Module Proofview

Abstract representation of the initial goals of a proof.

Optimize memory consumption

Initialises a proofview, the main argument is a list of environments (including a named_context which are used as hypotheses) pair with conclusion types, creating accordingly many initial goals. Because a proof does not necessarily starts in an empty evar_map (indeed a proof can be triggered by an incomplete pretyping), init takes an additional argument to represent the initial evar_map.

A telescope is a list of environment and conclusion like in init, except that each element may depend on the previous goals. The telescope passes the goals in the form of a Term.constr which represents the goal as an evar. The evar_map is threaded in state passing style.

Like init, but goals are allowed to be dependent on one another. Dependencies between goals is represented with the type telescope instead of list. Note that the first evar_map of the telescope plays the role of the evar_map argument in init.

finished pv is true if and only if pv is complete. That is, if it has an empty list of focused goals. There could still be unsolved subgoals, but they would then be out of focus.

Returns the current evar state.

A focus_context represents the part of the proof view which has been removed by a focusing action, it can be used to unfocus later on.

Returns a stylised view of a focus_context for use by, for instance, ide-s.

focus i j focuses a proofview on the goals from index i to index j (inclusive, goals are indexed from 1). I.e. goals number i to j become the only focused goals of the returned proofview. It returns the focused proofview, and a context for the focus stack.

Unfocuses a proofview with respect to a context.

The abstract type of tactics

Applies a tactic to the current proofview. Returns a tuple a,pv,(b,sh,gu) where a is the return value of the tactic, pv is the updated proofview, b a boolean which is true if the tactic has not done any action considered unsafe (such as admitting a lemma), sh is the list of goals which have been shelved by the tactic, and gu the list of goals on which the tactic has given up. In case of multiple success the first one is selected. If there is no success, fails with Logic_monad.TacticFailure

Unit of the tactic monad.

Bind operation of the tactic monad.

Interprets the ";" (semicolon) of Ltac. As a monadic operation, it's a specialized "bind".

tclIGNORE t has the same operational content as t, but drops the returned value.

Generic monadic combinators for tactics.

tclZERO e fails with exception e. It has no success. Exception is supposed to be non critical

tclOR t1 t2 behaves like t1 as long as t1 succeeds. Whenever the successes of t1 have been depleted and it failed with e, then it behaves as t2 e. In other words, tclOR inserts a backtracking point. In t2, exception can be assumed non critical.

tclORELSE t1 t2 is equal to t1 if t1 has at least one success or t2 e if t1 fails with e. It is analogous to try/with handler of exception in that it is not a backtracking point. In t2, exception can be assumed non critical.

tclIFCATCH a s f is a generalisation of tclORELSE: if a succeeds at least once then it behaves as tclBIND a s otherwise, if a fails with e, then it behaves as f e. In f exception can be assumed non critical.

tclONCE t behave like t except it has at most one success: tclONCE t stops after the first success of t. If t fails with e, tclONCE t also fails with e.

tclEXACTLY_ONCE e t succeeds as t if t has exactly one success. Otherwise it fails. The tactic t is run until its first success, then a failure with exception e is simulated (e has to be non critical). If t yields another success, then tclEXACTLY_ONCE e t fails with MoreThanOneSuccess (it is a user error). Otherwise, tclEXACTLY_ONCE e t succeeds with the first success of t. Notice that the choice of e is relevant, as the presence of further successes may depend on e (see tclOR).

tclCASE t splits t into its first success and a continuation. It is the most general primitive to control backtracking.

tclBREAK p t is a generalization of tclONCE t. Instead of stopping after the first success, it succeeds like t until a failure with an exception e such that p e = Some e' is raised. At which point it drops the remaining successes, failing with e'. tclONCE t is equivalent to tclBREAK (fun e -> Some e) t.

tclFOCUS i j t applies t after focusing on the goals number i to j (see focus). The rest of the goals is restored after the tactic action. If the specified range doesn't correspond to existing goals, fails with the nosuchgoal argument, by default raising NoSuchGoals (a user error). This exception is caught at toplevel with a default message.

tclFOCUSLIST li t applies t on the list of focused goals described by li. Each element of li is a pair (i, j) denoting the goals numbered from i to j (inclusive, starting from 1). It will try to apply t to all the valid goals in any of these intervals. If the set of such goals is not a single range, then it will move goals such that it is a single range. (So, for instance, [1, 3-5]; idtac. is not the identity.) If the set of such goals is empty, it will fail with nosuchgoal, by default raising NoSuchGoals 0.

tclFOCUSID x t applies t on a (single) focused goal like tclFOCUS. The goal is found by its name rather than its number. Fails with nosuchgoal, by default raising NoSuchGoals 1.

tclTRYFOCUS i j t behaves like tclFOCUS, except that if the specified range doesn't correspond to existing goals, behaves like tclUNIT () instead of failing.

Dispatch tacticals are used to apply a different tactic to each goal under focus. They come in two flavours: tclDISPATCH takes a list of unit tactic-s and build a unit tactic. tclDISPATCHL takes a list of 'a tactic and returns an 'a list tactic.

They both work by applying each of the tactic in a focus restricted to the corresponding goal (starting with the first goal). In the case of tclDISPATCHL, the tactic returns a list of the same size as the argument list (of tactics), each element being the result of the tactic executed in the corresponding goal.

When the length of the tactic list is not the number of goal, raises SizeMismatch (g,t) where g is the number of available goals, and t the number of tactics passed.

tclEXTEND b r e is a variant of tclDISPATCH, where the r tactic is "repeated" enough time such that every goal has a tactic assigned to it (b is the list of tactics applied to the first goals, e to the last goals, and r is applied to every goal in between).

tclINDEPENDENT tac runs tac on each goal successively, from the first one to the last one. Backtracking in one goal is independent of backtracking in another. It is equivalent to tclEXTEND [] tac [].

Shelves all the goals under focus. The goals are placed on the shelf for later use (or being solved by side-effects).

Shelves the given list of goals, which might include some that are under focus and some that aren't. All the goals are placed on the shelf for later use (or being solved by side-effects).

unifiable sigma g l checks whether g appears in another subgoal of l. The list l may contain g, but it does not affect the result. Used by shelve_unifiable.

Shelves the unifiable goals under focus, i.e. the goals which appear in other goals under focus (the unfocused goals are not considered).

guard_no_unifiable returns the list of unifiable goals if some goals are unifiable (see shelve_unifiable) in the current focus.

unshelve l p moves all the goals in l from the shelf and put them at the end of the focused goals of p, if they are still undefined after advance

depends_on g1 g2 sigma checks if g1 occurs in the type/ctx of g2

with_shelf tac executes tac and returns its result together with the set of goals shelved by tac. The current shelf is unchanged and the returned list contains only unsolved goals.

If n is positive, cycle n puts the n first goal last. If n is negative, then it puts the n last goals first.

swap i j swaps the position of goals number i and j (negative numbers can be used to address goals from the end. Goals are indexed from 1. For simplicity index 0 corresponds to goal 1 as well, rather than raising an error.

revgoals reverses the list of focused goals.

numgoals returns the number of goals under focus.

tclEVARMAP doesn't affect the proof, it returns the current evar_map.

tclENV doesn't affect the proof, it returns the current environment. It is not the environment of a particular goal, rather the "global" environment of the proof. The goal-wise environment is obtained via Proofview.Goal.env.

tclEFFECTS eff add the effects eff to the current state.

mark_as_unsafe declares the current tactic is unsafe.

Gives up on the goal under focus. Reports an unsafe status. Proofs with given up goals cannot be closed.

tclPROGRESS t checks the state of the proof after t. It it is identical to the state before, then tclPROGRESS t fails, otherwise it succeeds like t.

Checks for interrupts

tclTIMEOUT n t can have only one success. In case of timeout it fails with tclZERO Tac_Timeout.

tclTIME s t displays time for each atomic call to t, using s as an identifying annotation if present

Internal, don't use.

The primitives in the Unsafe module should be avoided as much as possible, since they can make the proof state inconsistent. They are nevertheless helpful, in particular when interfacing the pretyping and the proof engine.

This module gives access to the innards of the monad. Its use is restricted to very specific cases.

The NonLogical module allows the execution of effects (including I/O) in tactics (non-logical side-effects are not discarded at failures).

tclLIFT c is a tactic which behaves exactly as c.