author | wenzelm |
Sat, 20 Jul 2024 21:17:22 +0200 | |
changeset 80599 | f8c070249502 |
parent 79409 | e1895596e1b9 |
child 80607 | e23aab2df03c |
permissions | -rw-r--r-- |
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(* Title: Pure/term_subst.ML |
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Author: Makarius |
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Efficient type/term substitution. |
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*) |
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signature TERM_SUBST = |
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sig |
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val generalizeT_same: Names.set -> int -> typ Same.operation |
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val generalize_same: Names.set * Names.set -> int -> term Same.operation |
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val generalizeT: Names.set -> int -> typ -> typ |
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val generalize: Names.set * Names.set -> int -> term -> term |
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val instantiateT_frees_same: typ TFrees.table -> typ Same.operation |
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val instantiate_frees_same: typ TFrees.table * term Frees.table -> term Same.operation |
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val instantiateT_frees: typ TFrees.table -> typ -> typ |
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val instantiate_frees: typ TFrees.table * term Frees.table -> term -> term |
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val instantiateT_maxidx: (typ * int) TVars.table -> typ -> int -> typ * int |
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val instantiate_maxidx: (typ * int) TVars.table * (term * int) Vars.table -> |
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term -> int -> term * int |
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val instantiate_beta_maxidx: (typ * int) TVars.table * (term * int) Vars.table -> |
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term -> int -> term * int |
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val instantiateT_same: typ TVars.table -> typ Same.operation |
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val instantiate_same: typ TVars.table * term Vars.table -> term Same.operation |
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val instantiate_beta_same: typ TVars.table * term Vars.table -> term Same.operation |
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val instantiateT: typ TVars.table -> typ -> typ |
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val instantiate: typ TVars.table * term Vars.table -> term -> term |
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val instantiate_beta: typ TVars.table * term Vars.table -> term -> term |
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val zero_var_indexes_inst: Name.context -> term list -> typ TVars.table * term Vars.table |
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val zero_var_indexes: term -> term |
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val zero_var_indexes_list: term list -> term list |
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end; |
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structure Term_Subst: TERM_SUBST = |
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struct |
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(* generalization of fixed variables *) |
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fun generalizeT_same tfrees idx ty = |
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if Names.is_empty tfrees then raise Same.SAME |
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else |
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let |
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fun gen (Type (a, Ts)) = Type (a, Same.map gen Ts) |
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| gen (TFree (a, S)) = |
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if Names.defined tfrees a then TVar ((a, idx), S) |
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else raise Same.SAME |
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| gen _ = raise Same.SAME; |
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in gen ty end; |
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fun generalize_same (tfrees, frees) idx tm = |
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if Names.is_empty tfrees andalso Names.is_empty frees then raise Same.SAME |
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else |
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let |
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val genT = generalizeT_same tfrees idx; |
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fun gen (Free (x, T)) = |
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if Names.defined frees x then |
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Var (Name.clean_index (x, idx), Same.commit genT T) |
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else Free (x, genT T) |
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| gen (Var (xi, T)) = Var (xi, genT T) |
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| gen (Const (c, T)) = Const (c, genT T) |
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| gen (Bound _) = raise Same.SAME |
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| gen (Abs (x, T, t)) = |
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(Abs (x, genT T, Same.commit gen t) |
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handle Same.SAME => Abs (x, T, gen t)) |
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| gen (t $ u) = (gen t $ Same.commit gen u handle Same.SAME => t $ gen u); |
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in gen tm end; |
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fun generalizeT names i ty = Same.commit (generalizeT_same names i) ty; |
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fun generalize names i tm = Same.commit (generalize_same names i) tm; |
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(* instantiation of free variables (types before terms) *) |
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fun instantiateT_frees_same instT ty = |
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if TFrees.is_empty instT then raise Same.SAME |
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else |
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let |
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fun subst (Type (a, Ts)) = Type (a, Same.map subst Ts) |
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| subst (TFree v) = |
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(case TFrees.lookup instT v of |
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SOME T' => T' |
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| NONE => raise Same.SAME) |
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| subst _ = raise Same.SAME; |
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in subst ty end; |
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fun instantiate_frees_same (instT, inst) tm = |
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if TFrees.is_empty instT andalso Frees.is_empty inst then raise Same.SAME |
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else |
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let |
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val substT = instantiateT_frees_same instT; |
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fun subst (Const (c, T)) = Const (c, substT T) |
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| subst (Free (x, T)) = |
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let val (T', same) = Same.commit_id substT T in |
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(case Frees.lookup inst (x, T') of |
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SOME t' => t' |
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| NONE => if same then raise Same.SAME else Free (x, T')) |
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end |
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| subst (Var (xi, T)) = Var (xi, substT T) |
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| subst (Bound _) = raise Same.SAME |
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| subst (Abs (x, T, t)) = |
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(Abs (x, substT T, Same.commit subst t) |
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handle Same.SAME => Abs (x, T, subst t)) |
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| subst (t $ u) = (subst t $ Same.commit subst u handle Same.SAME => t $ subst u); |
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in subst tm end; |
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fun instantiateT_frees instT ty = Same.commit (instantiateT_frees_same instT) ty; |
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fun instantiate_frees inst tm = Same.commit (instantiate_frees_same inst) tm; |
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(* instantiation of schematic variables (types before terms) -- recomputes maxidx *) |
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local |
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fun no_indexesT instT = TVars.map (fn _ => rpair ~1) instT; |
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fun no_indexes inst = Vars.map (fn _ => rpair ~1) inst; |
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fun instT_same maxidx instT ty = |
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let |
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fun maxify i = if i > ! maxidx then maxidx := i else (); |
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fun subst_typ (Type (a, Ts)) = Type (a, subst_typs Ts) |
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| subst_typ (TVar ((a, i), S)) = |
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(case TVars.lookup instT ((a, i), S) of |
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SOME (T', j) => (maxify j; T') |
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| NONE => (maxify i; raise Same.SAME)) |
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| subst_typ _ = raise Same.SAME |
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and subst_typs (T :: Ts) = |
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(subst_typ T :: Same.commit subst_typs Ts |
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handle Same.SAME => T :: subst_typs Ts) |
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| subst_typs [] = raise Same.SAME; |
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in subst_typ ty end; |
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||
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fun inst_same maxidx (instT, inst) tm = |
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let |
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fun maxify i = if i > ! maxidx then maxidx := i else (); |
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||
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val substT = instT_same maxidx instT; |
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fun subst (Const (c, T)) = Const (c, substT T) |
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| subst (Free (x, T)) = Free (x, substT T) |
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| subst (Var ((x, i), T)) = |
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let val (T', same) = Same.commit_id substT T in |
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(case Vars.lookup inst ((x, i), T') of |
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SOME (t', j) => (maxify j; t') |
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| NONE => (maxify i; if same then raise Same.SAME else Var ((x, i), T'))) |
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end |
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| subst (Bound _) = raise Same.SAME |
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| subst (Abs (x, T, t)) = |
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(Abs (x, substT T, subst_commit t) |
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handle Same.SAME => Abs (x, T, subst t)) |
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| subst (t $ u) = (subst t $ subst_commit u handle Same.SAME => t $ subst u) |
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and subst_commit t = Same.commit subst t; |
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in subst tm end; |
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|
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(*version with local beta reduction*) |
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fun inst_beta_same maxidx (instT, inst) tm = |
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let |
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fun maxify i = if i > ! maxidx then maxidx := i else (); |
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val substT = instT_same maxidx instT; |
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fun expand_head t = |
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(case Term.head_of t of |
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Var ((x, i), T) => |
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let val (T', same) = Same.commit_id substT T in |
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clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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164 |
(case Vars.lookup inst ((x, i), T') of |
74578 | 165 |
SOME (t', j) => (maxify j; SOME t') |
74577
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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166 |
| NONE => (maxify i; if same then NONE else SOME (Var ((x, i), T')))) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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167 |
end |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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168 |
| _ => NONE); |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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169 |
|
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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|
170 |
fun subst t = |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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171 |
(case expand_head t of |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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172 |
NONE => |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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|
173 |
(case t of |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
174 |
Const (c, T) => Const (c, substT T) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
175 |
| Free (x, T) => Free (x, substT T) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
176 |
| Var _ => raise Same.SAME |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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|
177 |
| Bound _ => raise Same.SAME |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
178 |
| Abs (x, T, b) => |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
179 |
(Abs (x, substT T, subst_commit b) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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diff
changeset
|
180 |
handle Same.SAME => Abs (x, T, subst b)) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
181 |
| _ $ _ => subst_comb t) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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diff
changeset
|
182 |
| SOME (u as Abs _) => Term.betapplys (u, map subst_commit (Term.args_of t)) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
183 |
| SOME u => subst_head u t) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
184 |
and subst_comb (t $ u) = (subst_comb t $ subst_commit u handle Same.SAME => t $ subst u) |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
185 |
| subst_comb (Var _) = raise Same.SAME |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
186 |
| subst_comb t = subst t |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
187 |
and subst_head h (t $ u) = subst_head h t $ subst_commit u |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
188 |
| subst_head h _ = h |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
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parents:
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changeset
|
189 |
and subst_commit t = Same.commit subst t; |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
190 |
|
20513 | 191 |
in subst tm end; |
192 |
||
193 |
in |
|
194 |
||
195 |
fun instantiateT_maxidx instT ty i = |
|
32738 | 196 |
let val maxidx = Unsynchronized.ref i |
36620
e6bb250402b5
simplified/unified fundamental operations on types/terms/proofterms -- prefer Same.operation over "option" variant;
wenzelm
parents:
35408
diff
changeset
|
197 |
in (Same.commit (instT_same maxidx instT) ty, ! maxidx) end; |
20513 | 198 |
|
199 |
fun instantiate_maxidx insts tm i = |
|
32738 | 200 |
let val maxidx = Unsynchronized.ref i |
36620
e6bb250402b5
simplified/unified fundamental operations on types/terms/proofterms -- prefer Same.operation over "option" variant;
wenzelm
parents:
35408
diff
changeset
|
201 |
in (Same.commit (inst_same maxidx insts) tm, ! maxidx) end; |
20513 | 202 |
|
74577
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
203 |
fun instantiate_beta_maxidx insts tm i = |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
204 |
let val maxidx = Unsynchronized.ref i |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
205 |
in (Same.commit (inst_beta_same maxidx insts) tm, ! maxidx) end; |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
206 |
|
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
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diff
changeset
|
207 |
|
74220
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
208 |
fun instantiateT_same instT ty = |
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
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diff
changeset
|
209 |
if TVars.is_empty instT then raise Same.SAME |
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
210 |
else instT_same (Unsynchronized.ref ~1) (no_indexesT instT) ty; |
20513 | 211 |
|
74220
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
212 |
fun instantiate_same (instT, inst) tm = |
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
213 |
if TVars.is_empty instT andalso Vars.is_empty inst then raise Same.SAME |
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
214 |
else inst_same (Unsynchronized.ref ~1) (no_indexesT instT, no_indexes inst) tm; |
20513 | 215 |
|
74577
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
216 |
fun instantiate_beta_same (instT, inst) tm = |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
217 |
if TVars.is_empty instT andalso Vars.is_empty inst then raise Same.SAME |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
218 |
else inst_beta_same (Unsynchronized.ref ~1) (no_indexesT instT, no_indexes inst) tm; |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
219 |
|
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
220 |
|
36766 | 221 |
fun instantiateT instT ty = Same.commit (instantiateT_same instT) ty; |
74577
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
222 |
|
36766 | 223 |
fun instantiate inst tm = Same.commit (instantiate_same inst) tm; |
224 |
||
74577
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
225 |
fun instantiate_beta inst tm = Same.commit (instantiate_beta_same inst) tm; |
d4829a7333e2
clarified instantiation: local beta reduction after substitution, as for Envir.expand_term_defs;
wenzelm
parents:
74576
diff
changeset
|
226 |
|
20513 | 227 |
end; |
228 |
||
229 |
||
230 |
(* zero var indexes *) |
|
231 |
||
74220
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
232 |
fun zero_var_inst ins mk (v as ((x, i), X)) (inst, used) = |
80599 | 233 |
let val (x', used') = Name.variant_bound x used |
74220
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
234 |
in if x = x' andalso i = 0 then (inst, used') else (ins (v, mk ((x', 0), X)) inst, used') end; |
20513 | 235 |
|
69023
cef000855cf4
clarified standardization of variables, with proper treatment of local variables;
wenzelm
parents:
68234
diff
changeset
|
236 |
fun zero_var_indexes_inst used ts = |
20513 | 237 |
let |
45395
830c9b9b0d66
more scalable zero_var_indexes, depending on canonical order within table;
wenzelm
parents:
43326
diff
changeset
|
238 |
val (instT, _) = |
74220
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
239 |
(TVars.empty, used) |> TVars.fold (zero_var_inst TVars.add TVar o #1) |
74232 | 240 |
(TVars.build (ts |> (fold o fold_types o fold_atyps) |
241 |
(fn TVar v => TVars.add (v, ()) | _ => I))); |
|
45395
830c9b9b0d66
more scalable zero_var_indexes, depending on canonical order within table;
wenzelm
parents:
43326
diff
changeset
|
242 |
val (inst, _) = |
74220
c49134ee16c1
more scalable data structure (but: rarely used many arguments);
wenzelm
parents:
74200
diff
changeset
|
243 |
(Vars.empty, used) |> Vars.fold (zero_var_inst Vars.add Var o #1) |
74232 | 244 |
(Vars.build (ts |> (fold o fold_aterms) |
245 |
(fn Var (xi, T) => Vars.add ((xi, instantiateT instT T), ()) | _ => I))); |
|
20513 | 246 |
in (instT, inst) end; |
247 |
||
69023
cef000855cf4
clarified standardization of variables, with proper treatment of local variables;
wenzelm
parents:
68234
diff
changeset
|
248 |
fun zero_var_indexes_list ts = map (instantiate (zero_var_indexes_inst Name.context ts)) ts; |
68234 | 249 |
val zero_var_indexes = singleton zero_var_indexes_list; |
20513 | 250 |
|
251 |
end; |