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feat(library): add if_then_else Lean/C++ interface

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Signed-off-by: Leonardo de Moura <leonardo@microsoft.com>
This commit is contained in:
Leonardo de Moura 2014-01-14 16:10:49 -08:00
parent 8217a544cc
commit 07059b0531
9 changed files with 131 additions and 43 deletions
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9
src/builtin/CMakeLists.txt
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@ -95,7 +95,8 @@ add_theory("Real.lean" "${CMAKE_CURRENT_BINARY_DIR}/Int.olean")
add_theory("specialfn.lean" "${CMAKE_CURRENT_BINARY_DIR}/Real.olean")
add_theory("cast.lean" "${CMAKE_CURRENT_BINARY_DIR}/Nat.olean")
update_interface("kernel.olean" "kernel" "-n")
update_interface("Nat.olean" "library/arith" "-n")
update_interface("Int.olean" "library/arith" "")
update_interface("Real.olean" "library/arith" "")
update_interface("kernel.olean" "kernel" "-n")
update_interface("Nat.olean" "library/arith" "-n")
update_interface("Int.olean" "library/arith" "")
update_interface("Real.olean" "library/arith" "")
update_interface("if_then_else.olean" "library" "")

13
src/builtin/if_then_else.lean
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@ -1,3 +1,5 @@
import macros
-- if_then_else expression support
builtin ite {A : (Type U)} : Bool → A → A → A
notation 60 if _ then _ else _ : ite
@ -25,4 +27,15 @@ theorem if_congr {A : TypeU} {b c : Bool} {x y u v : A} (H_bc : b = c) (H_xu :
... = (if false then u else v) : symm (if_false _ _)
... = (if c then u else v) : { symm (eqf_intro H_nc) })
theorem if_imp_then {a b c : Bool} (H : if a then b else c) : a → b
:= assume Ha : a, eqt_elim (calc b = (if true then b else c) : symm (if_true b c)
... = (if a then b else c) : { symm (eqt_intro Ha) }
... = true : eqt_intro H)
theorem if_imp_else {a b c : Bool} (H : if a then b else c) : ¬ a → c
:= assume Hna : ¬ a, eqt_elim (calc c = (if false then b else c) : symm (if_false b c)
... = (if a then b else c) : { symm (eqf_intro Hna) }
... = true : eqt_intro H)
set_opaque ite true

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src/builtin/obj/if_then_else.olean
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38
src/kernel/builtin.cpp
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@ -78,44 +78,6 @@ bool is_false(expr const & e) {
}
// =======================================
// =======================================
// If-then-else builtin operator
static name g_if_name("ite");
static format g_if_fmt(g_if_name);
/**
\brief Semantic attachment for if-then-else operator with type
<code>Pi (A : Type), Bool -> A -> A -> A</code>
*/
class if_fn_value : public value {
expr m_type;
static expr mk_type() {
expr A = Const("A");
// Pi (A: Type), bool -> A -> A -> A
return Pi({A, TypeU}, Bool >> (A >> (A >> A)));
}
public:
if_fn_value():m_type(mk_type()) {}
virtual ~if_fn_value() {}
virtual expr get_type() const { return m_type; }
virtual name get_name() const { return g_if_name; }
virtual optional<expr> normalize(unsigned num_args, expr const * args) const {
if (num_args == 5 && is_bool_value(args[2]) && is_value(args[3]) && is_value(args[4])) {
if (to_bool(args[2]))
return some_expr(args[3]); // if A true a b --> a
else
return some_expr(args[4]); // if A false a b --> b
} else {
return none_expr();
}
}
virtual void write(serializer & s) const { s << "ite"; }
};
MK_BUILTIN(if_fn, if_fn_value);
MK_IS_BUILTIN(is_if_fn, mk_if_fn());
static register_builtin_fn if_blt("ite", []() { return mk_if_fn(); });
static value::register_deserializer_fn if_ds("ite", [](deserializer & ) { return mk_if_fn(); });
// =======================================
void import_kernel(environment const & env, io_state const & ios) {
env->import("kernel", ios);
}

2
src/library/CMakeLists.txt
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@ -1,6 +1,6 @@
add_library(library kernel_bindings.cpp deep_copy.cpp
context_to_lambda.cpp placeholder.cpp expr_lt.cpp substitution.cpp
fo_unify.cpp bin_op.cpp eq_heq.cpp io_state_stream.cpp printer.cpp
hop_match.cpp)
hop_match.cpp ite.cpp)
target_link_libraries(library ${LEAN_LIBS})

15
src/library/if_then_else_decls.cpp Normal file
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@ -0,0 +1,15 @@
/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
*/
// Automatically generated file, DO NOT EDIT
#include "kernel/environment.h"
#include "kernel/decl_macros.h"
namespace lean {
MK_CONSTANT(if_true_fn, name("if_true"));
MK_CONSTANT(if_false_fn, name("if_false"));
MK_CONSTANT(if_a_a_fn, name("if_a_a"));
MK_CONSTANT(if_congr_fn, name("if_congr"));
MK_CONSTANT(if_imp_then_fn, name("if_imp_then"));
MK_CONSTANT(if_imp_else_fn, name("if_imp_else"));
}

26
src/library/if_then_else_decls.h Normal file
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@ -0,0 +1,26 @@
/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
*/
// Automatically generated file, DO NOT EDIT
#include "kernel/expr.h"
namespace lean {
expr mk_if_true_fn();
bool is_if_true_fn(expr const & e);
inline expr mk_if_true_th(expr const & e1, expr const & e2, expr const & e3) { return mk_app({mk_if_true_fn(), e1, e2, e3}); }
expr mk_if_false_fn();
bool is_if_false_fn(expr const & e);
inline expr mk_if_false_th(expr const & e1, expr const & e2, expr const & e3) { return mk_app({mk_if_false_fn(), e1, e2, e3}); }
expr mk_if_a_a_fn();
bool is_if_a_a_fn(expr const & e);
inline expr mk_if_a_a_th(expr const & e1, expr const & e2, expr const & e3) { return mk_app({mk_if_a_a_fn(), e1, e2, e3}); }
expr mk_if_congr_fn();
bool is_if_congr_fn(expr const & e);
inline expr mk_if_congr_th(expr const & e1, expr const & e2, expr const & e3, expr const & e4, expr const & e5, expr const & e6, expr const & e7, expr const & e8, expr const & e9, expr const & e10) { return mk_app({mk_if_congr_fn(), e1, e2, e3, e4, e5, e6, e7, e8, e9, e10}); }
expr mk_if_imp_then_fn();
bool is_if_imp_then_fn(expr const & e);
inline expr mk_if_imp_then_th(expr const & e1, expr const & e2, expr const & e3, expr const & e4, expr const & e5) { return mk_app({mk_if_imp_then_fn(), e1, e2, e3, e4, e5}); }
expr mk_if_imp_else_fn();
bool is_if_imp_else_fn(expr const & e);
inline expr mk_if_imp_else_th(expr const & e1, expr const & e2, expr const & e3, expr const & e4, expr const & e5) { return mk_app({mk_if_imp_else_fn(), e1, e2, e3, e4, e5}); }
}

55
src/library/ite.cpp Normal file
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@ -0,0 +1,55 @@
/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#include "kernel/builtin.h"
#include "kernel/abstract.h"
#include "kernel/decl_macros.h"
#include "library/if_then_else_decls.h"
#include "library/if_then_else_decls.cpp"
namespace lean {
// =======================================
// If-then-else builtin operator
static name g_if_name("ite");
static format g_if_fmt(g_if_name);
/**
\brief Semantic attachment for if-then-else operator with type
<code>Pi (A : Type), Bool -> A -> A -> A</code>
*/
class if_fn_value : public value {
expr m_type;
static expr mk_type() {
expr A = Const("A");
// Pi (A: Type), bool -> A -> A -> A
return Pi({A, TypeU}, Bool >> (A >> (A >> A)));
}
public:
if_fn_value():m_type(mk_type()) {}
virtual ~if_fn_value() {}
virtual expr get_type() const { return m_type; }
virtual name get_name() const { return g_if_name; }
virtual optional<expr> normalize(unsigned num_args, expr const * args) const {
if (num_args == 5 && is_bool_value(args[2]) && is_value(args[3]) && is_value(args[4])) {
if (to_bool(args[2]))
return some_expr(args[3]); // if A true a b --> a
else
return some_expr(args[4]); // if A false a b --> b
} else {
return none_expr();
}
}
virtual void write(serializer & s) const { s << "ite"; }
};
MK_BUILTIN(if_fn, if_fn_value);
MK_IS_BUILTIN(is_if_fn, mk_if_fn());
static register_builtin_fn if_blt("ite", []() { return mk_if_fn(); });
static value::register_deserializer_fn if_ds("ite", [](deserializer & ) { return mk_if_fn(); });
// =======================================
void import_ite(environment const & env, io_state const & ios) {
env->import("if_then_else", ios);
}
}

16
src/library/ite.h Normal file
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@ -0,0 +1,16 @@
/*
Copyright (c) 2013 Microsoft Corporation. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Author: Leonardo de Moura
*/
#pragma once
#include "kernel/io_state.h"
#include "library/if_then_else_decls.h"
namespace lean {
expr mk_ite_fn();
bool is_ite_fn(expr const & e);
inline expr mk_ite(expr const & e1, expr const & e2, expr const & e3, expr const & e4) { return mk_app(mk_ite_fn, e1, e2, e3, e4); }
void import_ite(environment const & env, io_state const & ios);
}