+++ /dev/null
-(* Copyright (C) 2000, HELM Team.
- *
- * This file is part of HELM, an Hypertextual, Electronic
- * Library of Mathematics, developed at the Computer Science
- * Department, University of Bologna, Italy.
- *
- * HELM is free software; you can redistribute it and/or
- * modify it under the terms of the GNU General Public License
- * as published by the Free Software Foundation; either version 2
- * of the License, or (at your option) any later version.
- *
- * HELM is distributed in the hope that it will be useful,
- * but WITHOUT ANY WARRANTY; without even the implied warranty of
- * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
- * GNU General Public License for more details.
- *
- * You should have received a copy of the GNU General Public License
- * along with HELM; if not, write to the Free Software
- * Foundation, Inc., 59 Temple Place - Suite 330, Boston,
- * MA 02111-1307, USA.
- *
- * For details, see the HELM World-Wide-Web page,
- * http://cs.unibo.it/helm/.
- *)
-
-exception Impossible of int;;
-exception NotWellTyped of string;;
-exception WrongUriToConstant of string;;
-exception WrongUriToVariable of string;;
-exception WrongUriToMutualInductiveDefinitions of string;;
-exception ListTooShort;;
-exception RelToHiddenHypothesis;;
-
-type types = {synthesized : Cic.term ; expected : Cic.term option};;
-
-(*CSC: potrebbe creare applicazioni di applicazioni *)
-(*CSC: ora non e' piu' head, ma completa!!! *)
-let rec head_beta_reduce =
- let module S = CicSubstitution in
- let module C = Cic in
- function
- C.Rel _
- | C.Var _ as t -> t
- | C.Meta (n,l) ->
- C.Meta (n,
- List.map
- (function None -> None | Some t -> Some (head_beta_reduce t)) l
- )
- | C.Sort _ as t -> t
- | C.Implicit -> assert false
- | C.Cast (te,ty) ->
- C.Cast (head_beta_reduce te, head_beta_reduce ty)
- | C.Prod (n,s,t) ->
- C.Prod (n, head_beta_reduce s, head_beta_reduce t)
- | C.Lambda (n,s,t) ->
- C.Lambda (n, head_beta_reduce s, head_beta_reduce t)
- | C.LetIn (n,s,t) ->
- C.LetIn (n, head_beta_reduce s, head_beta_reduce t)
- | C.Appl ((C.Lambda (name,s,t))::he::tl) ->
- let he' = S.subst he t in
- if tl = [] then
- head_beta_reduce he'
- else
- head_beta_reduce (C.Appl (he'::tl))
- | C.Appl l ->
- C.Appl (List.map head_beta_reduce l)
- | C.Const _ as t -> t
- | C.MutInd _
- | C.MutConstruct _ as t -> t
- | C.MutCase (sp,cno,i,outt,t,pl) ->
- C.MutCase (sp,cno,i,head_beta_reduce outt,head_beta_reduce t,
- List.map head_beta_reduce pl)
- | C.Fix (i,fl) ->
- let fl' =
- List.map
- (function (name,i,ty,bo) ->
- name,i,head_beta_reduce ty,head_beta_reduce bo
- ) fl
- in
- C.Fix (i,fl')
- | C.CoFix (i,fl) ->
- let fl' =
- List.map
- (function (name,ty,bo) ->
- name,head_beta_reduce ty,head_beta_reduce bo
- ) fl
- in
- C.CoFix (i,fl')
-;;
-
-(* syntactic_equality up to cookingsno for uris *)
-(* (which is often syntactically irrilevant), *)
-(* distinction between fake dependent products *)
-(* and non-dependent products, alfa-conversion *)
-(*CSC: must alfa-conversion be considered or not? *)
-let syntactic_equality t t' =
- let module C = Cic in
- let rec syntactic_equality t t' =
- if t = t' then true
- else
- match t, t' with
- C.Rel _, C.Rel _
- | C.Var _, C.Var _
- | C.Meta _, C.Meta _
- | C.Sort _, C.Sort _
- | C.Implicit, C.Implicit -> false (* we already know that t != t' *)
- | C.Cast (te,ty), C.Cast (te',ty') ->
- syntactic_equality te te' &&
- syntactic_equality ty ty'
- | C.Prod (_,s,t), C.Prod (_,s',t') ->
- syntactic_equality s s' &&
- syntactic_equality t t'
- | C.Lambda (_,s,t), C.Lambda (_,s',t') ->
- syntactic_equality s s' &&
- syntactic_equality t t'
- | C.LetIn (_,s,t), C.LetIn(_,s',t') ->
- syntactic_equality s s' &&
- syntactic_equality t t'
- | C.Appl l, C.Appl l' ->
- List.fold_left2 (fun b t1 t2 -> b && syntactic_equality t1 t2) true l l'
- | C.Const (uri,_), C.Const (uri',_) -> UriManager.eq uri uri'
- | C.MutInd (uri,_,i), C.MutInd (uri',_,i') ->
- UriManager.eq uri uri' && i = i'
- | C.MutConstruct (uri,_,i,j), C.MutConstruct (uri',_,i',j') ->
- UriManager.eq uri uri' && i = i' && j = j'
- | C.MutCase (sp,_,i,outt,t,pl), C.MutCase (sp',_,i',outt',t',pl') ->
- UriManager.eq sp sp' && i = i' &&
- syntactic_equality outt outt' &&
- syntactic_equality t t' &&
- List.fold_left2
- (fun b t1 t2 -> b && syntactic_equality t1 t2) true pl pl'
- | C.Fix (i,fl), C.Fix (i',fl') ->
- i = i' &&
- List.fold_left2
- (fun b (_,i,ty,bo) (_,i',ty',bo') ->
- b && i = i' &&
- syntactic_equality ty ty' &&
- syntactic_equality bo bo') true fl fl'
- | C.CoFix (i,fl), C.CoFix (i',fl') ->
- i = i' &&
- List.fold_left2
- (fun b (_,ty,bo) (_,ty',bo') ->
- b &&
- syntactic_equality ty ty' &&
- syntactic_equality bo bo') true fl fl'
- | _,_ -> false
- in
- try
- syntactic_equality t t'
- with
- _ -> false
-;;
-
-let rec split l n =
- match (l,n) with
- (l,0) -> ([], l)
- | (he::tl, n) -> let (l1,l2) = split tl (n-1) in (he::l1,l2)
- | (_,_) -> raise ListTooShort
-;;
-
-let cooked_type_of_constant uri cookingsno =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- let cobj =
- match CicEnvironment.is_type_checked uri cookingsno with
- CicEnvironment.CheckedObj cobj -> cobj
- | CicEnvironment.UncheckedObj uobj ->
- raise (NotWellTyped "Reference to an unchecked constant")
- in
- match cobj with
- C.Definition (_,_,ty,_) -> ty
- | C.Axiom (_,ty,_) -> ty
- | C.CurrentProof (_,_,_,ty) -> ty
- | _ -> raise (WrongUriToConstant (U.string_of_uri uri))
-;;
-
-let type_of_variable uri =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- (* 0 because a variable is never cooked => no partial cooking at one level *)
- match CicEnvironment.is_type_checked uri 0 with
- CicEnvironment.CheckedObj (C.Variable (_,_,ty)) -> ty
- | CicEnvironment.UncheckedObj (C.Variable _) ->
- raise (NotWellTyped "Reference to an unchecked variable")
- | _ -> raise (WrongUriToVariable (UriManager.string_of_uri uri))
-;;
-
-let cooked_type_of_mutual_inductive_defs uri cookingsno i =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- let cobj =
- match CicEnvironment.is_type_checked uri cookingsno with
- CicEnvironment.CheckedObj cobj -> cobj
- | CicEnvironment.UncheckedObj uobj ->
- raise (NotWellTyped "Reference to an unchecked inductive type")
- in
- match cobj with
- C.InductiveDefinition (dl,_,_) ->
- let (_,_,arity,_) = List.nth dl i in
- arity
- | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
-;;
-
-let cooked_type_of_mutual_inductive_constr uri cookingsno i j =
- let module C = Cic in
- let module R = CicReduction in
- let module U = UriManager in
- let cobj =
- match CicEnvironment.is_type_checked uri cookingsno with
- CicEnvironment.CheckedObj cobj -> cobj
- | CicEnvironment.UncheckedObj uobj ->
- raise (NotWellTyped "Reference to an unchecked constructor")
- in
- match cobj with
- C.InductiveDefinition (dl,_,_) ->
- let (_,_,_,cl) = List.nth dl i in
- let (_,ty,_) = List.nth cl (j-1) in
- ty
- | _ -> raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
-;;
-
-module CicHash =
- Hashtbl.Make
- (struct
- type t = Cic.term
- let equal = (==)
- let hash = Hashtbl.hash
- end)
-;;
-
-(* type_of_aux' is just another name (with a different scope) for type_of_aux *)
-let rec type_of_aux' subterms_to_types metasenv context t expectedty =
- (* Coscoy's double type-inference algorithm *)
- (* It computes the inner-types of every subterm of [t], *)
- (* even when they are not needed to compute the types *)
- (* of other terms. *)
- let rec type_of_aux context t expectedty =
- let module C = Cic in
- let module R = CicReduction in
- let module S = CicSubstitution in
- let module U = UriManager in
- let synthesized =
- match t with
- C.Rel n ->
- (try
- match List.nth context (n - 1) with
- Some (_,C.Decl t) -> S.lift n t
- | Some (_,C.Def bo) -> type_of_aux context (S.lift n bo) expectedty
- | None -> raise RelToHiddenHypothesis
- with
- _ -> raise (NotWellTyped "Not a close term")
- )
- | C.Var uri -> type_of_variable uri
- | C.Meta (n,l) ->
- (* Let's visit all the subterms that will not be visited later *)
- let (_,canonical_context,_) =
- List.find (function (m,_,_) -> n = m) metasenv
- in
- let lifted_canonical_context =
- let rec aux i =
- function
- [] -> []
- | (Some (n,C.Decl t))::tl ->
- (Some (n,C.Decl (S.lift_meta l (S.lift i t))))::(aux (i+1) tl)
- | (Some (n,C.Def t))::tl ->
- (Some (n,C.Def (S.lift_meta l (S.lift i t))))::(aux (i+1) tl)
- | None::tl -> None::(aux (i+1) tl)
- in
- aux 1 canonical_context
- in
- let _ =
- List.iter2
- (fun t ct ->
- match t,ct with
- _,None -> ()
- | Some t,Some (_,C.Def ct) ->
- let expected_type =
- R.whd context
- (CicTypeChecker.type_of_aux' metasenv context ct)
- in
- (* Maybe I am a bit too paranoid, because *)
- (* if the term is well-typed than t and ct *)
- (* are convertible. Nevertheless, I compute *)
- (* the expected type. *)
- ignore (type_of_aux context t (Some expected_type))
- | Some t,Some (_,C.Decl ct) ->
- ignore (type_of_aux context t (Some ct))
- | _,_ -> assert false (* the term is not well typed!!! *)
- ) l lifted_canonical_context
- in
- let (_,canonical_context,ty) =
- List.find (function (m,_,_) -> n = m) metasenv
- in
- (* Checks suppressed *)
- CicSubstitution.lift_meta l ty
- | C.Sort s -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
- | C.Implicit -> raise (Impossible 21)
- | C.Cast (te,ty) ->
- (* Let's visit all the subterms that will not be visited later *)
- let _ = type_of_aux context te (Some (head_beta_reduce ty)) in
- let _ = type_of_aux context ty None in
- (* Checks suppressed *)
- ty
- | C.Prod (name,s,t) ->
- let sort1 = type_of_aux context s None
- and sort2 = type_of_aux ((Some (name,(C.Decl s)))::context) t None in
- sort_of_prod context (name,s) (sort1,sort2)
- | C.Lambda (n,s,t) ->
- (* Let's visit all the subterms that will not be visited later *)
- let _ = type_of_aux context s None in
- let expected_target_type =
- match expectedty with
- None -> None
- | Some expectedty' ->
- let ty =
- match R.whd context expectedty' with
- C.Prod (_,_,expected_target_type) ->
- head_beta_reduce expected_target_type
- | _ -> assert false
- in
- Some ty
- in
- let type2 =
- type_of_aux ((Some (n,(C.Decl s)))::context) t expected_target_type
- in
- (* Checks suppressed *)
- C.Prod (n,s,type2)
- | C.LetIn (n,s,t) ->
-(*CSC: What are the right expected types for the source and *)
-(*CSC: target of a LetIn? None used. *)
- (* Let's visit all the subterms that will not be visited later *)
- let _ = type_of_aux context s None in
- (* Checks suppressed *)
- C.LetIn (n,s, type_of_aux ((Some (n,(C.Def s)))::context) t None)
- | C.Appl (he::tl) when List.length tl > 0 ->
- let expected_hetype =
- (* Inefficient, the head is computed twice. But I know *)
- (* of no other solution. *)
- R.whd context (CicTypeChecker.type_of_aux' metasenv context he)
- in
- let hetype = type_of_aux context he (Some expected_hetype) in
- let tlbody_and_type =
- let rec aux =
- function
- _,[] -> []
- | C.Prod (n,s,t),he::tl ->
- (he, type_of_aux context he (Some (head_beta_reduce s)))::
- (aux (R.whd context (S.subst he t), tl))
- | _ -> assert false
- in
- aux (expected_hetype, tl)
- in
- eat_prods context hetype tlbody_and_type
- | C.Appl _ -> raise (NotWellTyped "Appl: no arguments")
- | C.Const (uri,cookingsno) ->
- cooked_type_of_constant uri cookingsno
- | C.MutInd (uri,cookingsno,i) ->
- cooked_type_of_mutual_inductive_defs uri cookingsno i
- | C.MutConstruct (uri,cookingsno,i,j) ->
- let cty = cooked_type_of_mutual_inductive_constr uri cookingsno i j in
- cty
- | C.MutCase (uri,cookingsno,i,outtype,term,pl) ->
- let outsort = type_of_aux context outtype None in
- let (need_dummy, k) =
- let rec guess_args context t =
- match CicReduction.whd context t with
- C.Sort _ -> (true, 0)
- | C.Prod (name, s, t) ->
- let (b, n) = guess_args ((Some (name,(C.Decl s)))::context) t in
- if n = 0 then
- (* last prod before sort *)
- match CicReduction.whd context s with
- (*CSC vedi nota delirante su cookingsno in cicReduction.ml *)
- C.MutInd (uri',_,i') when U.eq uri' uri && i' = i ->
- (false, 1)
- | C.Appl ((C.MutInd (uri',_,i')) :: _)
- when U.eq uri' uri && i' = i -> (false, 1)
- | _ -> (true, 1)
- else
- (b, n + 1)
- | _ -> raise (NotWellTyped "MutCase: outtype ill-formed")
- in
- let (b, k) = guess_args context outsort in
- if not b then (b, k - 1) else (b, k)
- in
- let (parameters, arguments) =
- let type_of_term =
- CicTypeChecker.type_of_aux' metasenv context term
- in
- match
- R.whd context (type_of_aux context term
- (Some (head_beta_reduce type_of_term)))
- with
- (*CSC manca il caso dei CAST *)
- C.MutInd (uri',_,i') ->
- (* Checks suppressed *)
- [],[]
- | C.Appl (C.MutInd (uri',_,i') :: tl) ->
- split tl (List.length tl - k)
- | _ ->
- raise (NotWellTyped "MutCase: the term is not an inductive one")
- in
- (* Checks suppressed *)
- (* Let's visit all the subterms that will not be visited later *)
- let (cl,parsno) =
- match CicEnvironment.get_cooked_obj uri cookingsno with
- C.InductiveDefinition (tl,_,parsno) ->
- let (_,_,_,cl) = List.nth tl i in (cl,parsno)
- | _ ->
- raise (WrongUriToMutualInductiveDefinitions (U.string_of_uri uri))
- in
- let _ =
- List.fold_left
- (fun j (p,(_,c,_)) ->
- let cons =
- if parameters = [] then
- (C.MutConstruct (uri,cookingsno,i,j))
- else
- (C.Appl (C.MutConstruct (uri,cookingsno,i,j)::parameters))
- in
- let expectedtype =
- type_of_branch context parsno need_dummy outtype cons
- (CicTypeChecker.type_of_aux' metasenv context cons)
- in
- ignore (type_of_aux context p
- (Some (head_beta_reduce expectedtype))) ;
- j+1
- ) 1 (List.combine pl cl)
- in
- if not need_dummy then
- C.Appl ((outtype::arguments)@[term])
- else if arguments = [] then
- outtype
- else
- C.Appl (outtype::arguments)
- | C.Fix (i,fl) ->
- (* Let's visit all the subterms that will not be visited later *)
- let context' =
- List.rev
- (List.map
- (fun (n,_,ty,_) ->
- let _ = type_of_aux context ty None in
- (Some (C.Name n,(C.Decl ty)))
- ) fl
- ) @
- context
- in
- let _ =
- List.iter
- (fun (_,_,ty,bo) ->
- let expectedty =
- head_beta_reduce (CicSubstitution.lift (List.length fl) ty)
- in
- ignore (type_of_aux context' bo (Some expectedty))
- ) fl
- in
- (* Checks suppressed *)
- let (_,_,ty,_) = List.nth fl i in
- ty
- | C.CoFix (i,fl) ->
- (* Let's visit all the subterms that will not be visited later *)
- let context' =
- List.rev
- (List.map
- (fun (n,ty,_) ->
- let _ = type_of_aux context ty None in
- (Some (C.Name n,(C.Decl ty)))
- ) fl
- ) @
- context
- in
- let _ =
- List.iter
- (fun (_,ty,bo) ->
- let expectedty =
- head_beta_reduce (CicSubstitution.lift (List.length fl) ty)
- in
- ignore (type_of_aux context' bo (Some expectedty))
- ) fl
- in
- (* Checks suppressed *)
- let (_,ty,_) = List.nth fl i in
- ty
- in
- let synthesized' = head_beta_reduce synthesized in
- let types,res =
- match expectedty with
- None ->
- (* No expected type *)
- {synthesized = synthesized' ; expected = None}, synthesized
- | Some ty when syntactic_equality synthesized' ty ->
- (* The expected type is synthactically equal to *)
- (* the synthesized type. Let's forget it. *)
- {synthesized = synthesized' ; expected = None}, synthesized
- | Some expectedty' ->
- {synthesized = synthesized' ; expected = Some expectedty'},
- expectedty'
- in
- CicHash.add subterms_to_types t types ;
- res
-
- and sort_of_prod context (name,s) (t1, t2) =
- let module C = Cic in
- let t1' = CicReduction.whd context t1 in
- let t2' = CicReduction.whd ((Some (name,C.Decl s))::context) t2 in
- match (t1', t2') with
- (C.Sort s1, C.Sort s2)
- when (s2 = C.Prop or s2 = C.Set) -> (* different from Coq manual!!! *)
- C.Sort s2
- | (C.Sort s1, C.Sort s2) -> C.Sort C.Type (*CSC manca la gestione degli universi!!! *)
- | (_,_) ->
- raise
- (NotWellTyped
- ("Prod: sort1= " ^ CicPp.ppterm t1' ^ " ; sort2= " ^ CicPp.ppterm t2'))
-
- and eat_prods context hetype =
- (*CSC: siamo sicuri che le are_convertible non lavorino con termini non *)
- (*CSC: cucinati *)
- function
- [] -> hetype
- | (hete, hety)::tl ->
- (match (CicReduction.whd context hetype) with
- Cic.Prod (n,s,t) ->
- (* Checks suppressed *)
- eat_prods context (CicSubstitution.subst hete t) tl
- | _ -> raise (NotWellTyped "Appl: wrong Prod-type")
- )
-
-and type_of_branch context argsno need_dummy outtype term constype =
- let module C = Cic in
- let module R = CicReduction in
- match R.whd context constype with
- C.MutInd (_,_,_) ->
- if need_dummy then
- outtype
- else
- C.Appl [outtype ; term]
- | C.Appl (C.MutInd (_,_,_)::tl) ->
- let (_,arguments) = split tl argsno
- in
- if need_dummy && arguments = [] then
- outtype
- else
- C.Appl (outtype::arguments@(if need_dummy then [] else [term]))
- | C.Prod (name,so,de) ->
- let term' =
- match CicSubstitution.lift 1 term with
- C.Appl l -> C.Appl (l@[C.Rel 1])
- | t -> C.Appl [t ; C.Rel 1]
- in
- C.Prod (C.Anonimous,so,type_of_branch
- ((Some (name,(C.Decl so)))::context) argsno need_dummy
- (CicSubstitution.lift 1 outtype) term' de)
- | _ -> raise (Impossible 20)
-
- in
- type_of_aux context t expectedty
-;;
-
-let double_type_of metasenv context t expectedty =
- let subterms_to_types = CicHash.create 503 in
- ignore (type_of_aux' subterms_to_types metasenv context t expectedty) ;
- subterms_to_types
-;;
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