integrate lambda expressions

Signed-off-by: Nikolaj Bjorner <nbjorner@microsoft.com>

src/api/z3_api.h

@@ -482,6 +482,10 @@ typedef enum
        T1: (~ p q)
        [quant-intro T1]: (~ (forall (x) p) (forall (x) q))
 
+   - Z3_OP_PR_BIND: Given a proof p, produces a proof of lambda x . p, where x are free variables in p.
+       T1: f
+       [proof-bind T1] forall (x) f
+
    - Z3_OP_PR_DISTRIBUTIVITY: Distributivity proof object.
           Given that f (= or) distributes over g (= and), produces a proof for
 
@@ -1109,6 +1113,7 @@ typedef enum {
     Z3_OP_PR_TRANSITIVITY_STAR,
     Z3_OP_PR_MONOTONICITY,
     Z3_OP_PR_QUANT_INTRO,
+    Z3_OP_PR_BIND,
     Z3_OP_PR_DISTRIBUTIVITY,
     Z3_OP_PR_AND_ELIM,
     Z3_OP_PR_NOT_OR_ELIM,
@@ -1857,7 +1862,6 @@ extern "C" {
     */
     Z3_sort Z3_API Z3_mk_array_sort_n(Z3_context c, unsigned n, Z3_sort const * domain, Z3_sort range);
 
-
     /**
        \brief Create a tuple type.
 
@@ -2946,6 +2950,8 @@ extern "C" {
     */
     Z3_ast Z3_API Z3_mk_select(Z3_context c, Z3_ast a, Z3_ast i);
 
+    
+
     /**
        \brief n-ary Array read.
        The argument \c a is the array and \c idxs are the indices of the array that gets read.
@@ -2955,6 +2961,7 @@ extern "C" {
     */
     Z3_ast Z3_API Z3_mk_select_n(Z3_context c, Z3_ast a, unsigned n, Z3_ast const* idxs);
 
+
     /**
        \brief Array update.
 
@@ -2973,6 +2980,7 @@ extern "C" {
     */
     Z3_ast Z3_API Z3_mk_store(Z3_context c, Z3_ast a, Z3_ast i, Z3_ast v);
 
+
     /**
        \brief n-ary Array update.
 
@@ -3763,6 +3771,54 @@ extern "C" {
         Z3_ast body
         );
 
+    /**
+       \brief Create a lambda expression. It taks an expression \c body that contains bound variables 
+       of the same sorts as the sorts listed in the array \c sorts. The bound variables are de-Bruijn indices created
+       using #Z3_mk_bound. The array \c decl_names contains the names that the quantified formula uses for the
+       bound variables. Z3 applies the convention that the last element in the \c decl_names and \c sorts array
+       refers to the variable with index 0, the second to last element of \c decl_names and \c sorts refers
+       to the variable with index 1, etc.
+       The sort of the resulting expression is \c (Array sorts range) where \c range is the sort of \c body.
+       For example, if the lambda binds two variables of sort \c Int and \c Bool, and the \c body has sort \c Real, 
+       the sort of the expression is \c (Array Int Bool Real).
+
+       \param c logical context
+       \param num_decls number of variables to be bound.
+       \param sorts the sorts of the bound variables.
+       \param decl_names names of the bound variables
+       \param body the body of the lambda expression.       
+
+       \sa Z3_mk_bound
+       \sa Z3_mk_forall
+       \sa Z3_mk_lambda_const
+
+       def_API('Z3_mk_lambda', AST, (_in(CONTEXT), _in(UINT), _in_array(1, SORT), _in_array(1, SYMBOL), _in(AST)))
+    */
+    Z3_ast Z3_API Z3_mk_lambda(Z3_context c, 
+                               unsigned num_decls, Z3_sort const sorts[],
+                               Z3_symbol const decl_names[],
+                               Z3_ast body);
+
+    /**
+       \brief Create a lambda expression using a list of constants that form the set
+       of bound variables
+
+       \param c logical context.
+       \param num_bound number of constants to be abstracted into bound variables.
+       \param bound array of constants to be abstracted into bound variables.
+       \param body the body of the lambda expression.
+
+       \sa Z3_mk_bound
+       \sa Z3_mk_forall
+       \sa Z3_mk_lambda
+
+       def_API('Z3_mk_lambda_const', AST, (_in(CONTEXT), _in(UINT), _in_array(1, APP), _in(AST)))
+    */
+    Z3_ast Z3_API Z3_mk_lambda_const(Z3_context c, 
+                                     unsigned num_bound, Z3_app const bound[],
+                                     Z3_ast body);
+
+
     /*@}*/
 
     /** @name Accessors */
@@ -4529,14 +4585,29 @@ extern "C" {
     unsigned Z3_API Z3_get_index_value(Z3_context c, Z3_ast a);
 
     /**
-       \brief Determine if quantifier is universal.
-
-       \pre Z3_get_ast_kind(a) == Z3_QUANTIFIER_AST
+       \brief Determine if an ast is a universal quantifier.
 
        def_API('Z3_is_quantifier_forall', BOOL, (_in(CONTEXT), _in(AST)))
     */
     Z3_bool Z3_API Z3_is_quantifier_forall(Z3_context c, Z3_ast a);
 
+    /**
+       \brief Determine if ast is an existential quantifier.
+
+
+       def_API('Z3_is_quantifier_exists', BOOL, (_in(CONTEXT), _in(AST)))
+    */
+    Z3_bool Z3_API Z3_is_quantifier_exists(Z3_context c, Z3_ast a);
+
+    /**
+       \brief Determine if ast is a lambda expresion.
+
+       \pre Z3_get_ast_kind(a) == Z3_QUANTIFIER_AST
+
+       def_API('Z3_is_lambda', BOOL, (_in(CONTEXT), _in(AST)))
+    */
+    Z3_bool Z3_API Z3_is_lambda(Z3_context c, Z3_ast a);
+
     /**
        \brief Obtain weight of quantifier.