author | wenzelm |
Fri, 29 Oct 2010 22:54:54 +0200 | |
changeset 40286 | b928e3960446 |
parent 39296 | e275d581a218 |
child 42143 | 786ccfffcd67 |
permissions | -rw-r--r-- |
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(* Title: Pure/type_infer.ML |
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Author: Stefan Berghofer and Markus Wenzel, TU Muenchen |
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Representation of type-inference problems. Simple type inference. |
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Type inference (isolated from type.ML, completely reimplemented).
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*) |
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Type inference (isolated from type.ML, completely reimplemented).
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Type inference (isolated from type.ML, completely reimplemented).
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signature TYPE_INFER = |
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sig |
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val is_param: indexname -> bool |
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val is_paramT: typ -> bool |
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val param: int -> string * sort -> typ |
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val mk_param: int -> sort -> typ |
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val anyT: sort -> typ |
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val paramify_vars: typ -> typ |
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val paramify_dummies: typ -> int -> typ * int |
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val deref: typ Vartab.table -> typ -> typ |
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val finish: Proof.context -> typ Vartab.table -> typ list * term list -> typ list * term list |
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val fixate: Proof.context -> term list -> term list |
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val prepare: Proof.context -> (string -> typ option) -> (string * int -> typ option) -> |
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term list -> int * term list |
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load type_infer.ML later -- proper context for Type_Infer.infer_types;
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val infer_types: Proof.context -> (string -> typ option) -> (indexname -> typ option) -> |
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term list -> term list |
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Type inference (isolated from type.ML, completely reimplemented).
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end; |
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structure Type_Infer: TYPE_INFER = |
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Type inference (isolated from type.ML, completely reimplemented).
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struct |
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(** type parameters and constraints **) |
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(* type inference parameters -- may get instantiated *) |
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fun is_param (x, _: int) = String.isPrefix "?" x; |
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fun is_paramT (TVar (xi, _)) = is_param xi |
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| is_paramT _ = false; |
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fun param i (x, S) = TVar (("?" ^ x, i), S); |
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fun mk_param i S = TVar (("?'a", i), S); |
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(* pre-stage parameters *) |
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fun anyT S = TFree ("'_dummy_", S); |
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val paramify_vars = |
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Same.commit |
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(Term_Subst.map_atypsT_same |
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(fn TVar ((x, i), S) => (param i (x, S)) | _ => raise Same.SAME)); |
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val paramify_dummies = |
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let |
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fun dummy S maxidx = (param (maxidx + 1) ("'dummy", S), maxidx + 1); |
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fun paramify (TFree ("'_dummy_", S)) maxidx = dummy S maxidx |
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| paramify (Type ("dummy", _)) maxidx = dummy [] maxidx |
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| paramify (Type (a, Ts)) maxidx = |
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let val (Ts', maxidx') = fold_map paramify Ts maxidx |
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in (Type (a, Ts'), maxidx') end |
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| paramify T maxidx = (T, maxidx); |
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in paramify end; |
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(** prepare types/terms: create inference parameters **) |
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(* prepare_typ *) |
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fun prepare_typ typ params_idx = |
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let |
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val (params', idx) = fold_atyps |
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(fn TVar (xi as (x, _), S) => |
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(fn ps_idx as (ps, idx) => |
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if is_param xi andalso not (Vartab.defined ps xi) |
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then (Vartab.update (xi, mk_param idx S) ps, idx + 1) else ps_idx) |
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| _ => I) typ params_idx; |
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fun prepare (T as Type (a, Ts)) idx = |
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if T = dummyT then (mk_param idx [], idx + 1) |
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else |
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let val (Ts', idx') = fold_map prepare Ts idx |
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in (Type (a, Ts'), idx') end |
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| prepare (T as TVar (xi, _)) idx = |
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(case Vartab.lookup params' xi of |
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NONE => T |
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| SOME p => p, idx) |
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| prepare (TFree ("'_dummy_", S)) idx = (mk_param idx S, idx + 1) |
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| prepare (T as TFree _) idx = (T, idx); |
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val (typ', idx') = prepare typ idx; |
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in (typ', (params', idx')) end; |
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(* prepare_term *) |
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fun prepare_term const_type tm (vparams, params, idx) = |
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let |
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fun add_vparm xi (ps_idx as (ps, idx)) = |
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if not (Vartab.defined ps xi) then |
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(Vartab.update (xi, mk_param idx []) ps, idx + 1) |
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else ps_idx; |
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val (vparams', idx') = fold_aterms |
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(fn Var (_, Type ("_polymorphic_", _)) => I |
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| Var (xi, _) => add_vparm xi |
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| Free (x, _) => add_vparm (x, ~1) |
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| _ => I) |
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tm (vparams, idx); |
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fun var_param xi = the (Vartab.lookup vparams' xi); |
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fun polyT_of T idx = apsnd snd (prepare_typ (paramify_vars T) (Vartab.empty, idx)); |
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fun constraint T t ps = |
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if T = dummyT then (t, ps) |
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else |
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let val (T', ps') = prepare_typ T ps |
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in (Type.constraint T' t, ps') end; |
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fun prepare (Const ("_type_constraint_", T) $ t) ps_idx = |
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let |
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val (T', ps_idx') = prepare_typ T ps_idx; |
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val (t', ps_idx'') = prepare t ps_idx'; |
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in (Const ("_type_constraint_", T') $ t', ps_idx'') end |
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| prepare (Const (c, T)) (ps, idx) = |
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(case const_type c of |
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SOME U => |
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let val (U', idx') = polyT_of U idx |
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in constraint T (Const (c, U')) (ps, idx') end |
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| NONE => error ("Undeclared constant: " ^ quote c)) |
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| prepare (Var (xi, Type ("_polymorphic_", [T]))) (ps, idx) = |
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let val (T', idx') = polyT_of T idx |
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in (Var (xi, T'), (ps, idx')) end |
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| prepare (Var (xi, T)) ps_idx = constraint T (Var (xi, var_param xi)) ps_idx |
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| prepare (Free (x, T)) ps_idx = constraint T (Free (x, var_param (x, ~1))) ps_idx |
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| prepare (Bound i) ps_idx = (Bound i, ps_idx) |
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| prepare (Abs (x, T, t)) ps_idx = |
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137 |
let |
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val (T', ps_idx') = prepare_typ T ps_idx; |
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val (t', ps_idx'') = prepare t ps_idx'; |
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in (Abs (x, T', t'), ps_idx'') end |
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| prepare (t $ u) ps_idx = |
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let |
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143 |
val (t', ps_idx') = prepare t ps_idx; |
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val (u', ps_idx'') = prepare u ps_idx'; |
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in (t' $ u', ps_idx'') end; |
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|
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147 |
val (tm', (params', idx'')) = prepare tm (params, idx'); |
32141 | 148 |
in (tm', (vparams', params', idx'')) end; |
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(** results **) |
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153 |
|
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154 |
(* dereferenced views *) |
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155 |
|
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156 |
fun deref tye (T as TVar (xi, _)) = |
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157 |
(case Vartab.lookup tye xi of |
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158 |
NONE => T |
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159 |
| SOME U => deref tye U) |
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160 |
| deref tye T = T; |
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161 |
|
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162 |
fun add_parms tye T = |
32146 | 163 |
(case deref tye T of |
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164 |
Type (_, Ts) => fold (add_parms tye) Ts |
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165 |
| TVar (xi, _) => if is_param xi then insert (op =) xi else I |
32146 | 166 |
| _ => I); |
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167 |
|
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168 |
fun add_names tye T = |
32146 | 169 |
(case deref tye T of |
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170 |
Type (_, Ts) => fold (add_names tye) Ts |
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171 |
| TFree (x, _) => Name.declare x |
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172 |
| TVar ((x, i), _) => if is_param (x, i) then I else Name.declare x); |
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173 |
|
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174 |
|
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(* finish -- standardize remaining parameters *) |
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176 |
|
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177 |
fun finish ctxt tye (Ts, ts) = |
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178 |
let |
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179 |
val used = |
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180 |
(fold o fold_types) (add_names tye) ts (fold (add_names tye) Ts (Variable.names_of ctxt)); |
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181 |
val parms = rev ((fold o fold_types) (add_parms tye) ts (fold (add_parms tye) Ts [])); |
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182 |
val names = Name.invents used ("?" ^ Name.aT) (length parms); |
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183 |
val tab = Vartab.make (parms ~~ names); |
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184 |
|
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185 |
fun finish_typ T = |
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186 |
(case deref tye T of |
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187 |
Type (a, Ts) => Type (a, map finish_typ Ts) |
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188 |
| U as TFree _ => U |
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189 |
| U as TVar (xi, S) => |
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190 |
(case Vartab.lookup tab xi of |
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191 |
NONE => U |
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192 |
| SOME a => TVar ((a, 0), S))); |
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193 |
in (map finish_typ Ts, map (Type.strip_constraints o Term.map_types finish_typ) ts) end; |
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194 |
|
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195 |
|
39296 | 196 |
(* fixate -- introduce fresh type variables *) |
197 |
||
198 |
fun fixate ctxt ts = |
|
199 |
let |
|
200 |
fun subst_param (xi, S) (inst, used) = |
|
201 |
if is_param xi then |
|
202 |
let |
|
203 |
val [a] = Name.invents used Name.aT 1; |
|
204 |
val used' = Name.declare a used; |
|
205 |
in (((xi, S), TFree (a, S)) :: inst, used') end |
|
206 |
else (inst, used); |
|
207 |
val used = (fold o fold_types) Term.declare_typ_names ts (Variable.names_of ctxt); |
|
208 |
val (inst, _) = fold_rev subst_param (fold Term.add_tvars ts []) ([], used); |
|
209 |
in (map o map_types) (Term_Subst.instantiateT inst) ts end; |
|
210 |
||
211 |
||
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212 |
|
32141 | 213 |
(** order-sorted unification of types **) |
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214 |
|
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215 |
exception NO_UNIFIER of string * typ Vartab.table; |
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216 |
|
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|
217 |
fun unify ctxt pp = |
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218 |
let |
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|
219 |
val thy = ProofContext.theory_of ctxt; |
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220 |
val arity_sorts = Type.arity_sorts pp (Sign.tsig_of thy); |
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221 |
|
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|
222 |
|
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223 |
(* adjust sorts of parameters *) |
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224 |
|
19465 | 225 |
fun not_of_sort x S' S = |
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|
226 |
"Variable " ^ x ^ "::" ^ Syntax.string_of_sort ctxt S' ^ " not of sort " ^ |
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227 |
Syntax.string_of_sort ctxt S; |
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228 |
|
32141 | 229 |
fun meet (_, []) tye_idx = tye_idx |
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230 |
| meet (Type (a, Ts), S) (tye_idx as (tye, _)) = |
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|
231 |
meets (Ts, arity_sorts a S handle ERROR msg => raise NO_UNIFIER (msg, tye)) tye_idx |
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|
232 |
| meet (TFree (x, S'), S) (tye_idx as (tye, _)) = |
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|
233 |
if Sign.subsort thy (S', S) then tye_idx |
32141 | 234 |
else raise NO_UNIFIER (not_of_sort x S' S, tye) |
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|
235 |
| meet (TVar (xi, S'), S) (tye_idx as (tye, idx)) = |
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|
236 |
if Sign.subsort thy (S', S) then tye_idx |
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|
237 |
else if is_param xi then |
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|
238 |
(Vartab.update_new (xi, mk_param idx (Sign.inter_sort thy (S', S))) tye, idx + 1) |
32141 | 239 |
else raise NO_UNIFIER (not_of_sort (Term.string_of_vname xi) S' S, tye) |
240 |
and meets (T :: Ts, S :: Ss) (tye_idx as (tye, _)) = |
|
241 |
meets (Ts, Ss) (meet (deref tye T, S) tye_idx) |
|
242 |
| meets _ tye_idx = tye_idx; |
|
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|
243 |
|
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|
244 |
|
35013 | 245 |
(* occurs check and assignment *) |
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|
246 |
|
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|
247 |
fun occurs_check tye xi (TVar (xi', S)) = |
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|
248 |
if xi = xi' then raise NO_UNIFIER ("Occurs check!", tye) |
32146 | 249 |
else |
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|
250 |
(case Vartab.lookup tye xi' of |
32141 | 251 |
NONE => () |
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changeset
|
252 |
| SOME T => occurs_check tye xi T) |
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|
253 |
| occurs_check tye xi (Type (_, Ts)) = List.app (occurs_check tye xi) Ts |
32141 | 254 |
| occurs_check _ _ _ = (); |
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|
255 |
|
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|
256 |
fun assign xi (T as TVar (xi', _)) S env = |
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|
257 |
if xi = xi' then env |
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|
258 |
else env |> meet (T, S) |>> Vartab.update_new (xi, T) |
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|
259 |
| assign xi T S (env as (tye, _)) = |
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|
260 |
(occurs_check tye xi T; env |> meet (T, S) |>> Vartab.update_new (xi, T)); |
2957
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
261 |
|
d35fca99b3be
Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
262 |
|
d35fca99b3be
Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
263 |
(* unification *) |
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Type inference (isolated from type.ML, completely reimplemented).
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parents:
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changeset
|
264 |
|
39286 | 265 |
fun show_tycon (a, Ts) = |
39290
44e4d8dfd6bf
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changeset
|
266 |
quote (Syntax.string_of_typ ctxt (Type (a, replicate (length Ts) dummyT))); |
39286 | 267 |
|
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|
268 |
fun unif (T1, T2) (env as (tye, _)) = |
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changeset
|
269 |
(case pairself (`is_paramT o deref tye) (T1, T2) of |
27fae73fe769
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changeset
|
270 |
((true, TVar (xi, S)), (_, T)) => assign xi T S env |
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changeset
|
271 |
| ((_, T), (true, TVar (xi, S))) => assign xi T S env |
27fae73fe769
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changeset
|
272 |
| ((_, Type (a, Ts)), (_, Type (b, Us))) => |
2979 | 273 |
if a <> b then |
39286 | 274 |
raise NO_UNIFIER |
275 |
("Clash of types " ^ show_tycon (a, Ts) ^ " and " ^ show_tycon (b, Us), tye) |
|
39294
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|
276 |
else fold unif (Ts ~~ Us) env |
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changeset
|
277 |
| ((_, T), (_, U)) => if T = U then env else raise NO_UNIFIER ("", tye)); |
2957
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
278 |
|
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Type inference (isolated from type.ML, completely reimplemented).
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|
279 |
in unif end; |
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
280 |
|
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
281 |
|
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
282 |
|
39296 | 283 |
(** simple type inference **) |
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
284 |
|
32141 | 285 |
(* infer *) |
2957
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
286 |
|
39290
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load type_infer.ML later -- proper context for Type_Infer.infer_types;
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changeset
|
287 |
fun infer ctxt = |
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Type inference (isolated from type.ML, completely reimplemented).
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|
288 |
let |
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289 |
val pp = Syntax.pp ctxt; |
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load type_infer.ML later -- proper context for Type_Infer.infer_types;
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290 |
|
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load type_infer.ML later -- proper context for Type_Infer.infer_types;
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291 |
|
2979 | 292 |
(* errors *) |
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293 |
|
32141 | 294 |
fun prep_output tye bs ts Ts = |
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let |
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296 |
val (Ts_bTs', ts') = finish ctxt tye (Ts @ map snd bs, ts); |
19012 | 297 |
val (Ts', Ts'') = chop (length Ts) Ts_bTs'; |
27263 | 298 |
fun prep t = |
299 |
let val xs = rev (Term.variant_frees t (rev (map fst bs ~~ Ts''))) |
|
300 |
in Term.subst_bounds (map Syntax.mark_boundT xs, t) end; |
|
301 |
in (map prep ts', Ts') end; |
|
2979 | 302 |
|
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303 |
fun err_loose i = error ("Loose bound variable: B." ^ string_of_int i); |
2979 | 304 |
|
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common Type.appl_error, which also covers explicit constraints;
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305 |
fun unif_failed msg = |
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"Type unification failed" ^ (if msg = "" then "" else ": " ^ msg) ^ "\n\n"; |
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307 |
|
32141 | 308 |
fun err_appl msg tye bs t T u U = |
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309 |
let val ([t', u'], [T', U']) = prep_output tye bs [t, u] [T, U] |
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310 |
in error (unif_failed msg ^ Type.appl_error pp t' T' u' U' ^ "\n") end; |
2979 | 311 |
|
312 |
||
313 |
(* main *) |
|
314 |
||
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315 |
fun inf _ (Const (_, T)) tye_idx = (T, tye_idx) |
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| inf _ (Free (_, T)) tye_idx = (T, tye_idx) |
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317 |
| inf _ (Var (_, T)) tye_idx = (T, tye_idx) |
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318 |
| inf bs (Bound i) tye_idx = |
32141 | 319 |
(snd (nth bs i handle Subscript => err_loose i), tye_idx) |
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320 |
| inf bs (Abs (x, T, t)) tye_idx = |
32141 | 321 |
let val (U, tye_idx') = inf ((x, T) :: bs) t tye_idx |
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322 |
in (T --> U, tye_idx') end |
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|
323 |
| inf bs (t $ u) tye_idx = |
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324 |
let |
32141 | 325 |
val (T, tye_idx') = inf bs t tye_idx; |
326 |
val (U, (tye, idx)) = inf bs u tye_idx'; |
|
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|
327 |
val V = mk_param idx []; |
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|
328 |
val tye_idx'' = unify ctxt pp (U --> V, T) (tye, idx + 1) |
32141 | 329 |
handle NO_UNIFIER (msg, tye') => err_appl msg tye' bs t T u U; |
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|
330 |
in (V, tye_idx'') end; |
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Type inference (isolated from type.ML, completely reimplemented).
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|
331 |
|
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Type inference (isolated from type.ML, completely reimplemented).
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332 |
in inf [] end; |
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|
333 |
|
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Type inference (isolated from type.ML, completely reimplemented).
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334 |
|
39296 | 335 |
(* main interfaces *) |
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|
336 |
|
39296 | 337 |
fun prepare ctxt const_type var_type raw_ts = |
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changeset
|
338 |
let |
22698 | 339 |
val get_type = the_default dummyT o var_type; |
340 |
val constrain_vars = Term.map_aterms |
|
39288 | 341 |
(fn Free (x, T) => Type.constraint T (Free (x, get_type (x, ~1))) |
342 |
| Var (xi, T) => Type.constraint T (Var (xi, get_type xi)) |
|
22698 | 343 |
| t => t); |
344 |
||
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load type_infer.ML later -- proper context for Type_Infer.infer_types;
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diff
changeset
|
345 |
val ts = burrow_types (Syntax.check_typs ctxt) raw_ts; |
32141 | 346 |
val (ts', (_, _, idx)) = |
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simplified Type_Infer: eliminated separate datatypes pretyp/preterm -- only assign is_paramT TVars;
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parents:
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diff
changeset
|
347 |
fold_map (prepare_term const_type o constrain_vars) ts |
32141 | 348 |
(Vartab.empty, Vartab.empty, 0); |
39296 | 349 |
in (idx, ts') end; |
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Type inference (isolated from type.ML, completely reimplemented).
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changeset
|
350 |
|
39296 | 351 |
fun infer_types ctxt const_type var_type raw_ts = |
352 |
let |
|
353 |
val (idx, ts) = prepare ctxt const_type var_type raw_ts; |
|
354 |
val (tye, _) = fold (snd oo infer ctxt) ts (Vartab.empty, idx); |
|
355 |
val (_, ts') = finish ctxt tye ([], ts); |
|
356 |
in ts' end; |
|
14788
9776f0c747c8
incorporate type inference interface from type.ML;
wenzelm
parents:
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diff
changeset
|
357 |
|
2957
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Type inference (isolated from type.ML, completely reimplemented).
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parents:
diff
changeset
|
358 |
end; |