feat(library): add goodies for binary functions

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

src/library/CMakeLists.txt

@@ -1,5 +1,5 @@
 add_library(library deep_copy.cpp expr_lt.cpp io_state.cpp
-  occurs.cpp kernel_bindings.cpp io_state_stream.cpp)
+  occurs.cpp kernel_bindings.cpp io_state_stream.cpp bin_app.cpp)
 # placeholder.cpp fo_unify.cpp hop_match.cpp)
 
 target_link_libraries(library ${LEAN_LIBS})

src/library/bin_app.cpp

@@ -0,0 +1,51 @@
+/*
+Copyright (c) 2014 Microsoft Corporation. All rights reserved.
+Released under Apache 2.0 license as described in the file LICENSE.
+
+Author: Leonardo de Moura
+*/
+#include "library/bin_app.h"
+
+namespace lean {
+bool is_bin_app(expr const & t, expr const & f, expr & lhs, expr & rhs) {
+    if (is_app(t) && is_app(app_fn(t)) && app_fn(app_fn(t)) == f) {
+        lhs = app_arg(app_fn(t));
+        rhs = app_arg(t);
+        return true;
+    } else {
+        return false;
+    }
+}
+
+expr mk_bin_rop(expr const & op, expr const & unit, unsigned num_args, expr const * args) {
+    if (num_args == 0) {
+        return unit;
+    } else {
+        expr r = args[num_args - 1];
+        unsigned i = num_args - 1;
+        while (i > 0) {
+            --i;
+            r = mk_app(op, args[i], r);
+        }
+        return r;
+    }
+}
+expr mk_bin_rop(expr const & op, expr const & unit, std::initializer_list<expr> const & l) {
+    return mk_bin_rop(op, unit, l.size(), l.begin());
+}
+
+expr mk_bin_lop(expr const & op, expr const & unit, unsigned num_args, expr const * args) {
+    if (num_args == 0) {
+        return unit;
+    } else {
+        expr r = args[0];
+        for (unsigned i = 1; i < num_args; i++) {
+            r = mk_app(op, r, args[i]);
+        }
+        return r;
+    }
+}
+expr mk_bin_lop(expr const & op, expr const & unit, std::initializer_list<expr> const & l) {
+    return mk_bin_lop(op, unit, l.size(), l.begin());
+}
+}

src/library/bin_app.h

@@ -0,0 +1,27 @@
+/*
+Copyright (c) 2014 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/expr.h"
+
+namespace lean {
+/** \brief Return true iff \c t is of the form <tt>((f s1) s2)</tt>, if the result is true, then store a1 -> lhs, a2 -> rhs */
+bool is_bin_app(expr const & t, expr const & f, expr & lhs, expr & rhs);
+
+/**
+   \brief Return unit if <tt>num_args == 0</tt>, args[0] if <tt>num_args == 1</tt>, and
+   <tt>(op args[0] (op args[1] (op ... )))</tt>
+*/
+expr mk_bin_rop(expr const & op, expr const & unit, unsigned num_args, expr const * args);
+expr mk_bin_rop(expr const & op, expr const & unit, std::initializer_list<expr> const & l);
+
+/**
+   \brief Return unit if <tt>num_args == 0</tt>, args[0] if <tt>num_args == 1</tt>, and
+   <tt>(op ... (op (op args[0] args[1]) args[2]) ...)</tt>
+*/
+expr mk_bin_lop(expr const & op, expr const & unit, unsigned num_args, expr const * args);
+expr mk_bin_lop(expr const & op, expr const & unit, std::initializer_list<expr> const & l);
+}