author | wenzelm |
Mon, 06 Oct 1997 18:22:22 +0200 | |
changeset 3776 | 38f8ec304b95 |
parent 2959 | 071bfb16586f |
child 3781 | ec519ba6196e |
permissions | -rw-r--r-- |
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(* Title: Pure/term.ML |
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ID: $Id$ |
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Author: Lawrence C Paulson, Cambridge University Computer Laboratory |
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Copyright Cambridge University 1992 |
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Simply typed lambda-calculus: types, terms, and basic operations |
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*) |
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infix 9 $; |
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infixr 5 -->; |
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infixr --->; |
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infix aconv; |
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structure Term = |
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struct |
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(*Indexnames can be quickly renamed by adding an offset to the integer part, |
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for resolution.*) |
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type indexname = string*int; |
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(* Types are classified by classes. *) |
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type class = string; |
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type sort = class list; |
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(* The sorts attached to TFrees and TVars specify the sort of that variable *) |
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datatype typ = Type of string * typ list |
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| TFree of string * sort |
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| TVar of indexname * sort; |
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fun S --> T = Type("fun",[S,T]); |
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(*handy for multiple args: [T1,...,Tn]--->T gives T1-->(T2--> ... -->T)*) |
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val op ---> = foldr (op -->); |
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(*terms. Bound variables are indicated by depth number. |
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Free variables, (scheme) variables and constants have names. |
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An term is "closed" if there every bound variable of level "lev" |
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is enclosed by at least "lev" abstractions. |
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It is possible to create meaningless terms containing loose bound vars |
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or type mismatches. But such terms are not allowed in rules. *) |
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datatype term = |
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Const of string * typ |
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| Free of string * typ |
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| Var of indexname * typ |
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| Bound of int |
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| Abs of string*typ*term |
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| op $ of term*term; |
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(*For errors involving type mismatches*) |
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exception TYPE of string * typ list * term list; |
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fun raise_type msg tys ts = raise TYPE (msg, tys, ts); |
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(*For system errors involving terms*) |
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exception TERM of string * term list; |
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fun raise_term msg ts = raise TERM (msg, ts); |
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(*Note variable naming conventions! |
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a,b,c: string |
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f,g,h: functions (including terms of function type) |
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i,j,m,n: int |
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t,u: term |
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v,w: indexnames |
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x,y: any |
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A,B,C: term (denoting formulae) |
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T,U: typ |
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*) |
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(** Discriminators **) |
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fun is_Const (Const _) = true |
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| is_Const _ = false; |
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fun is_Free (Free _) = true |
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| is_Free _ = false; |
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fun is_Var (Var _) = true |
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| is_Var _ = false; |
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fun is_TVar (TVar _) = true |
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| is_TVar _ = false; |
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(** Destructors **) |
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fun dest_Const (Const x) = x |
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| dest_Const t = raise TERM("dest_Const", [t]); |
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fun dest_Free (Free x) = x |
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| dest_Free t = raise TERM("dest_Free", [t]); |
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fun dest_Var (Var x) = x |
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| dest_Var t = raise TERM("dest_Var", [t]); |
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(* maps [T1,...,Tn]--->T to the list [T1,T2,...,Tn]*) |
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fun binder_types (Type("fun",[S,T])) = S :: binder_types T |
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| binder_types _ = []; |
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(* maps [T1,...,Tn]--->T to T*) |
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fun body_type (Type("fun",[S,T])) = body_type T |
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| body_type T = T; |
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(* maps [T1,...,Tn]--->T to ([T1,T2,...,Tn], T) *) |
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fun strip_type T : typ list * typ = |
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(binder_types T, body_type T); |
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(*Compute the type of the term, checking that combinations are well-typed |
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Ts = [T0,T1,...] holds types of bound variables 0, 1, ...*) |
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fun type_of1 (Ts, Const (_,T)) = T |
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| type_of1 (Ts, Free (_,T)) = T |
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| type_of1 (Ts, Bound i) = (nth_elem (i,Ts) |
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handle LIST _ => raise TYPE("type_of: bound variable", [], [Bound i])) |
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| type_of1 (Ts, Var (_,T)) = T |
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| type_of1 (Ts, Abs (_,T,body)) = T --> type_of1(T::Ts, body) |
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| type_of1 (Ts, f$u) = |
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let val U = type_of1(Ts,u) |
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and T = type_of1(Ts,f) |
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in case T of |
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Type("fun",[T1,T2]) => |
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if T1=U then T2 else raise TYPE |
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("type_of: type mismatch in application", [T1,U], [f$u]) |
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| _ => raise TYPE |
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("type_of: function type is expected in application", |
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[T,U], [f$u]) |
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end; |
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fun type_of t : typ = type_of1 ([],t); |
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(*Determines the type of a term, with minimal checking*) |
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fun fastype_of1 (Ts, f$u) = |
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(case fastype_of1 (Ts,f) of |
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Type("fun",[_,T]) => T |
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| _ => raise TERM("fastype_of: expected function type", [f$u])) |
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| fastype_of1 (_, Const (_,T)) = T |
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| fastype_of1 (_, Free (_,T)) = T |
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| fastype_of1 (Ts, Bound i) = (nth_elem(i,Ts) |
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handle LIST _ => raise TERM("fastype_of: Bound", [Bound i])) |
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| fastype_of1 (_, Var (_,T)) = T |
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| fastype_of1 (Ts, Abs (_,T,u)) = T --> fastype_of1 (T::Ts, u); |
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fun fastype_of t : typ = fastype_of1 ([],t); |
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(* maps (x1,...,xn)t to t *) |
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fun strip_abs_body (Abs(_,_,t)) = strip_abs_body t |
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| strip_abs_body u = u; |
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(* maps (x1,...,xn)t to [x1, ..., xn] *) |
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fun strip_abs_vars (Abs(a,T,t)) = (a,T) :: strip_abs_vars t |
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| strip_abs_vars u = [] : (string*typ) list; |
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fun strip_qnt_body qnt = |
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let fun strip(tm as Const(c,_)$Abs(_,_,t)) = if c=qnt then strip t else tm |
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| strip t = t |
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in strip end; |
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fun strip_qnt_vars qnt = |
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let fun strip(Const(c,_)$Abs(a,T,t)) = if c=qnt then (a,T)::strip t else [] |
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| strip t = [] : (string*typ) list |
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in strip end; |
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(* maps (f, [t1,...,tn]) to f(t1,...,tn) *) |
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val list_comb : term * term list -> term = foldl (op $); |
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(* maps f(t1,...,tn) to (f, [t1,...,tn]) ; naturally tail-recursive*) |
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fun strip_comb u : term * term list = |
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let fun stripc (f$t, ts) = stripc (f, t::ts) |
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| stripc x = x |
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in stripc(u,[]) end; |
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(* maps f(t1,...,tn) to f , which is never a combination *) |
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fun head_of (f$t) = head_of f |
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| head_of u = u; |
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(*Number of atoms and abstractions in a term*) |
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fun size_of_term (Abs (_,_,body)) = 1 + size_of_term body |
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| size_of_term (f$t) = size_of_term f + size_of_term t |
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| size_of_term _ = 1; |
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fun map_type_tvar f (Type(a,Ts)) = Type(a, map (map_type_tvar f) Ts) |
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| map_type_tvar f (T as TFree _) = T |
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| map_type_tvar f (TVar x) = f x; |
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fun map_type_tfree f (Type(a,Ts)) = Type(a, map (map_type_tfree f) Ts) |
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| map_type_tfree f (TFree x) = f x |
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| map_type_tfree f (T as TVar _) = T; |
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(* apply a function to all types in a term *) |
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fun map_term_types f = |
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let fun map(Const(a,T)) = Const(a, f T) |
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| map(Free(a,T)) = Free(a, f T) |
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| map(Var(v,T)) = Var(v, f T) |
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| map(t as Bound _) = t |
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| map(Abs(a,T,t)) = Abs(a, f T, map t) |
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| map(f$t) = map f $ map t; |
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in map end; |
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(* iterate a function over all types in a term *) |
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fun it_term_types f = |
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let fun iter(Const(_,T), a) = f(T,a) |
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| iter(Free(_,T), a) = f(T,a) |
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| iter(Var(_,T), a) = f(T,a) |
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| iter(Abs(_,T,t), a) = iter(t,f(T,a)) |
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| iter(f$u, a) = iter(f, iter(u, a)) |
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| iter(Bound _, a) = a |
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in iter end |
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(** Connectives of higher order logic **) |
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val logicC: class = "logic"; |
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val logicS: sort = [logicC]; |
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fun itselfT ty = Type ("itself", [ty]); |
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val a_itselfT = itselfT (TFree ("'a", logicS)); |
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val propT : typ = Type("prop",[]); |
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val implies = Const("==>", propT-->propT-->propT); |
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fun all T = Const("all", (T-->propT)-->propT); |
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fun equals T = Const("==", T-->T-->propT); |
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fun flexpair T = Const("=?=", T-->T-->propT); |
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(* maps !!x1...xn. t to t *) |
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fun strip_all_body (Const("all",_)$Abs(_,_,t)) = strip_all_body t |
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| strip_all_body t = t; |
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(* maps !!x1...xn. t to [x1, ..., xn] *) |
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fun strip_all_vars (Const("all",_)$Abs(a,T,t)) = |
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(a,T) :: strip_all_vars t |
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| strip_all_vars t = [] : (string*typ) list; |
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(*increments a term's non-local bound variables |
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required when moving a term within abstractions |
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inc is increment for bound variables |
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lev is level at which a bound variable is considered 'loose'*) |
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fun incr_bv (inc, lev, u as Bound i) = if i>=lev then Bound(i+inc) else u |
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| incr_bv (inc, lev, Abs(a,T,body)) = |
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Abs(a, T, incr_bv(inc,lev+1,body)) |
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| incr_bv (inc, lev, f$t) = |
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incr_bv(inc,lev,f) $ incr_bv(inc,lev,t) |
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| incr_bv (inc, lev, u) = u; |
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fun incr_boundvars 0 t = t |
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| incr_boundvars inc t = incr_bv(inc,0,t); |
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(*Accumulate all 'loose' bound vars referring to level 'lev' or beyond. |
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(Bound 0) is loose at level 0 *) |
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fun add_loose_bnos (Bound i, lev, js) = |
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if i<lev then js else (i-lev) ins_int js |
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| add_loose_bnos (Abs (_,_,t), lev, js) = add_loose_bnos (t, lev+1, js) |
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| add_loose_bnos (f$t, lev, js) = |
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add_loose_bnos (f, lev, add_loose_bnos (t, lev, js)) |
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| add_loose_bnos (_, _, js) = js; |
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fun loose_bnos t = add_loose_bnos (t, 0, []); |
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(* loose_bvar(t,k) iff t contains a 'loose' bound variable referring to |
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level k or beyond. *) |
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fun loose_bvar(Bound i,k) = i >= k |
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| loose_bvar(f$t, k) = loose_bvar(f,k) orelse loose_bvar(t,k) |
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| loose_bvar(Abs(_,_,t),k) = loose_bvar(t,k+1) |
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| loose_bvar _ = false; |
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fun loose_bvar1(Bound i,k) = i = k |
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| loose_bvar1(f$t, k) = loose_bvar1(f,k) orelse loose_bvar1(t,k) |
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| loose_bvar1(Abs(_,_,t),k) = loose_bvar1(t,k+1) |
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| loose_bvar1 _ = false; |
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(*Substitute arguments for loose bound variables. |
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Beta-reduction of arg(n-1)...arg0 into t replacing (Bound i) with (argi). |
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Note that for ((x,y)c)(a,b), the bound vars in c are x=1 and y=0 |
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and the appropriate call is subst_bounds([b,a], c) . |
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Loose bound variables >=n are reduced by "n" to |
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compensate for the disappearance of lambdas. |
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*) |
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fun subst_bounds (args: term list, t) : term = |
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let val n = length args; |
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fun subst (t as Bound i, lev) = |
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(if i<lev then t (*var is locally bound*) |
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else incr_boundvars lev (List.nth(args, i-lev)) |
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handle Subscript => Bound(i-n) (*loose: change it*)) |
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| subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) |
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| subst (f$t, lev) = subst(f,lev) $ subst(t,lev) |
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| subst (t,lev) = t |
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in case args of [] => t | _ => subst (t,0) end; |
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(*Special case: one argument*) |
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fun subst_bound (arg, t) : term = |
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let fun subst (t as Bound i, lev) = |
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if i<lev then t (*var is locally bound*) |
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else if i=lev then incr_boundvars lev arg |
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else Bound(i-1) (*loose: change it*) |
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| subst (Abs(a,T,body), lev) = Abs(a, T, subst(body,lev+1)) |
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| subst (f$t, lev) = subst(f,lev) $ subst(t,lev) |
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| subst (t,lev) = t |
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in subst (t,0) end; |
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(*beta-reduce if possible, else form application*) |
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fun betapply (Abs(_,_,t), u) = subst_bound (u,t) |
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| betapply (f,u) = f$u; |
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(** Equality, membership and insertion of indexnames (string*ints) **) |
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Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
325 |
|
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
326 |
(*optimized equality test for indexnames. Yields a huge gain under Poly/ML*) |
2959 | 327 |
fun eq_ix ((a, i):indexname, (a',i'):indexname) = (a=a') andalso i=i'; |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
328 |
|
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
329 |
(*membership in a list, optimized version for indexnames*) |
2959 | 330 |
fun mem_ix (_, []) = false |
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
331 |
| mem_ix (x, y :: ys) = eq_ix(x,y) orelse mem_ix (x, ys); |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
332 |
|
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
333 |
(*insertion into list, optimized version for indexnames*) |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
334 |
fun ins_ix (x,xs) = if mem_ix (x, xs) then xs else x :: xs; |
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
2182
diff
changeset
|
335 |
|
0 | 336 |
(*Tests whether 2 terms are alpha-convertible and have same type. |
337 |
Note that constants and Vars may have more than one type.*) |
|
338 |
fun (Const(a,T)) aconv (Const(b,U)) = a=b andalso T=U |
|
2752 | 339 |
| (Free(a,T)) aconv (Free(b,U)) = a=b andalso T=U |
340 |
| (Var(v,T)) aconv (Var(w,U)) = eq_ix(v,w) andalso T=U |
|
341 |
| (Bound i) aconv (Bound j) = i=j |
|
0 | 342 |
| (Abs(_,T,t)) aconv (Abs(_,U,u)) = t aconv u andalso T=U |
2752 | 343 |
| (f$t) aconv (g$u) = (f aconv g) andalso (t aconv u) |
0 | 344 |
| _ aconv _ = false; |
345 |
||
2176 | 346 |
(** Membership, insertion, union for terms **) |
347 |
||
348 |
fun mem_term (_, []) = false |
|
349 |
| mem_term (t, t'::ts) = t aconv t' orelse mem_term(t,ts); |
|
350 |
||
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
351 |
fun subset_term ([], ys) = true |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
352 |
| subset_term (x :: xs, ys) = mem_term (x, ys) andalso subset_term(xs, ys); |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
353 |
|
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
354 |
fun eq_set_term (xs, ys) = |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
355 |
xs = ys orelse (subset_term (xs, ys) andalso subset_term (ys, xs)); |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
356 |
|
2176 | 357 |
fun ins_term(t,ts) = if mem_term(t,ts) then ts else t :: ts; |
358 |
||
359 |
fun union_term (xs, []) = xs |
|
360 |
| union_term ([], ys) = ys |
|
361 |
| union_term ((x :: xs), ys) = union_term (xs, ins_term (x, ys)); |
|
362 |
||
363 |
(** Equality, membership and insertion of sorts (string lists) **) |
|
364 |
||
365 |
fun eq_sort ([]:sort, []) = true |
|
366 |
| eq_sort ((s::ss), (t::ts)) = s=t andalso eq_sort(ss,ts) |
|
367 |
| eq_sort (_, _) = false; |
|
368 |
||
369 |
fun mem_sort (_:sort, []) = false |
|
370 |
| mem_sort (S, S'::Ss) = eq_sort (S, S') orelse mem_sort(S,Ss); |
|
371 |
||
372 |
fun ins_sort(S,Ss) = if mem_sort(S,Ss) then Ss else S :: Ss; |
|
373 |
||
374 |
fun union_sort (xs, []) = xs |
|
375 |
| union_sort ([], ys) = ys |
|
376 |
| union_sort ((x :: xs), ys) = union_sort (xs, ins_sort (x, ys)); |
|
377 |
||
2182
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
378 |
fun subset_sort ([], ys) = true |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
379 |
| subset_sort (x :: xs, ys) = mem_sort (x, ys) andalso subset_sort(xs, ys); |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
380 |
|
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
381 |
fun eq_set_sort (xs, ys) = |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
382 |
xs = ys orelse (subset_sort (xs, ys) andalso subset_sort (ys, xs)); |
29e56f003599
Removal of polymorphic equality via mem, subset, eq_set, etc
paulson
parents:
2176
diff
changeset
|
383 |
|
0 | 384 |
(*are two term lists alpha-convertible in corresponding elements?*) |
385 |
fun aconvs ([],[]) = true |
|
386 |
| aconvs (t::ts, u::us) = t aconv u andalso aconvs(ts,us) |
|
387 |
| aconvs _ = false; |
|
388 |
||
389 |
(*A fast unification filter: true unless the two terms cannot be unified. |
|
390 |
Terms must be NORMAL. Treats all Vars as distinct. *) |
|
391 |
fun could_unify (t,u) = |
|
392 |
let fun matchrands (f$t, g$u) = could_unify(t,u) andalso matchrands(f,g) |
|
1460 | 393 |
| matchrands _ = true |
0 | 394 |
in case (head_of t , head_of u) of |
1460 | 395 |
(_, Var _) => true |
0 | 396 |
| (Var _, _) => true |
397 |
| (Const(a,_), Const(b,_)) => a=b andalso matchrands(t,u) |
|
398 |
| (Free(a,_), Free(b,_)) => a=b andalso matchrands(t,u) |
|
399 |
| (Bound i, Bound j) => i=j andalso matchrands(t,u) |
|
400 |
| (Abs _, _) => true (*because of possible eta equality*) |
|
401 |
| (_, Abs _) => true |
|
402 |
| _ => false |
|
403 |
end; |
|
404 |
||
405 |
(*Substitute new for free occurrences of old in a term*) |
|
406 |
fun subst_free [] = (fn t=>t) |
|
407 |
| subst_free pairs = |
|
408 |
let fun substf u = |
|
1460 | 409 |
case gen_assoc (op aconv) (pairs, u) of |
410 |
Some u' => u' |
|
411 |
| None => (case u of Abs(a,T,t) => Abs(a, T, substf t) |
|
412 |
| t$u' => substf t $ substf u' |
|
413 |
| _ => u) |
|
0 | 414 |
in substf end; |
415 |
||
416 |
(*a total, irreflexive ordering on index names*) |
|
417 |
fun xless ((a,i), (b,j): indexname) = i<j orelse (i=j andalso a<b); |
|
418 |
||
419 |
||
420 |
(*Abstraction of the term "body" over its occurrences of v, |
|
421 |
which must contain no loose bound variables. |
|
422 |
The resulting term is ready to become the body of an Abs.*) |
|
423 |
fun abstract_over (v,body) = |
|
424 |
let fun abst (lev,u) = if (v aconv u) then (Bound lev) else |
|
425 |
(case u of |
|
426 |
Abs(a,T,t) => Abs(a, T, abst(lev+1, t)) |
|
1460 | 427 |
| f$rand => abst(lev,f) $ abst(lev,rand) |
428 |
| _ => u) |
|
0 | 429 |
in abst(0,body) end; |
430 |
||
431 |
||
432 |
(*Form an abstraction over a free variable.*) |
|
433 |
fun absfree (a,T,body) = Abs(a, T, abstract_over (Free(a,T), body)); |
|
434 |
||
435 |
(*Abstraction over a list of free variables*) |
|
436 |
fun list_abs_free ([ ] , t) = t |
|
437 |
| list_abs_free ((a,T)::vars, t) = |
|
438 |
absfree(a, T, list_abs_free(vars,t)); |
|
439 |
||
440 |
(*Quantification over a list of free variables*) |
|
441 |
fun list_all_free ([], t: term) = t |
|
442 |
| list_all_free ((a,T)::vars, t) = |
|
443 |
(all T) $ (absfree(a, T, list_all_free(vars,t))); |
|
444 |
||
445 |
(*Quantification over a list of variables (already bound in body) *) |
|
446 |
fun list_all ([], t) = t |
|
447 |
| list_all ((a,T)::vars, t) = |
|
448 |
(all T) $ (Abs(a, T, list_all(vars,t))); |
|
449 |
||
450 |
(*Replace the ATOMIC term ti by ui; instl = [(t1,u1), ..., (tn,un)]. |
|
451 |
A simultaneous substitution: [ (a,b), (b,a) ] swaps a and b. *) |
|
452 |
fun subst_atomic [] t = t : term |
|
453 |
| subst_atomic (instl: (term*term) list) t = |
|
454 |
let fun subst (Abs(a,T,body)) = Abs(a, T, subst body) |
|
1460 | 455 |
| subst (f$t') = subst f $ subst t' |
456 |
| subst t = (case assoc(instl,t) of |
|
457 |
Some u => u | None => t) |
|
0 | 458 |
in subst t end; |
459 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
460 |
(*Substitute for type Vars in a type*) |
0 | 461 |
fun typ_subst_TVars iTs T = if null iTs then T else |
462 |
let fun subst(Type(a,Ts)) = Type(a, map subst Ts) |
|
1460 | 463 |
| subst(T as TFree _) = T |
464 |
| subst(T as TVar(ixn,_)) = |
|
0 | 465 |
(case assoc(iTs,ixn) of None => T | Some(U) => U) |
466 |
in subst T end; |
|
467 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
468 |
(*Substitute for type Vars in a term*) |
0 | 469 |
val subst_TVars = map_term_types o typ_subst_TVars; |
470 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
471 |
(*Substitute for Vars in a term; see also envir/norm_term*) |
0 | 472 |
fun subst_Vars itms t = if null itms then t else |
473 |
let fun subst(v as Var(ixn,_)) = |
|
474 |
(case assoc(itms,ixn) of None => v | Some t => t) |
|
475 |
| subst(Abs(a,T,t)) = Abs(a,T,subst t) |
|
476 |
| subst(f$t) = subst f $ subst t |
|
477 |
| subst(t) = t |
|
478 |
in subst t end; |
|
479 |
||
728
9a973c3ba350
Pure/term: commented typ_subst_TVars, subst_TVars, subst_Vars, subst_vars
lcp
parents:
375
diff
changeset
|
480 |
(*Substitute for type/term Vars in a term; see also envir/norm_term*) |
0 | 481 |
fun subst_vars(iTs,itms) = if null iTs then subst_Vars itms else |
482 |
let fun subst(Const(a,T)) = Const(a,typ_subst_TVars iTs T) |
|
483 |
| subst(Free(a,T)) = Free(a,typ_subst_TVars iTs T) |
|
484 |
| subst(v as Var(ixn,T)) = (case assoc(itms,ixn) of |
|
485 |
None => Var(ixn,typ_subst_TVars iTs T) |
|
486 |
| Some t => t) |
|
487 |
| subst(b as Bound _) = b |
|
488 |
| subst(Abs(a,T,t)) = Abs(a,typ_subst_TVars iTs T,subst t) |
|
489 |
| subst(f$t) = subst f $ subst t |
|
490 |
in subst end; |
|
491 |
||
492 |
||
493 |
(*Computing the maximum index of a typ*) |
|
2146 | 494 |
fun maxidx_of_typ(Type(_,Ts)) = maxidx_of_typs Ts |
0 | 495 |
| maxidx_of_typ(TFree _) = ~1 |
2146 | 496 |
| maxidx_of_typ(TVar((_,i),_)) = i |
497 |
and maxidx_of_typs [] = ~1 |
|
498 |
| maxidx_of_typs (T::Ts) = Int.max(maxidx_of_typ T, maxidx_of_typs Ts); |
|
0 | 499 |
|
500 |
||
501 |
(*Computing the maximum index of a term*) |
|
502 |
fun maxidx_of_term (Const(_,T)) = maxidx_of_typ T |
|
503 |
| maxidx_of_term (Bound _) = ~1 |
|
504 |
| maxidx_of_term (Free(_,T)) = maxidx_of_typ T |
|
2146 | 505 |
| maxidx_of_term (Var ((_,i), T)) = Int.max(i, maxidx_of_typ T) |
506 |
| maxidx_of_term (Abs (_,T,u)) = Int.max(maxidx_of_term u, maxidx_of_typ T) |
|
507 |
| maxidx_of_term (f$t) = Int.max(maxidx_of_term f, maxidx_of_term t); |
|
0 | 508 |
|
509 |
||
510 |
(* Increment the index of all Poly's in T by k *) |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
511 |
fun incr_tvar k = map_type_tvar (fn ((a,i),S) => TVar((a,i+k),S)); |
0 | 512 |
|
513 |
||
514 |
(**** Syntax-related declarations ****) |
|
515 |
||
516 |
||
517 |
(*Dummy type for parsing. Will be replaced during type inference. *) |
|
518 |
val dummyT = Type("dummy",[]); |
|
519 |
||
520 |
(*scan a numeral of the given radix, normally 10*) |
|
521 |
fun scan_radixint (radix: int, cs) : int * string list = |
|
522 |
let val zero = ord"0" |
|
523 |
val limit = zero+radix |
|
524 |
fun scan (num,[]) = (num,[]) |
|
1460 | 525 |
| scan (num, c::cs) = |
526 |
if zero <= ord c andalso ord c < limit |
|
527 |
then scan(radix*num + ord c - zero, cs) |
|
528 |
else (num, c::cs) |
|
0 | 529 |
in scan(0,cs) end; |
530 |
||
531 |
fun scan_int cs = scan_radixint(10,cs); |
|
532 |
||
533 |
||
534 |
(*** Printing ***) |
|
535 |
||
536 |
||
537 |
(*Makes a variant of the name c distinct from the names in bs. |
|
538 |
First attaches the suffix "a" and then increments this. *) |
|
539 |
fun variant bs c : string = |
|
2138
056dead45ae8
Changed some mem calls to mem_string for greater efficiency (not that it could matter)
paulson
parents:
1460
diff
changeset
|
540 |
let fun vary2 c = if (c mem_string bs) then vary2 (bump_string c) else c |
056dead45ae8
Changed some mem calls to mem_string for greater efficiency (not that it could matter)
paulson
parents:
1460
diff
changeset
|
541 |
fun vary1 c = if (c mem_string bs) then vary2 (c ^ "a") else c |
0 | 542 |
in vary1 (if c="" then "u" else c) end; |
543 |
||
544 |
(*Create variants of the list of names, with priority to the first ones*) |
|
545 |
fun variantlist ([], used) = [] |
|
546 |
| variantlist(b::bs, used) = |
|
547 |
let val b' = variant used b |
|
548 |
in b' :: variantlist (bs, b'::used) end; |
|
549 |
||
550 |
(** TFrees and TVars **) |
|
551 |
||
552 |
(*maps (bs,v) to v'::bs this reverses the identifiers bs*) |
|
553 |
fun add_new_id (bs, c) : string list = variant bs c :: bs; |
|
554 |
||
555 |
(*Accumulates the names in the term, suppressing duplicates. |
|
556 |
Includes Frees and Consts. For choosing unambiguous bound var names.*) |
|
2176 | 557 |
fun add_term_names (Const(a,_), bs) = a ins_string bs |
558 |
| add_term_names (Free(a,_), bs) = a ins_string bs |
|
0 | 559 |
| add_term_names (f$u, bs) = add_term_names (f, add_term_names(u, bs)) |
560 |
| add_term_names (Abs(_,_,t), bs) = add_term_names(t,bs) |
|
561 |
| add_term_names (_, bs) = bs; |
|
562 |
||
563 |
(*Accumulates the TVars in a type, suppressing duplicates. *) |
|
564 |
fun add_typ_tvars(Type(_,Ts),vs) = foldr add_typ_tvars (Ts,vs) |
|
565 |
| add_typ_tvars(TFree(_),vs) = vs |
|
566 |
| add_typ_tvars(TVar(v),vs) = v ins vs; |
|
567 |
||
568 |
(*Accumulates the TFrees in a type, suppressing duplicates. *) |
|
569 |
fun add_typ_tfree_names(Type(_,Ts),fs) = foldr add_typ_tfree_names (Ts,fs) |
|
2176 | 570 |
| add_typ_tfree_names(TFree(f,_),fs) = f ins_string fs |
0 | 571 |
| add_typ_tfree_names(TVar(_),fs) = fs; |
572 |
||
573 |
fun add_typ_tfrees(Type(_,Ts),fs) = foldr add_typ_tfrees (Ts,fs) |
|
574 |
| add_typ_tfrees(TFree(f),fs) = f ins fs |
|
575 |
| add_typ_tfrees(TVar(_),fs) = fs; |
|
576 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
577 |
fun add_typ_varnames(Type(_,Ts),nms) = foldr add_typ_varnames (Ts,nms) |
2176 | 578 |
| add_typ_varnames(TFree(nm,_),nms) = nm ins_string nms |
579 |
| add_typ_varnames(TVar((nm,_),_),nms) = nm ins_string nms; |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
580 |
|
0 | 581 |
(*Accumulates the TVars in a term, suppressing duplicates. *) |
582 |
val add_term_tvars = it_term_types add_typ_tvars; |
|
583 |
||
584 |
(*Accumulates the TFrees in a term, suppressing duplicates. *) |
|
585 |
val add_term_tfrees = it_term_types add_typ_tfrees; |
|
586 |
val add_term_tfree_names = it_term_types add_typ_tfree_names; |
|
587 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
588 |
val add_term_tvarnames = it_term_types add_typ_varnames; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
589 |
|
0 | 590 |
(*Non-list versions*) |
591 |
fun typ_tfrees T = add_typ_tfrees(T,[]); |
|
592 |
fun typ_tvars T = add_typ_tvars(T,[]); |
|
593 |
fun term_tfrees t = add_term_tfrees(t,[]); |
|
594 |
fun term_tvars t = add_term_tvars(t,[]); |
|
595 |
||
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
596 |
(*special code to enforce left-to-right collection of TVar-indexnames*) |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
597 |
|
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
598 |
fun add_typ_ixns(ixns,Type(_,Ts)) = foldl add_typ_ixns (ixns,Ts) |
2176 | 599 |
| add_typ_ixns(ixns,TVar(ixn,_)) = if mem_ix (ixn, ixns) then ixns |
600 |
else ixns@[ixn] |
|
949
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
601 |
| add_typ_ixns(ixns,TFree(_)) = ixns; |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
602 |
|
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
603 |
fun add_term_tvar_ixns(Const(_,T),ixns) = add_typ_ixns(ixns,T) |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
728
diff
changeset
|
604 |
| add_term_tvar_ixns(Free(_,T),ixns) = add_typ_ixns(ixns,T) |
83c588d6fee9
Changed treatment of during type inference internally generated type
nipkow
parents:
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diff
changeset
|
605 |
| add_term_tvar_ixns(Var(_,T),ixns) = add_typ_ixns(ixns,T) |
83c588d6fee9
Changed treatment of during type inference internally generated type
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parents:
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|
606 |
| add_term_tvar_ixns(Bound _,ixns) = ixns |
83c588d6fee9
Changed treatment of during type inference internally generated type
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parents:
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diff
changeset
|
607 |
| add_term_tvar_ixns(Abs(_,T,t),ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
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parents:
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diff
changeset
|
608 |
add_term_tvar_ixns(t,add_typ_ixns(ixns,T)) |
83c588d6fee9
Changed treatment of during type inference internally generated type
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parents:
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diff
changeset
|
609 |
| add_term_tvar_ixns(f$t,ixns) = |
83c588d6fee9
Changed treatment of during type inference internally generated type
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parents:
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diff
changeset
|
610 |
add_term_tvar_ixns(t,add_term_tvar_ixns(f,ixns)); |
83c588d6fee9
Changed treatment of during type inference internally generated type
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parents:
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diff
changeset
|
611 |
|
0 | 612 |
(** Frees and Vars **) |
613 |
||
614 |
(*a partial ordering (not reflexive) for atomic terms*) |
|
615 |
fun atless (Const (a,_), Const (b,_)) = a<b |
|
616 |
| atless (Free (a,_), Free (b,_)) = a<b |
|
617 |
| atless (Var(v,_), Var(w,_)) = xless(v,w) |
|
618 |
| atless (Bound i, Bound j) = i<j |
|
619 |
| atless _ = false; |
|
620 |
||
621 |
(*insert atomic term into partially sorted list, suppressing duplicates (?)*) |
|
622 |
fun insert_aterm (t,us) = |
|
623 |
let fun inserta [] = [t] |
|
624 |
| inserta (us as u::us') = |
|
1460 | 625 |
if atless(t,u) then t::us |
626 |
else if t=u then us (*duplicate*) |
|
627 |
else u :: inserta(us') |
|
0 | 628 |
in inserta us end; |
629 |
||
630 |
(*Accumulates the Vars in the term, suppressing duplicates*) |
|
631 |
fun add_term_vars (t, vars: term list) = case t of |
|
632 |
Var _ => insert_aterm(t,vars) |
|
633 |
| Abs (_,_,body) => add_term_vars(body,vars) |
|
634 |
| f$t => add_term_vars (f, add_term_vars(t, vars)) |
|
635 |
| _ => vars; |
|
636 |
||
637 |
fun term_vars t = add_term_vars(t,[]); |
|
638 |
||
639 |
(*Accumulates the Frees in the term, suppressing duplicates*) |
|
640 |
fun add_term_frees (t, frees: term list) = case t of |
|
641 |
Free _ => insert_aterm(t,frees) |
|
642 |
| Abs (_,_,body) => add_term_frees(body,frees) |
|
643 |
| f$t => add_term_frees (f, add_term_frees(t, frees)) |
|
644 |
| _ => frees; |
|
645 |
||
646 |
fun term_frees t = add_term_frees(t,[]); |
|
647 |
||
648 |
(*Given an abstraction over P, replaces the bound variable by a Free variable |
|
649 |
having a unique name. *) |
|
650 |
fun variant_abs (a,T,P) = |
|
651 |
let val b = variant (add_term_names(P,[])) a |
|
2192
3bf092b5310b
Optimizations: removal of polymorphic equality; one-argument case
paulson
parents:
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diff
changeset
|
652 |
in (b, subst_bound (Free(b,T), P)) end; |
0 | 653 |
|
654 |
(* renames and reverses the strings in vars away from names *) |
|
655 |
fun rename_aTs names vars : (string*typ)list = |
|
656 |
let fun rename_aT (vars,(a,T)) = |
|
1460 | 657 |
(variant (map #1 vars @ names) a, T) :: vars |
0 | 658 |
in foldl rename_aT ([],vars) end; |
659 |
||
660 |
fun rename_wrt_term t = rename_aTs (add_term_names(t,[])); |
|
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
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parents:
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diff
changeset
|
661 |
|
1417 | 662 |
|
663 |
||
1426 | 664 |
(*** Compression of terms and types by sharing common subtrees. |
665 |
Saves 50-75% on storage requirements. As it is fairly slow, |
|
666 |
it is called only for axioms, stored theorems, etc. ***) |
|
1417 | 667 |
|
668 |
(** Sharing of types **) |
|
669 |
||
670 |
fun atomic_tag (Type (a,_)) = if a<>"fun" then a else raise Match |
|
671 |
| atomic_tag (TFree (a,_)) = a |
|
672 |
| atomic_tag (TVar ((a,_),_)) = a; |
|
673 |
||
674 |
fun type_tag (Type("fun",[S,T])) = atomic_tag S ^ type_tag T |
|
675 |
| type_tag T = atomic_tag T; |
|
676 |
||
677 |
val memo_types = ref (Symtab.null : typ list Symtab.table); |
|
678 |
||
679 |
fun find_type (T, []: typ list) = None |
|
680 |
| find_type (T, T'::Ts) = |
|
681 |
if T=T' then Some T' |
|
682 |
else find_type (T, Ts); |
|
683 |
||
684 |
fun compress_type T = |
|
685 |
let val tag = type_tag T |
|
686 |
val tylist = the (Symtab.lookup (!memo_types, tag)) |
|
1460 | 687 |
handle _ => [] |
1417 | 688 |
in |
689 |
case find_type (T,tylist) of |
|
1460 | 690 |
Some T' => T' |
1417 | 691 |
| None => |
1460 | 692 |
let val T' = |
693 |
case T of |
|
694 |
Type (a,Ts) => Type (a, map compress_type Ts) |
|
695 |
| _ => T |
|
696 |
in memo_types := Symtab.update ((tag, T'::tylist), !memo_types); |
|
697 |
T |
|
698 |
end |
|
1417 | 699 |
end |
700 |
handle Match => |
|
701 |
let val Type (a,Ts) = T |
|
702 |
in Type (a, map compress_type Ts) end; |
|
703 |
||
704 |
(** Sharing of atomic terms **) |
|
705 |
||
706 |
val memo_terms = ref (Symtab.null : term list Symtab.table); |
|
707 |
||
708 |
fun find_term (t, []: term list) = None |
|
709 |
| find_term (t, t'::ts) = |
|
710 |
if t=t' then Some t' |
|
711 |
else find_term (t, ts); |
|
712 |
||
713 |
fun const_tag (Const (a,_)) = a |
|
714 |
| const_tag (Free (a,_)) = a |
|
715 |
| const_tag (Var ((a,i),_)) = a |
|
716 |
| const_tag (t as Bound _) = ".B."; |
|
717 |
||
718 |
fun share_term (t $ u) = share_term t $ share_term u |
|
719 |
| share_term (Abs (a,T,u)) = Abs (a, T, share_term u) |
|
720 |
| share_term t = |
|
721 |
let val tag = const_tag t |
|
1460 | 722 |
val ts = the (Symtab.lookup (!memo_terms, tag)) |
723 |
handle _ => [] |
|
1417 | 724 |
in |
1460 | 725 |
case find_term (t,ts) of |
726 |
Some t' => t' |
|
727 |
| None => (memo_terms := Symtab.update ((tag, t::ts), !memo_terms); |
|
728 |
t) |
|
1417 | 729 |
end; |
730 |
||
731 |
val compress_term = share_term o map_term_types compress_type; |
|
732 |
||
1364
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
733 |
end; |
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
734 |
|
8ea1a962ad72
files now define a structure to allow SML/NJ to optimize the code
clasohm
parents:
1029
diff
changeset
|
735 |
open Term; |