aboutsummaryrefslogtreecommitdiffhomepage
path: root/pretyping/evardefine.ml
blob: f9ab75cea93aca88c52b7b5a400fd89def280e2a (plain)
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
(************************************************************************)
(*  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 Util
open Pp
open Names
open Term
open Vars
open Termops
open Namegen
open Environ
open Evd
open Evarutil
open Pretype_errors
open Sigma.Notations

let new_evar_unsafe env evd ?src ?filter ?candidates ?store ?naming ?principal typ =
  let evd = Sigma.Unsafe.of_evar_map evd in
  let Sigma (evk, evd, _) = new_evar env evd ?src ?filter ?candidates ?store ?naming ?principal typ in
  (Sigma.to_evar_map evd, evk)

let env_nf_evar sigma env =
  let open Context.Rel.Declaration in
  process_rel_context
    (fun d e -> push_rel (map_constr (nf_evar sigma) d) e) env

let env_nf_betaiotaevar sigma env =
  let open Context.Rel.Declaration in
  process_rel_context
    (fun d e ->
      push_rel (map_constr (Reductionops.nf_betaiota sigma) d) e) env

(****************************************)
(* Operations on value/type constraints *)
(****************************************)

type type_constraint = types option

type val_constraint = constr option

(* Old comment...
 * Basically, we have the following kind of constraints (in increasing
 * strength order):
 *   (false,(None,None)) -> no constraint at all
 *   (true,(None,None))  -> we must build a judgement which _TYPE is a kind
 *   (_,(None,Some ty))  -> we must build a judgement which _TYPE is ty
 *   (_,(Some v,_))      -> we must build a judgement which _VAL is v
 * Maybe a concrete datatype would be easier to understand.
 * We differentiate (true,(None,None)) from (_,(None,Some Type))
 * because otherwise Case(s) would be misled, as in
 * (n:nat) Case n of bool [_]nat end  would infer the predicate Type instead
 * of Set.
 *)

(* The empty type constraint *)
let empty_tycon = None

(* Builds a type constraint *)
let mk_tycon ty = Some ty

(* Constrains the value of a type *)
let empty_valcon = None

(* Builds a value constraint *)
let mk_valcon c = Some c

let idx = Namegen.default_dependent_ident

(* Refining an evar to a product *)

let define_pure_evar_as_product evd evk =
  let open Context.Named.Declaration in
  let evi = Evd.find_undefined evd evk in
  let evenv = evar_env evi in
  let id = next_ident_away idx (ids_of_named_context (evar_context evi)) in
  let concl = Reductionops.whd_all evenv evd evi.evar_concl in
  let s = destSort concl in
  let evd1,(dom,u1) =
    let evd = Sigma.Unsafe.of_evar_map evd in
    let Sigma (e, evd1, _) = new_type_evar evenv evd univ_flexible_alg ~filter:(evar_filter evi) in
    (Sigma.to_evar_map evd1, e)
  in
  let evd2,rng =
    let newenv = push_named (LocalAssum (id, dom)) evenv in
    let src = evar_source evk evd1 in
    let filter = Filter.extend 1 (evar_filter evi) in
      if is_prop_sort s then
       (* Impredicative product, conclusion must fall in [Prop]. *)
        new_evar_unsafe newenv evd1 concl ~src ~filter
      else
	let status = univ_flexible_alg in
	let evd3, (rng, srng) =
          let evd1 = Sigma.Unsafe.of_evar_map evd1 in
          let Sigma (e, evd3, _) = new_type_evar newenv evd1 status ~src ~filter in
          (Sigma.to_evar_map evd3, e)
        in
	let prods = Univ.sup (univ_of_sort u1) (univ_of_sort srng) in
	let evd3 = Evd.set_leq_sort evenv evd3 (Type prods) s in
	  evd3, rng
  in
  let prod = mkProd (Name id, dom, subst_var id rng) in
  let evd3 = Evd.define evk prod evd2 in
    evd3,prod

(* Refine an applied evar to a product and returns its instantiation *)

let define_evar_as_product evd (evk,args) =
  let evd,prod = define_pure_evar_as_product evd evk in
  (* Quick way to compute the instantiation of evk with args *)
  let na,dom,rng = destProd prod in
  let evdom = mkEvar (fst (destEvar dom), args) in
  let evrngargs = Array.cons (mkRel 1) (Array.map (lift 1) args) in
  let evrng =  mkEvar (fst (destEvar rng), evrngargs) in
  evd,mkProd (na, evdom, evrng)

(* Refine an evar with an abstraction

   I.e., solve x1..xq |- ?e:T(x1..xq) with e:=λy:A.?e'[x1..xq,y] where:
   - either T(x1..xq) = πy:A(x1..xq).B(x1..xq,y)
     or T(x1..xq) = ?d[x1..xq] and we define ?d := πy:?A.?B
        with x1..xq |- ?A:Type and x1..xq,y |- ?B:Type
   - x1..xq,y:A |- ?e':B
*)

let define_pure_evar_as_lambda env evd evk =
  let open Context.Named.Declaration in
  let evi = Evd.find_undefined evd evk in
  let evenv = evar_env evi in
  let typ = Reductionops.whd_all evenv evd (evar_concl evi) in
  let evd1,(na,dom,rng) = match kind_of_term typ with
  | Prod (na,dom,rng) -> (evd,(na,dom,rng))
  | Evar ev' -> let evd,typ = define_evar_as_product evd ev' in evd,destProd typ
  | _ -> error_not_product_loc Loc.ghost env evd typ in
  let avoid = ids_of_named_context (evar_context evi) in
  let id =
    next_name_away_with_default_using_types "x" na avoid (Reductionops.whd_evar evd dom) in
  let newenv = push_named (LocalAssum (id, dom)) evenv in
  let filter = Filter.extend 1 (evar_filter evi) in
  let src = evar_source evk evd1 in
  let evd2,body = new_evar_unsafe newenv evd1 ~src (subst1 (mkVar id) rng) ~filter in
  let lam = mkLambda (Name id, dom, subst_var id body) in
  Evd.define evk lam evd2, lam

let define_evar_as_lambda env evd (evk,args) =
  let evd,lam = define_pure_evar_as_lambda env evd evk in
  (* Quick way to compute the instantiation of evk with args *)
  let na,dom,body = destLambda lam in
  let evbodyargs = Array.cons (mkRel 1) (Array.map (lift 1) args) in
  let evbody = mkEvar (fst (destEvar body), evbodyargs) in
  evd,mkLambda (na, dom, evbody)

let rec evar_absorb_arguments env evd (evk,args as ev) = function
  | [] -> evd,ev
  | a::l ->
      (* TODO: optimize and avoid introducing intermediate evars *)
      let evd,lam = define_pure_evar_as_lambda env evd evk in
      let _,_,body = destLambda lam in
      let evk = fst (destEvar body) in
      evar_absorb_arguments env evd (evk, Array.cons a args) l

(* Refining an evar to a sort *)

let define_evar_as_sort env evd (ev,args) =
  let evd, u = new_univ_variable univ_rigid evd in
  let evi = Evd.find_undefined evd ev in 
  let s = Type u in
  let concl = Reductionops.whd_all (evar_env evi) evd evi.evar_concl in
  let sort = destSort concl in
  let evd' = Evd.define ev (mkSort s) evd in
  Evd.set_leq_sort env evd' (Type (Univ.super u)) sort, s

(* Propagation of constraints through application and abstraction:
   Given a type constraint on a functional term, returns the type
   constraint on its domain and codomain. If the input constraint is
   an evar instantiate it with the product of 2 new evars. *)

let split_tycon loc env evd tycon =
  let rec real_split evd c =
    let t = Reductionops.whd_all env evd c in
      match kind_of_term t with
	| Prod (na,dom,rng) -> evd, (na, dom, rng)
	| Evar ev (* ev is undefined because of whd_all *) ->
	    let (evd',prod) = define_evar_as_product evd ev in
	    let (_,dom,rng) = destProd prod in
	      evd',(Anonymous, dom, rng)
	| App (c,args) when isEvar c ->
	    let (evd',lam) = define_evar_as_lambda env evd (destEvar c) in
	    real_split evd' (mkApp (lam,args))
	| _ -> error_not_product_loc loc env evd c
  in
    match tycon with
      | None -> evd,(Anonymous,None,None)
      | Some c ->
	  let evd', (n, dom, rng) = real_split evd c in
	    evd', (n, mk_tycon dom, mk_tycon rng)

let valcon_of_tycon x = x
let lift_tycon n = Option.map (lift n)

let pr_tycon env = function
    None -> str "None"
  | Some t -> Termops.print_constr_env env t