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|
(************************************************************************)
(* v * The Coq Proof Assistant / The Coq Development Team *)
(* <O___,, * INRIA - CNRS - LIX - LRI - PPS - Copyright 1999-2016 *)
(* \VV/ **************************************************************)
(* // * This file is distributed under the terms of the *)
(* * GNU Lesser General Public License Version 2.1 *)
(************************************************************************)
open Names
open Term
open Coqlib
(** High-order patterns *)
(** Given a term with second-order variables in it,
represented by Meta's, and possibly applied using SoApp
terms, this function will perform second-order, binding-preserving,
matching, in the case where the pattern is a pattern in the sense
of Dale Miller.
ALGORITHM:
Given a pattern, we decompose it, flattening casts and apply's,
recursing on all operators, and pushing the name of the binder each
time we descend a binder.
When we reach a first-order variable, we ask that the corresponding
term's free-rels all be higher than the depth of the current stack.
When we reach a second-order application, we ask that the
intersection of the free-rels of the term and the current stack be
contained in the arguments of the application *)
(** I implemented the following functions which test whether a term [t]
is an inductive but non-recursive type, a general conjuction, a
general disjunction, or a type with no constructors.
They are more general than matching with [or_term], [and_term], etc,
since they do not depend on the name of the type. Hence, they
also work on ad-hoc disjunctions introduced by the user.
(Eduardo, 6/8/97). *)
type 'a matching_function = constr -> 'a option
type testing_function = constr -> bool
val match_with_non_recursive_type : (constr * constr list) matching_function
val is_non_recursive_type : testing_function
(** Non recursive type with no indices and exactly one argument for each
constructor; canonical definition of n-ary disjunction if strict *)
val match_with_disjunction : ?strict:bool -> ?onlybinary:bool -> (constr * constr list) matching_function
val is_disjunction : ?strict:bool -> ?onlybinary:bool -> testing_function
(** Non recursive tuple (one constructor and no indices) with no inner
dependencies; canonical definition of n-ary conjunction if strict *)
val match_with_conjunction : ?strict:bool -> ?onlybinary:bool -> (constr * constr list) matching_function
val is_conjunction : ?strict:bool -> ?onlybinary:bool -> testing_function
(** Non recursive tuple, possibly with inner dependencies *)
val match_with_record : (constr * constr list) matching_function
val is_record : testing_function
(** Like record but supports and tells if recursive (e.g. Acc) *)
val match_with_tuple : (constr * constr list * bool) matching_function
val is_tuple : testing_function
(** No constructor, possibly with indices *)
val match_with_empty_type : constr matching_function
val is_empty_type : testing_function
(** type with only one constructor and no arguments, possibly with indices *)
val match_with_unit_or_eq_type : constr matching_function
val is_unit_or_eq_type : testing_function
(** type with only one constructor and no arguments, no indices *)
val is_unit_type : testing_function
(** type with only one constructor, no arguments and at least one dependency *)
val is_inductive_equality : inductive -> bool
val match_with_equality_type : (constr * constr list) matching_function
val is_equality_type : testing_function
val match_with_nottype : (constr * constr) matching_function
val is_nottype : testing_function
val match_with_forall_term : (Name.t * constr * constr) matching_function
val is_forall_term : testing_function
val match_with_imp_term : (constr * constr) matching_function
val is_imp_term : testing_function
(** I added these functions to test whether a type contains dependent
products or not, and if an inductive has constructors with dependent types
(excluding parameters). this is useful to check whether a conjunction is a
real conjunction and not a dependent tuple. (Pierre Corbineau, 13/5/2002) *)
val has_nodep_prod_after : int -> testing_function
val has_nodep_prod : testing_function
val match_with_nodep_ind : (constr * constr list * int) matching_function
val is_nodep_ind : testing_function
val match_with_sigma_type : (constr * constr list) matching_function
val is_sigma_type : testing_function
(** Recongnize inductive relation defined by reflexivity *)
type equation_kind =
| MonomorphicLeibnizEq of constr * constr
| PolymorphicLeibnizEq of constr * constr * constr
| HeterogenousEq of constr * constr * constr * constr
exception NoEquationFound
val match_with_equation:
constr -> coq_eq_data option * constr * equation_kind
(***** Destructing patterns bound to some theory *)
(** Match terms [eq A t u], [identity A t u] or [JMeq A t A u]
Returns associated lemmas and [A,t,u] or fails PatternMatchingFailure *)
val find_eq_data_decompose : ([ `NF ], 'r) Proofview.Goal.t -> constr ->
coq_eq_data * Univ.universe_instance * (types * constr * constr)
(** Idem but fails with an error message instead of PatternMatchingFailure *)
val find_this_eq_data_decompose : ([ `NF ], 'r) Proofview.Goal.t -> constr ->
coq_eq_data * Univ.universe_instance * (types * constr * constr)
(** A variant that returns more informative structure on the equality found *)
val find_eq_data : constr -> coq_eq_data * Univ.universe_instance * equation_kind
(** Match a term of the form [(existT A P t p)]
Returns associated lemmas and [A,P,t,p] *)
val find_sigma_data_decompose : constr ->
coq_sigma_data * (Univ.universe_instance * constr * constr * constr * constr)
(** Match a term of the form [{x:A|P}], returns [A] and [P] *)
val match_sigma : constr -> constr * constr
val is_matching_sigma : constr -> bool
(** Match a decidable equality judgement (e.g [{t=u:>T}+{~t=u}]), returns
[t,u,T] and a boolean telling if equality is on the left side *)
val match_eqdec : constr -> bool * constr * constr * constr * constr
(** Match an equality up to conversion; returns [(eq,t1,t2)] in normal form *)
val dest_nf_eq : ([ `NF ], 'r) Proofview.Goal.t -> constr -> (constr * constr * constr)
(** Match a negation *)
val is_matching_not : constr -> bool
val is_matching_imp_False : constr -> bool
|
