|
|
|
@ -1,11 +1,11 @@
|
|||
Variables p q r : Bool
|
||||
|
||||
(**
|
||||
(*
|
||||
local env = get_environment()
|
||||
local conjecture = parse_lean('p => q => p && q')
|
||||
local tac = Repeat(conj_tac() ^ imp_tac() ^ assumption_tac())
|
||||
local proof = tac:solve(env, context(), conjecture)
|
||||
env:add_theorem("T1", conjecture, proof)
|
||||
**)
|
||||
*)
|
||||
|
||||
Show Environment 1.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Definition f(a : Bool) : Bool := not a.
|
||||
Definition g(a b : Bool) : Bool := a \/ b.
|
||||
|
||||
|
@ -11,9 +11,9 @@ Theorem T1 (a b : Bool) : (g a b) => (f b) => a := _.
|
|||
absurd
|
||||
done.
|
||||
|
||||
(**
|
||||
(*
|
||||
simple_tac = Repeat(unfold_tac()) .. Repeat(OrElse(imp_tac(), conj_hyp_tac(), assumption_tac(), absurd_tac(), conj_hyp_tac(), disj_hyp_tac()))
|
||||
**)
|
||||
*)
|
||||
|
||||
Definition h(a b : Bool) : Bool := g a b.
|
||||
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T (a b : Bool) : ((fun x, x /\ b) a) => ((fun x, x) a) := _ .
|
||||
beta.
|
||||
apply Discharge.
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T (a b : Bool) : ((fun x, x /\ b) a) => ((fun x, x) a).
|
||||
beta.
|
||||
apply Discharge.
|
||||
|
|
|
@ -1,15 +1,15 @@
|
|||
Import Int.
|
||||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Variable f : Int -> Int -> Int
|
||||
|
||||
(**
|
||||
(*
|
||||
refl_tac = apply_tac("Refl")
|
||||
congr_tac = apply_tac("Congr")
|
||||
symm_tac = apply_tac("Symm")
|
||||
trans_tac = apply_tac("Trans")
|
||||
unfold_homo_eq_tac = unfold_tac("eq")
|
||||
auto = unfold_homo_eq_tac .. Repeat(OrElse(refl_tac, congr_tac, assumption_tac(), Then(symm_tac, assumption_tac(), now_tac())))
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T1 (a b c : Int) (H1 : a = b) (H2 : a = c) : (f (f a a) b) = (f (f b c) a).
|
||||
auto.
|
||||
|
|
|
@ -1,10 +1,10 @@
|
|||
Import Int.
|
||||
(**
|
||||
(*
|
||||
|
||||
-- Tactic for trying to prove goal using Reflexivity, Congruence and available assumptions
|
||||
congr_tac = Try(unfold_tac("eq")) .. Repeat(OrElse(apply_tac("Refl"), apply_tac("Congr"), assumption_tac()))
|
||||
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T1 (a b : Int) (f : Int -> Int) : a = b -> (f (f a)) = (f (f b)) :=
|
||||
fun assumption : a = b,
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Variables p q r : Bool
|
||||
|
||||
Theorem T1 : p => q => p /\ q :=
|
||||
|
@ -13,9 +13,9 @@ Theorem T1 : p => q => p /\ q :=
|
|||
exact -- solve second metavar
|
||||
done
|
||||
|
||||
(**
|
||||
(*
|
||||
simple_tac = Repeat(imp_tac() ^ conj_tac() ^ assumption_tac())
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T2 : p => q => p /\ q /\ p := _.
|
||||
simple_tac
|
||||
|
@ -24,7 +24,7 @@ Theorem T2 : p => q => p /\ q /\ p := _.
|
|||
Show Environment 1
|
||||
|
||||
Theorem T3 : p => p /\ q => r => q /\ r /\ p := _.
|
||||
(** Repeat(OrElse(imp_tac(), conj_tac(), conj_hyp_tac(), assumption_tac())) **)
|
||||
(* Repeat(OrElse(imp_tac(), conj_tac(), conj_hyp_tac(), assumption_tac())) *)
|
||||
done
|
||||
|
||||
-- Display proof term generated by previous tac
|
||||
|
|
|
@ -1,8 +1,8 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Variables p q r : Bool
|
||||
|
||||
Theorem T1 : p => p /\ q => r => q /\ r /\ p := _.
|
||||
(** Repeat(OrElse(imp_tac(), conj_tac(), conj_hyp_tac(), assumption_tac())) **)
|
||||
(* Repeat(OrElse(imp_tac(), conj_tac(), conj_hyp_tac(), assumption_tac())) *)
|
||||
done
|
||||
|
||||
-- Display proof term generated by previous tactic
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
(**
|
||||
(*
|
||||
simple_tac = Repeat(OrElse(imp_tac(), conj_tac())) .. assumption_tac()
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T4 (a b : Bool) : a => b => a /\ b := _.
|
||||
simple_tac
|
||||
|
|
|
@ -1,6 +1,6 @@
|
|||
(**
|
||||
(*
|
||||
simple_tac = Repeat(OrElse(imp_tac(), conj_tac())) .. assumption_tac()
|
||||
**)
|
||||
*)
|
||||
|
||||
Theorem T4 (a b : Bool) : a => b => a /\ b /\ a := _.
|
||||
simple_tac
|
||||
|
|
|
@ -1,10 +1,10 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T (a b c : Bool): a => b /\ c => c /\ a /\ b := _.
|
||||
apply Discharge
|
||||
apply Discharge
|
||||
conj_hyp
|
||||
apply Conj
|
||||
(** Focus(Then(show_tac(), conj_tac(), show_tac(), assumption_tac()), 2) **)
|
||||
(* Focus(Then(show_tac(), conj_tac(), show_tac(), assumption_tac()), 2) *)
|
||||
exact
|
||||
done
|
||||
|
||||
|
@ -13,10 +13,10 @@ Theorem T2 (a b c : Bool): a => b /\ c => c /\ a /\ b := _.
|
|||
apply Discharge
|
||||
conj_hyp
|
||||
apply Conj
|
||||
(** show_tac() **)
|
||||
(** Focus(Then(show_tac(), conj_tac(), Focus(assumption_tac(), 1)), 2) **)
|
||||
(** show_tac() **)
|
||||
(** Focus(assumption_tac(), 1) **)
|
||||
(** show_tac() **)
|
||||
(** Focus(assumption_tac(), 1) **)
|
||||
(* show_tac() *)
|
||||
(* Focus(Then(show_tac(), conj_tac(), Focus(assumption_tac(), 1)), 2) *)
|
||||
(* show_tac() *)
|
||||
(* Focus(assumption_tac(), 1) *)
|
||||
(* show_tac() *)
|
||||
(* Focus(assumption_tac(), 1) *)
|
||||
done
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Theorem T (a b : Bool) : a \/ b => (not b) => a := _.
|
||||
apply Discharge
|
||||
apply Discharge
|
||||
|
|
|
@ -1,4 +1,4 @@
|
|||
(** import("tactic.lua") **)
|
||||
(* import("tactic.lua") *)
|
||||
Definition f(a : Bool) : Bool := not a.
|
||||
|
||||
Theorem T (a b : Bool) : a \/ b => (f b) => a := _.
|
||||
|
|
Loading…
Reference in a new issue